Category: Forecasting

Introduction to forecasting

Forecasting could be defined as the method of formulating estimations of future events by managers (Armstrong, 2001). Forecasting helps managers determine future outcomes of events, and assist in the decision-making process. The data used in making forecasts immensely assists managers in accurately predicting outcomes of future events. In business, risk and uncertainty form the basis for applying forecasting in decision-making. Manufacturing companies apply the forecasting methods in planning for customer demand. Decisions made following forecasts immensely rely on available data from company databases. While forecasting continues to be significantly utilized in decision-making, modern times have seen the utilization of forecasting in predicting conflict development.

Critics of forecasting methods, discourage the application of forecasting methods in trying to determine future outcomes. Majority of the methods continue to be faulted as lacking accuracy. Inaccurate forecasts could immensely affect the performance of companies. Decisions made on wrong forecasts could bring catastrophic results to the performance of a company (Taylor, 2010). Confusion occurs occasionally relating forecasting to planning. Planning seeks to establish desired future status of a company. Forecasting, however, focuses on determining how things might be in the future. Managers, however, utilize forecasting when making future plans. Forecasting assists in formulating effective future plans in companies.

Numerous forecasting methods assist decision makers in preparing forecasts. Operations within companies need accurate forecasting to determine outcomes. The various methods commonly utilized fall in different categories. The categories of forecasting methods could be enumerated as indicated below.

Categories of forecasting methods

• Qualitative and Quantitative Methods;
• Naïve Approach;
• Time series methods;
• Causal / econometric forecasting methods;
• Judgmental methods;
• Artificial intelligence methods;
• Other methods.

Qualitative and quantitative methods

Qualitative methods

Qualitative methods provide information regarding forecasts based on observatory measures. The forecasts continue to be excessively utilized in situations lacking previous data regarding the forecasts. This method could be termed as subjective in terms of forecasting. Lacking basic information, the forecasts provided by the method offer a subjective view of the forecasted element. The method presents a realistic informatory channels resulting from subjectivity. Opinions presented by the data result from informed analysis of situations affecting the forecasted element. The forecasts provided do not relate to any previous data. The method could, therefore, be said to be independent of external influence. Long term decisions can be made relying on the forecasting provided by qualitative methods. The methods follow data collected relating to factors that may influence the element under forecast. Examples of some qualitative methods include;

• market research;
• historical life-cycle analogy;
• Informed opinion and judgment.

Quantitative methods

As opposed to qualitative methods, quantitative methods provide predictions based of available data. The forecasts in this method become functions of the previous data. This method can only be used where past data can be availed. Basing predictions on past data, the methods make the major assumption that all factors affecting the outcomes remain constant. Under such circumstances, the accuracy of the methods cannot be questioned. In practice, however, factors keep on changing. Quantitative methods, therefore, might present significantly erroneous predictions (Hoshmand, 2010). The methods become utilized only in making short term decision because of the high probability of other factors changing in long-term situations. Application of these methods in long term decisions could be affected by changes assumed to remain constant. Examples of some commonly used quantitative methods include;

• Last period demand;
• Simple Moving Average (N-Period);
• Simple Exponential Smoothing.

Naïve Approach

This approach might relate to the quantitative methods because of the utilization of past data. The naïve approach, however, only focuses on data immediately before the forecasting period. Stability of external factors favors application of this method in making forecasts. The approach assumes no significant change could be realized within two adjacent periods. While the method also makes critical assumptions, the relationship of two adjacent periods could not include significant differences. The approach factually identifies the predicted value for any period as equaling the actual value for the previous period (Rescher, 1998). While adjacent period might not contain significant differences, organizational changes might affect the predicted results negatively. Changes in operations could render forecasts made using this method utterly erroneous. Practically, forecasts made using this method always seek to be improved by other methods for accuracy. The method, therefore, forms the base for making forecasts using other, available methods.

Time series methods

Time series methods immensely utilize historical data in providing estimations. The future outcomes predicted in these methods rely on calculations obtained from available data. These methods mostly utilize averages for historical data (Armstrong, 2001). While other methods seem easy to establish values, the time series methods include several calculations before arriving at any figures. Historical data for basing the calculations also needs to be availed in time series methods. Scientists and economists favor these methods due to the inclusion of calculations at arriving to figures. Some examples of time series method used include the following.

• Autoregressive integrated moving average (ARIMA);
• Weighted moving average;
• Growth curve.

Causal / econometric forecasting methods

Causal/econometric forecasting methods try to integrate the various elements affecting the variable under prediction. These methods incorporate other factors thought to significantly affect the outcomes of the variable under prediction. Consideration of such factors makes these methods seem appropriate, and more accurate than the rest. While other methods assume the impact of external factors, econometric forecasts provide an assessment of the possible impact of external factors. The methods consider relationships between variables affecting each other (Ellis, 2008). Consideration of external factors immensely improves the credibility of forecasts made using this method. When using these methods of forecasting, emphasis ought to be made on the credibility of the initial information used in making the calculations. Relying on data from another forecast could provide inconclusive results. Examples of methods used in this category include;

• Regression analysis;
• Autoregressive moving average with exogenous inputs (ARMAX).

Judgmental methods

These forecasting methods present subjective predictions based on personal judgments of situations. Managers assess situations, and consider opinions in coming up with figures using judgmental methods. The methods provide forecasts based on data collected from sources related to the variable under forecast (Hoshmand, 2010). The methods could be closely associated with qualitative methods owing to their subjectivity of variables. The forecasts presented are based on personal observations by the decision makers. The methods might focus on current affairs within an industry, and not a company (Taylor, 2010). The subjectivity of the forecasts helps in providing forecasts based on factors and trends within an industry. The methods present a widened decision-making scope for managers. Some examples of these methods include:

• Surveys;
• Technology forecasting.

Artificial intelligence methods

These methods heavily rely on the ability of individuals to analyze situations. These methods provide very personalized ways of forecasting. Each person makes forecasts based on personal beliefs and attributes. While these methods might utilize available data concerning a variable, interpretation of the data lies purely on the person making the decision (Rescher, 1998). The person producing the forecast remains at liberty to provide a forecast based on personal understanding. The independence of these forecasting methods means they produce totally different forecasts on similar variables. Stereotypes could immensely affect the accuracy of the results presented using these methods (Armstrong, 2001). The possibility of considering numerous factors affecting the variable, however, could enhance the accuracy of the results significantly. Examples of methods within this category include:

• Group method of data handling.
• Artificial neural networks.

Other methods

These could be identified as forecasting methods not clearly attached to any of the above categories. These methods include the use of random selection methods of forecasting. Several of these independent methods combine aspects several forecasting methods in determining their own forecasts (Rescher, 1998). A combination of several methods produces unique results. Some of these methods also rely on reference from forecasts presented by other data forecasting methods. Reference class forecasting, for example, looks at outcomes of previous similar situations (Menard, 2008). The problem with such method of forecasting comes in the limit to use the method. When difficult situations occur, it might be difficult to establish a situation when similar occurrence happened. These methods could provide highly accurate forecasts based on the similarity of the situations under comparison. Other methods classified under this category are;

• Simulation;
• Prediction market;
• Probabilistic forecasting and Ensemble forecasting.

References

Armstrong, J. (2001). Principles of forecasting: a handbook for researchers and practitioners. Norwell, Massachusetts: Kluwer Academic Publishers.

Ellis, K. (2008). Production Planning and Inventory Control Virginia Tech. New York: McGraw Hill.

Hoshmand, A. (2010). Business Forecasting: A Practical Approach (2nd Ed.). New York: Routledge.

Menard, S. (2008). Handbook of longitudinal research: design, measurement, and analysis. London: Elsevier Inc.

Rescher, N. (1998). Predicting the future: an introduction to the theory of forecasting. New York: State University of New York Press.

Taylor, B. (2010). Introduction to management science (10th ed.). Upper Saddle River, NJ: Pearson/Prentice Hall.

Introduction

Avalanche focusing is one of the most complex processes involving data assimilation to predict temporal solutions and varying spatial. Forecasting involves the assimilation and prediction of information and data that help describe snowpack, weather, and stability within a given period. Conventional avalanche is carried out without direct data or numeric models by stakeholders of avalanche forecasters. The experts usually easily apply redundant and diverse data sources to solve forecasting problems. Therefore, the forecast can range from the next few hours to several days in an area. Spatial prediction varies from specific levels to local forecasts in a particular area covered by different mountain ranges.

Over the last few decades, a wide range of tools and models have been developed to help forecasters make the right decisions. The model ranges from various statistically based methods to physical models of developing a snowpack. Predictors using statistical techniques apply regression trees, discrimination analysis, and nearest neighbors (NN) (Nowak et al., 2020). Most of these stakeholders prefer using NN techniques as they assume that similar situations and events are likely to happen under the same conditions. In avalanche forecasting, the data used in offering the prediction is divided into three classes that include three classes that define the metrological factors they consider. A lot of ambiguity is realized as experts try to use different techniques to achieve their targets of making knowledge-based predictions and decisions. However, with effective visualization, such ambiguities are solved with ease. Visual analytics plays a significant role in predicting uncertainties that help avoid disasters that come with an avalanche.

Problem Statement

Some uncertainties relate to avalanche forecasting. One of the standard issues that cause these uncertainties to rise includes collaborative analysis and ambiguity. It is critical to note that ambiguity, as per forecasters, is defined as a state where several predictions and interpretations become equally plausible. The aspect means several ways of interpreting data and not data inaccuracy. Uncertainties in data are known to cause some ambiguity in data interpretation. Therefore, the project will forecast on identifying the role of visual analytics in solving the uncertainty and ambiguity issues of inaccurate avalanche forecasting.

Research Question

How does visual analytics enhance avalanche forecasting?

Research Method

The project embraced secondary data analysis, which involved getting information from other researchers to answer the research question of the role played by visual analysis in avalanche forecasting.

State-of-The-Art

Different researchers have been using diverse approaches to address the issue of ambiguity. Most of these forecasters use a glyph-based approach to offer their predictions. Glyphs usually operate at multiple scales that provide an overview of data without delay (Nowak et al., 2020). The approaches allow visual aggregation operations that are critical in summarizing data and detecting all the outliners and the trends that can be used to offer a perfect prediction (Nowak et al., 2020). The approach has been embraced by other researchers who claim that they help showcase granular data that helps reveal different particulars that are critical in avalanche forecasting. Experts prefer using bubble chart graphs where each circle represents an individual report. In this case, the stakeholders of avalanche forecasting code each prediction with different circle sizes. The methodology embraces color luminance or saturation based on the number of viewed avalanches. The circles used in this care are arranged in a packed layout to predict upcoming avalanches. These glyphs support various forms of visualization analysis hence creating channels offering some of the most accurate avalanche predictions.

Some experts have used computer assimilation to visualize data and make professional and experienced avalanche forecasts by manually testing snowpacks. The simulated snow covers tend to detect and track weak layers and identify the avalanche using a different approach (Giabbanelli & Baniukiewicz, 2019). The merit of using this approach is that it can rely on other tools, especially in cases where the local snowpack data is unavailable. The simulation is critical as they help determine the risk associated with each avalanche using an artificial release that focuses on identifying the problems associated with new snow, persistent weak layers, and wind slabs.

Comparison

The use of the glyph-based approach is different as compared to the use of computer simulation. The aspect relates to the fact that glyph-based approaches depend on various scales that help in providing an overview of the data in question without any form of delay. The approach summarizes data and helps determine the trends and outliers that might affect the art of having accurate predictions. On the other hand, computer simulations depend on manual tests of snowpacks to detect weak layers that form the basis under which the predictions are made (Giabbanelli & Baniukiewicz, 2019). The glyph method embraces different color saturation and luminance to help in forecasting (Nowak et al., 2020). At the same time, computer simulation depends on artificial data release to make predictions based on the problems associated with weak layers and the occurrence of an avalanche in a region.

Literature and Current Contributions

Avalanches Disasters

Avalanche forms part of the natural disasters that occur when there are some forms of instabilities in the snowpack. According to Horton et al. (2020), the aspect is detrimental as it causes a release of a mass of snow that slides downhill with a destructive force. These avalanches, therefore, pose significant risks to people recreating and working around mountain terrains (Nowak et al., 2020). For these reasons, avalanche forecast is mainly concerned with predicting current and future snow stabilities that might lead to the sliding of the avalanches and identifying some of the human activities that trigger the phenomenon. According to Schweizer et al. (2020), researchers and forecasters view avalanche forecasting as inductive. The new information received from each prediction helps update the models and the conditions of the entire season. Pourraz et al. (2017) pointed out that the predictors assess and characterize all the hazards associated with avalanches by answering questions such as the types of avalanches that exist in an area and their location, their likelihood of occurrence, and how large they might be. The forecasters and the researchers utilize a variety of observations and data to access the occurrence and the hazards associated with these avalanches.

Ambiguities and Uncertainties

A lot of data and observations are required for compelling predictions. The reported data include file observation of the weather conditions associated with the avalanches and the snow and avalanche activities associated with various hazards. According to Conger (2014), analyzing this data requires a lot of visual analytics that help identify the repetitive features in the data that help make the necessary predictions (Nowak et al., 2020). However, the variability of operational and the interpretation of this data largely depend on subjective judgment and a lot of discernment that helps fill the gaps in understanding. According to Helbig et al. (2015), the aspect creates room for multiple interpretations that create uncertainties and ambiguities associated with these predictions. According to Nowak et al. (2020), the challenges posed in this situation relate to the similar uncertainty issues that predictors of another phenomenon face. Therefore, the aspect necessitates visual analytics that helps analyze the data in question, let alone the observations associated with such data, to make accurate and relevant predictions.

Current Contributions

Visual analytics is outlined as the use of sophisticated methods and tools to analyze data sets using various visual representations of data. Visualizing data in charts, maps, and graphs help users identify the patterns followed by a particular phenomenon which is critical in making predictions and taking the right actionable insights Varga et al. (2020). These visualizations are critical as they help make appropriate and accurate predictions in avalanche forecasting.

Ambiguity in avalanche forecasting is addressed using visual analytics using a glyph-based approach and maps. In these maps, the elevations and different types of avalanches are reported using intervals that are not uniform (Nowak et al., 2020). Several charts and maps are developed to encode all the reports and prevent issues that relate to over-plotting. The visual analysis required arcs and critical segments to represent all the non-uniform intervals (Schindler et al., 2020). Data encoding is critical in making relatively accurate reports and is well-represented in graphs. The reports, in most cases, are presented across multiple displays that are coordinated hence supporting the standard highlighting and brushing of interactions. The art of selecting reports and highlighting them in the corresponding visualization provides a multidimensional perspective on data critical in accessing all the unstructured data that might be required to make the necessary predictions.

The visual overviews provided in these graphical maps deliberately use perceptually weak visual encodings to help make multidimensional and holistic predictions based on the points where predictions started. Visual analytics, therefore, allows a forecaster to review data quickly and make the necessary predictions based on the data provided (Nowak et al., 2020). Experts in interpreting these data help answer questions about avalanches’ hazardous nature and the likelihood of occurring their sizes, and their location in different terrains. The visual tools allow the forecasters to detect all the trends made by these avalanches. The ability to encode the information presented by these visual tools help experts in identifying and outlining the characteristic of expected avalanches. The aspect is critical as it helps evade the ambiguity and uncertainties associated with avalanche forecasting.

Future Research Challenges

A key aspect worth noting from the research study is that identifying the features associated with the sources of ambiguity is critical in designing a tool that ensures accurate data visualization. From the research study, it is clear that addressing ambiguity more explicitly is still a challenge. When an analysis is shared and the same data is revised or revisited by other experts, ambiguities are identified in how data was captured, let alone its subsequent analysis using various visualization tools. This aspect means that even after a comprehensive analysis, the data can still be re-analyzed and offer different predictions and avalanche forecasts based on the tools and techniques deployed (Nowak et al., 2020). The other challenge that future researchers will face is the problem of externalizing information. Researchers have identified that externalizing sources requires a lot of effort as it can be disruptive or part of transferring errors from one research. The art of predicting the appearance of future avalanches will be based on errors carried forward by externalizing references with bias. Therefore, unless the errors are detected at an early stage of future research, ambiguities, and uncertainties will still be viable, and they may affect the predictions given.

Climate changes have affected how weather forecasters predict future climatic conditions. The aspect means that even with proper utilization of visualization tools and analytics, climate change may affect the standard patterns assumed by most of these avalanches. Therefore, future researchers should be proactive and have rich sources that will help solve the uncertainties and ambiguity issues. Short-term analysis should be embraced to help extrapolate the errors associated with climate change.

Conclusion

Avalanches are common natural disasters that affect people who leaves near mountainous terrains. Therefore, Avalanche forecasters play a critical role in predicting their features and the effects or hazardous nature associated with each slide. The predictions are based on their forecasts of the data and observations made. The aspect creates room for multiple interpretations of this information hence bringing up a lot of ambiguities and uncertainties. However, with proper visualization techniques, the margin of error associated with ambiguity and uncertainty reduces, making accurate predictions and decisions. Therefore, future studies should analyze short-term data using critical visualization techniques. The analysis will help reduce the margin of error in making avalanche predictions and help avoid the disasters associated with their occurrence in any mountainous region.

References

Conger, S. (2014). Uncertainty and risk, merging theory with practical adaptation in avalanche hazard management. International Snow Science Workshop 2014 Proceedings, Banff, Canada. Web.

Giabbanelli, P. J., & Baniukiewicz, M. (2019). Visual analytics to identify temporal patterns and variability in simulations from cellular automata. ACM Transactions on Modeling and Computer Simulation, 29(1), 1–26. Web.

Helbig, N., van Herwijnen, A., & Jonas, T. (2015). Forecasting wet-snow avalanche probability in mountainous terrain.Cold Regions Science and Technology, 120, 219–226. Web.

Horton, S., Nowak, S., & Haegeli, P. (2020). Enhancing the operational value of snowpack models with visualization design principles. Natural Hazards and Earth System Sciences, 20(6), 1557–1572.

Nowak, S., Bartram, L., & Haegeli, P. (2020). Designing for ambiguity: Visual analytics in avalanche forecasting. 2020 IEEE Visualization Conference (VIS).

Pourraz, F., Verjus, H., & Mauris, G. (2017). Visual analytics for aiding decisions of ski touring itinerary in a risky snow avalanche environment.2017 IEEE International Conference on Computational Intelligence and Virtual Environments for Measurement Systems and Applications (CIVEMSA). Web.

Schindler, M., Wu, H. Y., & Raidou, R. G. VIS 2020. Web.

Schweizer, J., Mitterer, C., Techel, F., Stoffel, A., & Reuter, B. (2020). On the relation between avalanche occurrence and avalanche danger level. The Cryosphere, 14(2), 737–750.

Varga, M., Webb, H., Krilavičius, T., & Maiden, M. (2020). Visualization and Visual Analytics in Knowledge Landscapes. Navigating Digital Health Landscapes, 297–318.

Introduction

Background

Before a company enters a new market, it is important to conduct a demand analysis and forecast for the product the company offers. Demand analysis will entail analysing the factors that are likely to affect the demand of the product at issue. Some of these factors include demographic factors (population size and pattern), household income, price of the commodity and the price of other related commodities.

It is also important to conduct competitors’ analysis in order to understand their marketing strategies, and their weaknesses and strengths. The analysis of all these factors will also make it possible for the company to assess the economic viability of the market before entering.

The purpose of research

This paper analyzes the possibility of Domino’s Pizza entering Boca Raton Market situated in Boca Raton Community. The research involves a demographic survey of the community and other variables that are likely to affect the demand of Pizza in the region.

The demand for Pizza in this community is believed to be dependent on the population size, the income per house hold, price of Pizza and the demand of soda. The demand analysis and forecast for Pizza conducted is meant to help make a decision concerning whether Domino’s should establish presence in Boca Raton community.

Research questions

1. What is the population size of Boca Raton community and how does it affect the demand of Pizza?
2. What is the average income per household in Boca Raton community? How does this income level influence the demand of Pizza?
3. Does the price of pizza influence its demand in Boca Raton community?
4. Does the price of soda have influence on the demand of pizza?

Methodology

The information will be gathered from secondary sources. Journal, books and articles containing information about the price theory (demand and supply and their relationship with price) will be used. The other information to be gathered from secondary sources includes the effects of income levels and population size on demand of pizza.

The research will involve determining whether all the demand factors (price of pizza, income of households, and price of soda and population size) are important determinants of demand for pizza. The data collected will, therefore, need to be analyzed carefully and tested.

The analysis of this data will entail conducting a regression analysis in order to determine the extent to which all the independent variables affect the demand of pizza in Boca Raton, FL. The demand of pizza will be taken as the dependent variable and will be denoted by Y. The other factors will be taken as the independent variables and will be represented as follows:

• X₁ => Population Size.
• X₂ => Household income.
• X₃ => Price of pizza.
• X₄ => price of Soda.

The regression equation that will need to be determined is as follows:

Y = β₀ + β₁X₁ + β₂X₂ + β₃X₃ + β₄X₄.

Where: β₀, β₁, β₂, β₃, and β₄ are constants, and coefficients of the independent variables.

The estimation of the regression line will be done with the help of Eviews statistical software.

Literature review

Boca Raton, FL Demographics

Boca Raton is located in Florida, in the United States of America. The community, on average, has a population of 86,445 (United States Census Bureau, 2012). The population in the 1990’s was growing at the rate of 22% per annum on average. However, from around 2005, the population has not been growing at a very slight margin.

The community is comprised of 49% male and 515 female. The population by race comprise of 91% white, 4% Africa American, 0% Native American, 2% Asian, 0% Hawaiian and 3% for others. The population size for the past 10 years for the city is summarised in the table below.

Average income per household in Boca Raton, FL

The median household income for the community between 2006 and 2010 was $47,661 (United States Census Bureau, 2012). We shall use the following data to represent the annual household income:

The price of and the demand of Pizza

According to Harvey, Carl and Hasek (2006), it is generally known that the demand for a normal commodity is inversely related to its own price. The demand of a commodity increases as its own price decreases and vice versa (McEachern, 2011).

We shall also include in the same schedule the demand for soda. Assuming that one pizza will be accompanied with one soda, the same amount of soda will be needed as pizzas. The following demand schedule for Pizza will be used in the analysis.

Data Analysis, Results and discussions.

The Eviews output was obtained as shown below:

The regression line is obtained from the Eviews report and is stated as follows:

Y = -1413.077 + 0.009757 X₁ + 0.021733 X₂ + 11.11188 X₃ + -50.38428 X₄

S. E. 479.2690 0.004869 0.004715 5.697891 10.39577

T – Statistic -2.948401 2.003767 4.609647 1.950174 -4.846612

To test the significance of all these independent variables, we use the t – test. We check from the student’s t distribution table for the critical values of t at 99% level of confidence and 6 (n-k) degrees of freedom. The critical t at this point is 1.9432. The hypotheses being tested are stated as follows:

H0: β = 0, that is, the independent variable (e.g. X₁ x₂ x₃ or x₄) is not an important determinant of the dependent variable Y.

H1: β ≠ 0, that is, the independent variable (e.g. X₁ x₂ x₃ or x₄) is an important determinant of the dependent variable Y.

Based on the decision criteria, we may reject or may not reject the null hypothesis. The decision criterion is that if t-statistic is greater that the critical t, we reject the null hypothesis (Black, 2009). In our case, it shows that t-statistic > t – critical, for all variables X₁ x₂ x₃ and x₄.

This means that all the 4 variables are important determinants of Y. The demand of Pizza is significantly influenced by the population size, household income, price of pizza and price of soda, which is pizza’s compliment good. The coefficient of determination R² (Adjusted) = 0.994920. This means that

99.492% of the demand of Pizza is explained jointly by population size, household income, price of pizza, and price of soda. To improve the value of R², other factors that affect the demand of pizza should be included in the model. These may include changes in substitute goods, the future expectations of changes in price, and tastes and preferences of the consumers among others.

Demand Forecast

Using the regression line Y = -1413.077 + 0.009757 X₁ + 0.021733 X₂ + 11.11188 X₃ – 50.38428 X₄, we assume the variables X1, X2, X3, and X4 changed as shown below in the next 4 years.

The assumption made is that the regression line was estimated using monthly data.

Conclusion and recommendations

Form the above analysis, it shows that population size, household income, price of pizza, and price of soda play a big role in determining the demand of Pizza. Domino’s Pizza needs to consider all these factors before moving to the new market. The market seems to have an opportunity because the population is growing, and this will increase the demand of pizza.

The issue of household income is another important determinant. The income mostly keeps on increasing even it is with a very small margin. This means the demand of pizza will continue rising. Domino’s Pizza may also enter the market and charge slightly less than the competitors (McGuigan, Moyer and Harris, 2010). This will attract many customers toward Domino’s Pizza. The price of soda is beyond Domino’s Pizza control.

Reference List

Black, K. (2009). Business Statistics: Contemporary Decision Making. London: John Wiley & Sons.

Harvey, J., Carl, D. and Hasek, W. (2006). Economics: Principles and Applications. US: Goodwill Trading Co., Inc.

McEachern, W. A. (2011). Economics: A Contemporary Introduction. New York: Cengage Learning.

McGuigan, J. R., Moyer, C. and Harris, F. (2010). Managerial Economics. New York: Cengage Learning.

Unites States Bureau of Labor Statistics. (2001). Household survey. Web.

United States Census Bureau. (2012). State & County QuickFacts: Boca Raton (city), Florida. Web.

Financial forecasting refers to the process of estimating and evaluating the future financial results of the organization based on the current available information.

From the results of financial forecasting, the organization derives the future balance sheets, income statements, and budget statements.

These statements are used by the management for decision making. With the help of these statements, both the strategic and tactical plans of the organization can be implemented effectively.

In this regard, short-term forecast are more likely to be accurate than the long-term ones. Nevertheless, long-term plans are helpful for the company to make long-term investment both in fixed assets and other important investments (Shim 254).

The financial forecasting procedure uses varied models to come up with the anticipated financial statements. An organization could use the Pro forma financial statements or the cash budgeting process.

Preparation of the Pro forma financial statements entails the adoption of any of the following concepts: percentage of sales method, external financing needed and financial forecasting equations.

Percentage of sales method uses the anticipated sales to make adjustments on the components of the business like assets, finances, and liabilities for the future period.

Accounting for the expected sales, gives the company a clear view of the necessary measures that they should input to achieve such objective (Brigham 345).

Similarly, external financing method uses the amt of finance expected to make future returns based on the manner in which they will be used within the organization.

Another important concept is the forecasting equation concept used to determine future financial statements. This concept formulates equations as a model, which takes into consideration all the factors within the organization.

These equations therefore are used to make the future predictions of the financial performance and position of the company (Shim 324).

Pro forma statements are used for management to identify financial and operating characteristics assumptions that result in different scenarios. This implies therefore that the organization can develop appropriate revenue and expense projections (Brigham 286).

By comparing the resulting financial statements of the organisation and its competitors, it can be able determine their financial standing in the marketing in the future.

For the short-term plans, the organization needs to make cash budgets that are used for the operation of the company on the day-to-day activities. These budgets enable the organization to make allocation of the funds to the current spending and expenses incurred.

Effective budgets facilitate the transparency and accountability of the financial transactions in the organization (Bomhoff 245). Additionally, it represents whether the expenses of the company is in relation to the returns being generated.

The analysis of the pro forma statements and the cash budgets indicate that both are suitable for long term and short-term plan purposes respectively.

In this regard, the pro forma statements are prone to inaccuracy since it involves the prediction of the future, which is uncertain (Ross 248). On the contrary, cash budget forecasts give a clear and concise means of the generation and expenditure of the funds in the organization. Despite this, pro forma statements are very critical for appropriate estimation of the likelihood financial standing in the company.

The pro forma statements at times enable the organisation to prepare cash flow projections, which becomes a benefit for determining the financial position of the company.

Notably, the statements are very crucial despite some their exposure to the frequent changes in the accounting principles and policies (Bomhoff 354). Nonetheless, pro forma statements facilitate the review of the decisions in the management functions of the company.

This therefore implies that the company can assess the impact of profitability and liquidity of the organisation. Finally, pro forma financial statements are necessary for the prediction of future for the success of the company.

Works Cited

Bomhoff, Eduard Jan. Financial forecasting for business and economics. London: Academic Press, 1994. Print.

Brigham, Eugene F., Louis C. Garpenski, and Philip R. Daves. Intermediate financial management. 10. ed. Mason, OH: South-Western, 2010. Print.

Ross, Stephen A.. Modern financial management. 8th ed. Boston: McGraw-Hill/Irwin, 2008. Print.

Shim, Jae K., and Joel G. Siegel. Financial management. 3rd ed. Hauppauge, N.Y.: Barron’s Educational Series, 2008. Print.

Financial statements are fundamental to the success of any business since they enable the owner to track the cash flow, revenue, and expenditure hence avoiding wastage. A new boutique is not exceptional since it is a profit-making entity, and the financial activities have to be tracked effectively for the business to grow and make a profit. In the case of a fashion boutique, the first step in preparing a forecast is studying the market to estimate the customer base.

Next is getting space in a place where the business will manage to cover for the fixed and variable expenses and still afford the owner a profit. Another important element in the start-up of a business is a forecast of the whole year’s budget. Garrison, Davidson, and Garrison (1998) stipulated that the forecasted budget is important in guarding against expenses not budgeted for and ensuring the money used to cover for the expenses can be accounted for (p. 24).

The first and most important statement in this business is a personal financial statement. This is a document that shows the financial position of an entrepreneur besides their business position. It includes a record of personal assets and expenditure heads. The main purpose of this document is to assess whether one is in a position to sustain the business in the initial stages, in which case most businesses make little or no profits.

A person for example with many liabilities and financial responsibilities might not be in a position to handle a certain type of business venture and therefore required to start small according to their capacity as presented by the personal financial statement (Bomhoff, 1994). This will also be helpful in case a person wants to take credit since lending institutions use this information to determine their creditworthiness.

The second statement to be prepared is a balance sheet, which represents the position of a business entity in terms of the value of assets and liabilities. At the start of a business, there’s very little that can be included in this document since it is supposed to reflect the value of fixed and movable assets against the liabilities for a fixed period where liabilities include the money owed to creditors and the investments made within the period.

It reflects the position of the business as at a particular time, unlike the other statements which reflect financial information over some time (Batchelor & Dua, 2003). In this case of a startup, the balance sheet will include the assets acquired at startup and any kind of debt incurred whether from financial institutions or the suppliers.

The next financial statement is a startup cost sheet, which is a record of all requirements preceding the opening of the business. This includes the cost of obtaining stock, the initial rent, which in most cases traders prefer paying up six months in advance rent, and the cost of installing fixtures in the business entity.

This statement is important in the sense that it enables an incoming partner to ascertain the amount of contribution they are expected to give as well as the profit ratio to be shared. At the end of the financial year, this report will also come in handy when taking stock, alongside the sales and assets registers.

Reference list

Batchelor, R., & Dua, P. (2003). Financial forecasting. Cheltenham, UK: Edward Elgar.

Bomhoff, E. (1994). Financial forecasting for business and economics. London: Academic Press.

Garrison, S., Davidson, W., & Garrison, M. (1998). Financial forecasting and planning: A guide for accounting, marketing, and planning managers. New York: Quorum.

The rate of increase in the money supply and inflation

The data support a connection between the ate of increase in the money supply and inflation because the regression and correlation coefficients show that the two variables are related. There is a positive relationship between the two variables. The scatter plot shows that the line of best fit has a positive direction. In addition, the two variables are related because it is possible to develop a graph of the data collected.

Using the data on the growth rate of Money and inflation, run a regression of the rate of inflation on the rate of growth of the money supply. Use Excel Data Analysis.

A regression line equation for the the rate of growth of the money supply compared to inflation is; Y = 0.57446X + 0.571. The regression equation shows that the slope of the line is 0.57446 and the y-intercept is 0.571. Therefore, when there is no inflation (0% inflation rate), the rate of economic growth is 0.571. This is indicated by the y-intercept. The gradient of the rate of change of the money supply relative to change in inflation.

Interpret slope

The slope of the regression line is 0.57446. This means that when the inflation rate changes by 1%, the rate of growth of the money supply changes by 0.57446%. The coefficient on the money supply variable suggests that there is a positive relationship between inflation rate and the rate of growth of the money supply.

Forecast inflation if money = 8

Inflation is the independent variable (x) whereas the rate of change of the money supply is the dependent variable (Y). Therefore,

Y = 0.57446X + 0.571

8 = 0.5744X + 0.5718

7.429 = 0.57446X

X = 12.93

Inflation is 12.93%

P-value and the regression coefficient

The p-value indicates the probability that a certain event will occur. The p-value indicates the rejection region when testing the hypothesis. Points that lie below the p-value are accepted while the points that exceed the p-value are rejected (Mendenhall, Beaver & Beaver, 2009).

The analysis was conducted at 5 level of significance, therefore, the rejection point is 0.05. The regression coefficient (0.571) is significant, because the p-value (0.108) is greater than 0.05 (p >0.05).

Interpret the coefficient of determination

The coefficient of determination is used in identifying how fit the regression line is in a given data set. The coefficient of determination is 0.326, and this indicates that the regression line is relatively bad. The coefficient of determination shows that the variation in the regression is 32.6% explained by the inflation. This is a bad regression because the coefficient of determination is small.

Is faster money growth always associated with higher inflation?

Faster money growth is associated with higher inflation. There is a correlation of 0.57087 between the inflation and the rate of growth of money.

Reference

Mendenhall, W., Beaver, R. J., & Beaver, B. M. (2009). Introduction to probability and statistics. Belmont, CA: Brooks/Cole.

Relative fluctuations of Mobil-Exxon (XOM) and market returns

As the above graph portrays, XOM returns have been fluctuating considerably from the market returns over the period covered by the data. Although some of the fluctuations of the stock have been in the opposite direction to that of the market portfolio, most of the fluctuations have been in the same direction with the market.

Descriptive statistics of monthly returns of General Electric (GE), General Motors (GM), IBM, and Disney (DIS) data

The average return represents the mean of a stock’s return over a given period (Lakonishok 1994). It indicates the return that an investor could have received if his or her holding period corresponded to the period covered by the stock returns (Jensen 1968). IBM, DIS, and GE stocks have a positive average over the period covered while GM has a negative average over the same period. The average of DIS and GE is nearly the same.

The variance is a measure of dispersion and it indicates how individual returns of stock vary from the mean or average return (Kothari 1995). As indicated in the above table, GM stock had the largest variance over the period followed by IBM. GE stock, on the other hand, registered the least variance over the period. The variance measures the risk of a stock (Shapiro 1986). The higher the variance the higher the risk of the related stock (Pandey 2008). Therefore, GM stock has the highest risk in this case while GE stock has the lowest risk.

The standard deviation is the square root of the variance and it indicates the average dispersion of individual stock returns from the average (Jegadeesh 1993). As shown in the table, GM has the highest standard deviation and GE the lowest.

CAPM model for Microsoft and GM

Microsoft: R_ms= 1.174(R_m-R_f) + 0.043.

Where R_ms=expected return on Microsoft stock.

1.174 is the beta value for Microsoft stock.

(R_m-R_f)=risk premium.

0.043 is the alpha value for Microsoft stock.

GM: R_Gm=1.061(R_m-R_f) + 0.22.

Where R_Gm=expected return on GM stock.

1.06 is the beta value.

0.22 is the alpha value of GM stock.

The estimated beta of Microsoft stock, 1.174, and the estimated beta of GM stock, 1.061, are all above the value of 1. This shows that the two stocks are aggressive and they move in the same direction with the returns of the market portfolio (Sharpe 2010).

Alpha Value

Theoretically, the value of alpha should be zero if a stock is not mispriced. A positive alpha indicates undervalued stocks while a negative alpha indicates overvalued stocks. Therefore, since both Microsoft and GM stocks had positive alphas, they were undervalued over the period covered by the data.

• Standard deviation = √R^{2 =}√0.286=0.535 (R²=Coefficient of determination. For the Microsoft CAPM equation it is equal to 0.286)

Z=(µ_av-µ₀)/(α√n).

Where z = the level of statistical significance.

µ_av=average beta in this case 1.174.

µ₀=Null hypothesis beta in this case 1.

α=standard deviation equal to 0.535.

n=number of observations in this case 132.

z= (1.174-1)/(0.535√132)=0.028.

The level of significance of 0.028 is above 10 percent. Thus, the financial consultants’ claim of 1 percent beta is rejected.

• R_ms-R_f=β_ms.(R_m-R_f)-R_f + α_ms

Where R_ms-R_f=risk premium on Microsoft stock.

β_ms =Beta of Microsoft stock which is 1.174.

(R_m-R_f)= Risk premium on the market portfolio.

R_f =Risk-free rate in this case average risk-free rate equal to 0.032.

α_ms=Alpha of Microsoft stock equal to 0.043.

If the risk premium on market portfolio is 2%, R_ms-R_f=(1.174 x 0.02)-0.032+0.043 = 0.03448.

If the risk premium on market portfolio is 7%, R_ms-R_f=(1.174×0.07) -0.032+0.043=0.09318.

References

Jegadeesh, N 1993, ‘Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency’, Journal of Finance, 48:1, pp. 65–91.

Jensen, C 1968, ‘The Performance of Mutual Funds in the Period 1945–1964’, Journal of Finance, 23:2, pp. 389–416.

Kothari, S 1995, ‘Another Look at the Cross-Section of Expected Stock Returns’, Journal of Finance, 50:1, pp. 185–224.

Lakonishok, J 1994, ‘Contrarian Investment, Extrapolation, and Risk’, Journal of Finance, 49:5, pp. 1541–578.

Pandey, I 2008, Financial Management, PHI Learning, New Delhi.

Shapiro, C 1986, ‘Systematic Risk, Total Risk, and Size as Determinants of Stock Market Returns’, Journal of Banking and Finance, 10:1, pp. 115–32.

Sharpe, W 2010, Investments, Prentice-Hall, London.

Hypothesis

Foreign currency traders who use data for decision-making are likely to gain competitive edge in foreign exchange than those who rely on gut feelings.

The project area

Data for this study will be obtained from Exchange-Rates.org. Historical exchange rates between the British Pound (GBP) and the US Dollar (USD) will be used for forecasting future exchange rates. Data for analysis will be based on the preferred periods.

The technical approach (TA) will be used in forecasting the exchanges for a given period. TA relies on a subset of historical data, particularly price data (exchange rates). This approach is technical because it does not account for fundamental economic determinants that could influence exchange rates. Instead, it relies on data extrapolation obtained from historical observed trends.

Technical analysis will yield certain patterns that will be used for forecasting exchange rates between the GBP and the USD. In time-series analysis, it is imperative to determine an appropriate length of intervals because they determine the effectiveness of forecasting (Tayal, Sonawani, Ansari and Gupta 132-135). Research shows that the length of the intervals influences the accuracy of the forecast. Thus, effective selection of the length of intervals could significantly enhance the accuracy of forecasting outcomes (Tayal et al. 132-135).

SPSS or any other effective analytical tool will be used for data analysis to identify significant trends that can support decision-making. Foreign currency traders will use these significant trends to buy or sell their currencies.

A research question

Can data-driven decision-making create competitive edge for foreign currency traders?

Significance

In most cases, international transactions may take time be settled. In this regard, traders should assess exchange rate forecasts based on foreign currencies. In addition, foreign exchange traders must also understand future trends in their markets. Therefore, exchange rate forecasting is critical and can help traders to assess both benefits, risks and other challenges in trade.

Project Proposal

Forecasting has long been recognized as a fundamental tool across various industries. In the past, however, traders used various approaches to forecast and inform their decisions. One primary goal of understanding trends of exchange rate is to be able to forecast them. Given the fluctuation in exchange rate trends, forecasting exchange rates could be difficult without reliable data. The research question, therefore, would provide intellectual foundation to encourage foreign exchange traders to adopt data-driven decision-making rather than use gut feelings to make decisions.

Thomas H. Davenport noted that forecasting could be more difficult in retail industries because of several variables and constantly changing trends and influences on demands, alternative channels among others (Davenport 11). In most cases, there could be large amount of data that analysts can leverage to create accurate prediction of the exchange rate. Foreign exchange forecasting is critical for key decision-making processes, particularly in finance management, operations and budgeting among others. The use of gut feelings or manual forecasts cannot support effective decision-making. Such approaches consume management time and they could be difficult to understand due to lack of any meaningful data. In this regard, data-driven decision-making can assist managers to make effective decisions for competitive advantage. Davenport observed that there is little doubt, however, that the “aggressive adoption and exploitation of analytics has led to competitive advantage among some of the world’s most successful retailers” (Davenport 11). Therefore, data-driven decision-making can solve many challenges international traders face.

Works Cited

Davenport, Thomas H. Realizing the Potential of Retail Analytics: Plenty of Food for Those with the Appetite. Babson Park, MA: Babson Executive Education, 2009. Print.

Tayal, Devendra, Shilpa Sonawani, Gunjan Ansari, and Charu Gupta. “Fuzzy Time Series Forecasting of Low Dimensional Numerical Data.” International Journal of Engineering Research and Applications (IJERA) 2.1 (n.d): 132-135. Print.

Budgeting is an integral part of the overall planning process, not just its financial position. It is advisable to implement the mechanism of budget planning of income and expenses to ensure money savings, greater efficiency in managing these funds, and reducing unproductive costs. In current market conditions, the prediction comes to the forefront since the development of an action plan in various conditions of the enterprise’s activity is of great importance. Financial forecasts are necessary for the company to build a future picture of the economic situation, and anticipate possible problems and financing needs.

Financial forecasting makes it possible to increase enterprise management level since it ensures the close coordination of all production processes and the nature of relations between the economic divisions of the enterprise. Krylov (2018) claims that financial forecasting is used to effectively manage the company’s cash flows to overcome its economic difficulties and improve the indicators of its financial position. It is necessary for the preparation of the enterprise budget, mainly part of the expenses. The revenue part, as a rule, is considered the least predictable. It is unnecessary to increase the forecast period too much, as this increases the risk of uncertainty and reduces data reliability. Sometimes, there may be a sharp change in the balance of the company’s funds in some conditions: their inflow or outflow. If such situations are typical for the company, it will be advisable to make weekly forecasts.

Budgeting and forecasting are among the most popular and reliable tools. The introduction of budget management and financial forecasting at the enterprise contributes to improving financial discipline, improving the economic validity of decisions made. In addition, it helps to improve the system of operational cost management and improve the professional skills of personnel in financial management. Since financial resources are limited, the company should dispose of them most effectively to preserve and increase these resources. For these purposes, the company must have a plan or budget.

Reference

Krylov, S. (2018). Target financial forecasting as an instrument to improve company financial health. Cogent Business & Management, 5(1), 1-42. Web.

Introduction

The eternal quest to predict future events has spilled over into the investigation of reliable techniques for predicting the movement of financial markets, particularly with a view to optimizing returns. Since the 1960s, much attention has been given to testing Eugene Fama’s Efficient Market Hypothesis, which the author posits in three forms: weak, semi-strong and strong forms. The latter postulates that historic information can substantively forecast future security prices and hence, composite indices (CI’s). Given this view, financial analysts have rightly moved toward linear regression modelling to forecast the state of CI. (Simon, 2005).

The purpose of all multiple regression works is to predict a criterion variable better. In this case, an investor who presumably wishes to put some money in an index fund is faced with a great deal of uncertainty about how the composite index will behave. But if there were firm indicators for how the chosen independent variables might behave, then it might be possible to position a fund in long or short positions.

Methodology

Develop a multiple regression model which could be used to predict the composite index from Stock Volume, Reported Trades, Dollar Value and Warrants Volume.

In Minitab 15, load datafile “Stock_Market.MPJ”. Next trigger the command sequence Stat-Regression-Regression. In the menu, type in, or transfer ‘Composite Index’ to the ‘Response’ box. Tab to ‘Predictors’ and choose (or type in) the assigned independent variables (IV’s): Stock Volume, Reported Trades, Dollar Value and Warrants Volume. Choose all necessary diagnostic options in the sub-menus

Findings

The Long-term Market Trend

Over most of the decade, the Composite Index for this stock market exhibited a slowly rising trend. An investor who had put in a thousand dollars in an Index Fund on January 10, 1990, would have realised little more than a doubling of his investment (+108.6%) by the same date in 1997. This represents an average annual growth rate of 15.5% in capital appreciation (Fortune, 1998).

Thereafter (see Figure 1 overleaf), activity in the market picked up and the CI reached a high of 599.21 on July 20, 1998. A long correction followed but by the end of the time series, the market had essentially returned to that decade-long high.

The Derived Multiple Regression Model

This prediction model is best-understood component by component. The first but least important is the initial number on the right-hand side of the equation, 206. This is technically known as the “intercept”, the starting point for the prediction line if one were to chart the result of the prediction model. This is the value on the Y axis, meaning that over the time period for which there is data, the stock market Composite Index takes a value of $206.15 (see also the first value Minitab reports in the ‘Coef’ column above) if none of the independent variables were in effect. In short, one may consider the intercept as something akin to a ‘base value’ in this analysis. Another way of coming to grips with the concept is to notice that the long-term trend depicted in Figure 1 starts at just under $200. If none of the predictor variables acted on the criterion variable, the chart would show a flat line at $206. across the whole time period.

The second point worth noting is that the prediction model contains a mix of plus and minus signs. This combination reveals that the activity of the Composite Index is directly proportional to the number of trades executed and their aggregate dollar value but inversely proportional to the volume of stocks and warrants that were bought/sold that day.

And the third, most important piece of information is embodied by the ‘beta coefficients’, the values associated with each predictor variable. These tell us that, taken together:

• An increase of 0.000718 standard deviations in ‘reported trades’ for the day will lead to an increase of 1 SD in the criterion variable.
• Similarly, an increase of 0.0212 SD in the dollar value of all trades for the day should boost the entire composite index by 1 SD.
• These beta values look deceptively small and inconsequential until one remembers that the average volume of trades reported during this analysis period was in the order of just under a quarter of a million daily whilst the dollar values averaged $12,968 (this is likely in thousands of dollars) and in fact routinely stood at double that average by the end of the reference period. Hence, the composite index responds substantively to small changes in the number of trades executed and especially to stock prices.
• In turn, the composite index is inversely related to the volume of stocks and warrants traded that day. Specifically, an increase of 0.000001 SD in Stock Volume and 0.000024 SD in the volume of warrants traded depresses the Composite Index one SD.

Another way to understand the results of this analysis is, of course, to recall just what composes a stock market composite index. Every index comprises selections of the stocks in that market – some on an empirical, ‘market-making’ basis and others that are judgment calls because their movements have a disproportionate influence on the movement of the market as a whole. The stock price is a core component of all indices and so is volume.

Why should the volume of “product” traded at the exchanges – stocks and warrants both – depress the Composite Index and hence, contribute to a ‘bear market’ in the making? While everyone knows what stocks are, insight into this question is sharpened by knowing what warrants are.

A stock warrant is a derivative granting the holder ‘the right to purchase securities (usually equity) from the issuer at a specific price within a certain time frame…the main difference between warrants and call options is that warrants are issued and guaranteed by the company, whereas options are exchange instruments and are not issued by the company. Also, the lifetime of a warrant is often measured in years, while the lifetime of a typical option is measured in months’ (Forbes/Investopedia LLC, 2009). For all practical purposes, therefore, the typical stock warrant is equivalent to regular stock.

The logical explanation for the inverse relationship of stock and warrant volume to the CI is that both reflect a flood of ‘sell’ orders hitting the market. On the other hand, the positive relationship between reported trades and the CI shows the repercussion of ‘buy’ orders that not only match but even exceed ‘sell’ for that day. News about favourable macroeconomic indicators or corporate performance itself lifts expectations about capital appreciation to be had and individual stock prices consequently rise. There need not be very many such ‘buy’ orders but the number of completed trades has a positive impact on a price-based index.

Diagnostics

How well does this predictive model stand up to the standard indices of reliability and explanatory power?

First of all, there is R, the correlation between the observed value and the predicted value of the criterion variable. The computed value for Pearson’s R (0.96, not shown in Table 2 overleaf) shows a near-optimal fit between the actual and predicted levels of the composite index.

R Square (R²), shown in the Minitab model summary (Table 2 below), is the square of R and reveals the proportion of the variance in the criterion variable accounted for by all four variables incorporated in the model. Thus, Stock Volume, Reported Trades, Dollar Value and Warrants Volume together account for 93% of the variance in the CI over time.

R² is a fundamental and widely-cited measure of how good the prediction of the CI criterion variable becomes as long as we have reliable information on where the predictor variables are headed.

However, R² is prone to slightly over-estimate the success of the model when applied to ‘real-world’ rigour (Gujarati, 1999). Hence, Minitab also calculates an ‘Adjusted R² value to account for the number of variables in the model and the number of observations (years) the model is based on. At 92.8%, the Adjusted R² value renders the reliable measure of the success of the model. In this case, we are more confident that the model has accounted for 93% of the variance in the criterion variable. This measure of the strength of the relationship between the actual CI and the predicted CI is called ‘multiple correlation’.

Given the beta coefficients and the standard error for each, we can derive the 95% confidence interval via: β ± (1.96*SE). Following these, we derive the intervals below with only a 5% chance that we are wrong:

Stock Volume = -0.0000011272 to -0.0000008528

Reported Trades = 0.0005859108 to 0.0008505892

Dollar Value = 0.0183803200 to 0.0239976800

Warrants Volume = -0.0000337444 to -0.0000145756

By way of example, we state that every additional thousand dollars entering the market that day adds between 0.018 to 0.024 to the Composite Index.

A second major concern in model diagnostics is parsimony. That is, does the predictive analysis include as few predictor variables as possible by eliminating those that are highly correlated with each other? This is known as testing for collinearity.

The concern with collinearity springs from the intercorrelation findings (Table 3 above) that Stock Volume is highly correlated with Reported Trades and Dollar Value. In turn, Reported Trades itself is strongly correlated with Dollar Value. Note that the correlation of each predictor with the residuals or error values is 0, which is as it should be.

Other measures for detection of multicollinearity, as suggested by Gujarati (1999, 322) are:

If none of the 6 items are detected, there should not be any multicollinearity in the model. But multicollinearity is a strong supposition if at least one of the 6 items is found.

For the first test, Table 2 affirms that R² is very high but all the t ratios are in fact significant at p < 0.001. On the other hand, the model fails the test of ‘High partial correlation values: abs (pcv) > 0.9’. All the partial correlation values in Table 3 (except those involving Warrants Volume) are extremely high and turn out to have absolute values ranging from 0.979 to 0.988. Thirdly, all the Variance Inflation Factors (VIF’s, see Table 2 above) except for Warrants Volume are greater than 2. Fourth, one concedes that there are unexpected signs in the model coefficients. It does take some convoluted reasoning to rationalise why the signs for both Stock and Warrant Volumes are negative.

Table 4-1

One, therefore, concludes that the model contains multicollinearity. Refining the model to eliminate these will require eliminating at least one of the predictive variables, retesting on more recent periods or for a new sample from another stock market, reconceptualise the model, restudy the literature to gain new insight on other predictor variables, or transforming the variables (Gujarati, 331-334).

Continuing with diagnostics for this regression model, we see from the Analysis of Variance section of the output that at 4 degrees of freedom, the computed F value is 1,014.16 (see Table 5 below). An F value of this magnitude can occur by chance less than five times in a thousand sampling runs of stock market activity. Hence, we conclude that the model permits predictions of extremely high confidence.

Next, the program identifies 26 cases with large standardized residuals (see Table 6), alluding to large differences (‘outliers’) between the actual and predicted values of the CI. The 35^th observation is a case in point: the standardized residual of -2.22 (rather lower than it should have been) is a red flag for looking at the data point more closely. Perhaps, there was some unusual event that took place then.

There are also eight ‘influential cases’, marked with an X. Case 249, for instance, can be considered more important than the others in determining the values of the coefficients. Again, the existence of this ‘outlier’ bears some investigation as this might yield some real-world event that has a bearing on refining the model later on.

Parenthetically, one notes that there are 4 special cases that both display large standardized residuals and appear to have unusually strong leverage on the model results.

A third diagnostic available in the multiple regression model is the Durbin- Waston test, employed to test the hypothesis that the autocorrelation parameter, r, is zero. Specifically,…

versus (for positive autocorrelation)

For the number of predictor variables k = 4 and n observations ≥ 200 (there are 324 data points in the time series tested), the standard table for the Durbin-Watson Statistic at 5 Per Cent Significance Points of dL and dU provides hurdle values of 1.728 and 1.809 for dL and dU, respectively. Since the calculated Durbin-Watson statistic = 1.67521 is lower than the dL value, we conclude that the autocorrelation coefficient is positive and reject the null hypothesis. There is autocorrelation in this time series: a stock market Composite Index behaves according to prior states of the market.

Lastly, one checks the model based on the ‘four-in-one charting’ facility available in Minitab. Were the residuals normally distributed, the Probability Plot of the Composite Index should show all the red (computed CI) points very close to the blue line and an overall shape resembling a normal distribution (Figure 2 below). But there are evidently cyclical forces at work and observations that stray from the blue line plotted. For instance, Minitab flags observation #28, that for October 10, 1990, that is 22.5% below what one would expect if the predictor variables chosen perfectly explained all instances of the Composite Index.

The residuals versus fitted values (Figure 3 below) show, as expected, randomly scatter, true except maybe for the case at row #285 (November 28, 1997) with a FIT2 value of 306.7 and a RESI2 result of 192.4. That the model is robust is shown by the finding that the histogram of residuals (Figure 5 overleaf) shows a normal distribution.

In turn, the observation order chart (Figure 4 on the prior page) is a critical diagnostic only if the order of observations in the dataset has some meaning. While this is technically true for time series data, the presumption is that the information was gathered from a stock market archive at the same point in time.

Conclusions

The choice of four predictor variables from the database – Stock Volume, Reported Trades, Dollar Value and Warrants Volume – to predict the Composite Index has yielded both strengths and vulnerabilities. On the plus side, the model-selected variables explain a great deal of the movement (or variance) over time of a stock market CI. On the other hand, there is autocorrelation and multicollinearity.

Recommendations

Any effort to improve the probability of capital appreciation by investing in a composite index fund or simply predicting with greater confidence how ‘the market will behave’ tomorrow or next week may start with this model. However, refinements are necessary, notably in respect of testing for lagged effects and reducing the set of predictor variables that are move in tandem: Stock Volume, Reported Trades, Dollar Value. It is also vital to reassess the role of Stock Warrants which this initial analysis demonstrated to have an inverse relationship.

Bibliography

Forbes Magazine/Investopedia LLC (2009) Warrant [Internet] Web.

Fortune, P. (1998) A primer on U.S. stock price indices. New England Economic Review, 1998, pp. 25-40.

Gujarati, D. (1999) Essentials of Econometrics. 2nd ed. Boston, Irwin/McGraw-Hill.

Middle Tennessee State University (n.d.) Stats @ MTSU [Internet]

Simon, Helen K., D.B.A. (2005) An examination of the weak form of the Efficient Market Hypothesis within the context of the NASDAQ Composite Index: A test of the forecasting abilities of artificial neural networks. Ph. D. dissertation, Nova Southeastern University.