When a man assumes the responsibility of running a business, he automatically takes the responsibility for attempting to forecast the future and to a very large extent his success or failure would depend upon the ability to forecast successfully the future course of events. Forecasting aims at reducing the areas of uncertainty that surround management decision making with respect to costs, profit, sales, Production, pricing, capital investment and so forth. If the future were known with certainty, forecasting would be unnecessary. Decisions could be made and plans formulated on a once-and-for-all basis, without the need for subsequent revision. But uncertainty does exist, future outcomes are rarely assured and therefore, organized system of forecasting is necessary rather than the establishment of predictions that are based on hunches, intuition or guesses. When estimates of future conditions are made on a systematic basis, the process is referred to as ‘forecasting’ and the figures or the statement obtained is known as forecast
The object of business forecasting, is not to determine a curve or series of figures that will tell exactly what will happen, say, a year in advance, but it is to make analysis based on definite statistical data, which will enable and execute to take advantage of future conditions to a greater extent than he could do without them. In many respects, the future tends to move like the past. This is a good thing, since without some element of continuity between past, present and future; there would be little possibility of success prediction. While forecasting, one should note that it is impossible to forecast the future precise there always must be some range of error allowed for in the forecast.
The business forecasting consists of following steps: Observation and analysis of the past behaviour is one of the most vital parts of forecasting Determine which phases of business activity must be measured Analysing the data Selecting and compiling data to be used as measuring devices
The important methods of forecasting are as follows: Business Barometers Extrapolation Regression analysis Econometric Models Forecasting by the use of Time series analysis Opinion polling Causal Models Exponential Smoothing Survey Method
The selection of an appropriate method depends on many factors-the context of the forecast, the relevance and availability of historical data, the degree of accuracy desired, the time period for which forecasts are required, the cost benefit (or value) of the forecast of the company and the time available for making the analysis. These factors must be weighed constantly and on a variety of levels. In general, for example, the forecaster should choose a technique that makes the best use of available data. If we can readily apply one technique of acceptable accuracy, we should not try to ‘gold plate’ by using a more advanced technique that offers potentially greater accuracy but requires non- existent information or information that is costly to obtain. Furthermore, where a company wishes to forecast with reference to a particular product, it must consider the stage of the product’s life cycle for which it is making the forecast.
Sequence or Time-lag theory Action and Reaction Theory Economic Rhythm Theory Specific Historical Theory Cross-section analysis
Forecasting business conditions is a complex task which cannot be accomplished with exactness. The economic, social and political forces which shape the future are many and varied; their relative importance changes almost constantly. It is obvious, therefore, that statistical methods cannot claim to be able to make the uncertain future certain- It does not follow from this disclaimer that statistical methods have nothing to contribute to business forecasting. Lack of a forecast implies a dangerous type of forecast, the mere warning of a possibility of a change is better than no wanting at all as is wisely said “Forewarned is forearmed”. Also is should be remembered that forecasts are not made just for the sake of forecasting ,that is, they are not ends in themselves. Forecasts are made in order to assist management determine a strategy and alternative strategies. lt may be pointed out that forecasting is much more than projecting a series mechanically. Though future is some sort of extension of the past. But it can hardly be expected to be an exact replica. Forces responsible for economic change are numerous and complex. They are often difficult to discover and to measure. They may appear in all kinds of combinations and may be constantly changing. The fact that past can never be a perfect guide to the future warns us that forecasting should not be thought of as a routine application of some techniques or theoretical ideas to a list of unchanging variables. Successful forecasting requires expert blending of economic theory with significant statistical expertise and thorough familiarity with the relevant statistical data. Both qualitative and quantitative information must be utilized. As a final word of caution, it may be emphasized that no matter what methods of forecasting are used, it is essential that the forecasts be checked by the judgment, of individuals who are familiar with the business. While it is true that the use of statistical data is an attempt to substitute facts for subjective judgment it does not mean that knowledge gained through experience in a given situation should be ignored in favor of quantitative data. It is particularly important to take into consideration any specific plans of the business that might affect the pattern of sales in relation to indicators used for forecasting. More successful forecasting will result by combining with statistical forecasting the judgment and knowledge of current business trends. `Also it is important to emphasize that any forecast should be reviewed frequently and revised in the light of the most recent information. Forecasting is not a one-shot operation. To be effective, it requires continuous attention. Unanticipated developments will often change our picture of the future, or at least clarity it, In terms of any original decisions and actions that have been taken, this rule implies continuous modification wherever necessary. The techniques of flexible budgets has been developed to permit the revision of-the budget estimates and everyone dealing with forecasts should be alerted to the need for constantly checking to see if anything, has happened to change the outlook. Keeping accurately informed about the current level of business is probably the simplest insurance that can be secured against making wrong decisions regarding the fixture. Despite all advances that have been made in the techniques of forecasting, forecasting remains more an art than a science. The value of a forecast lies not merely in its accuracy, but the fact that making it requires a balanced consideration of factors influencing future developments, right or wrong. Further, forecasting should not be regarded merely as a means of peering into the fixture and then accepting what one sees: it needs to be used actively as a way of guiding the firm along the path its management feels is most desirable. Business forecasting will not only help in the short-tem control of operations, its greatest contribution probably will come when it is able to improve short and long-term corporate strategies.
Corporations typically need forecasts that cover different time spans in order to achieve operational tactical and strategic intents.Firms typically use monthly data from the last one or two years to achieve operational or short-term forecasting.Tactical forecasting is generally based on quarterly data from the last five to six years or comparable annual data.strategic forecasting generally requires additional periods in order to make projections for 25 or more years into the future.Tactical and strategic forecasting is made more complex when the issue of seasonality is added to the analysis One goal of a forecasting model is to account for the largest amount of systemic variation in the behavior of time series data set as possible.Moving average,exponential smoothing, and linear regression models all attempt to account for systemic variations.However, each of these models may fail due to additional systemic variation that is not accounted for.In many business time series data sets a major source of systemic variation comes from seasonal effects>seasonal variation is characterized by increases or decreases in the time series data at regular time intervals, namely calendar or climatic changes.for example, sales demand for beer in the United States has increased over time but tends to vary during the year and to be higher in the spring and Summer months than in the Fall and Winter months(https://www.foodandbeveragereports.com).Therefore time is not only variable that has an impact on beer sales;multiple factors play a role Multile linear regression models are commonly used technique in forecasting when multiple independent variables impact a dependent variable.Beer sales could be considered the dependent variable, while time and seasonal factor could be consiserd indepdent variables, and is represented in the following general model for multiple linear regressions Where is the time and through are seasonal indicators.The X’s denote the independent variables while the Y donates the dependent variable.For Example the term represents the first independent variable for the time period t(e.g. , etc.).The term denotes the random variation in the time series not accounted for by the model.Since the value are assumed to vary randomly around the regression function the average or expected value of =0 Therefore, if an ordinary least square estimator is employed the best estimate of for any time period t is: Eq(2) represents the line passing through the time series that minimizes the sum of squared differences between actual values() and the estimated values().In the case, when n=1 the equation represents simple regression However if data set contains seasonal variation a standard multiple linear regression model generally does not provide very good results.With seasonal effects, the data tend to deviate from the trend lines in noticeable patterns.Forecasts for future time periods would be much more accurate if the regression model reflected these drops and ascents in the data.saeasonal effects can be modeled using regression by including indicator variables, which are created to indicate the time period to which each observation belongs. Many publicly held companies are required to submit quterly(data occurring in cycles of three months= a common business cycles) reports regarding the status of their business.It is also very common for quarterly forecasts to be used to develop future quarterly projections.Therfore , if quarterly data were being analysed, the indicator variables for quarterly regression model could be stated as follows Table 1 summarizes the coding structure that we have defined in , and in Eqs.3 through 6.Overall, this coding structure can apply to any time frame the forecaster chooses
For brevity purposes, only the quarterly models is illustrated here.The coding structures for the models are contained in Tables 1,2 and 3
Fig. l displays three views of the partial data set for United States Import Beer sales in millions of barrels (Brls) from January l999 to December 2007 in an Excel spreadsheet. The views are displayed to illustrate the differing setups or data structure that accompanies each seasonal regression model. The data structure or setup in Excel is particularly important when using Excel’s regression procedure. In other words,how the data is input and in which order it is featured Forecasting is an integeral business activity that is covered to varying degrees in most business scholl curricula.One of the features often uncoverd even in practitioners in the effect of granulizing the data.That is, data occurs annually,semi-annually,quarterly,bi-monthly, and even monthly.While most modelers simply assume that more data is better and Will always chose the most granular data.Monthly data is available for sales for the period 1999-2007.In forecasting data over time, one of the most important perspectives to consider is the level of detail required for the forecast. Figure 1 In this data, the first forecast estimate that should be generated is not monthly but is instead the predictable annual growth in sales as shown in figure 2 Figure 2 Depending on the management requirements, this forecast using simple linear regression may be sufficient.But, in many cases, such as managing inventory that does not have annual capacity, it is necessary to generate a forecast over similar interval.Such models are constructed below:semi annually,quarterly , and monthly Figure 3 Generally one perceives that finer focused data may produce better estimates.But as shown in figure 3, a linear forecst is constructed based upon the summary semi-annual sales actually reduces the overall explanatory power of the model because it introduces more variability.That is, not only is there variability from year-to-year, with more finer data there is also now variability within each year It should be noted that the values of the model are exactly 1/2 of the values of the annual model which would be expected. The two extensions considered next are the addition of an indicator variable for the second half of the year and an alternative definition of the annual increase as pro-rated across the semi-annual periods. We find that in either case, does that finer focus improves the estimated models value. However, the models do allow insight into the monthly characteristics of import beer sales A semi-annual indicator variable is added which has the value of 0 for the first six-month period of any year, and has the value of 1 for the second six-month period of any year. The result of this regression are shown in figure 4 Figure 4 We see that multiple regression with two independent variables Year and Semi-Annual period, does not produce a superior model with regard to .The t-statistics of the model show that the YrIndicator variable is highly statistically significant with a value of 0.672 as wellas the intercept with a value of -1334.61, but that the semi-Annual period is not statistically significant for any practical value of alpha since its t-statistics is only 0.04.Therefore , it is clear that it is not always the case that more and finer granularity to the data produces a superior estimate. One of the most common examples of granularity in time series modeling is using a time trend variables 1,2,3. In the present case, the year variable that was modeled had values 1,1,2,2,3,3 (where 1=first year of data,1999; etc.).That is, the year variable captured the annual increase which was not pro-rated across semi-annual periods.If, instead one used not the annual increase but the semi-annual increase, along with the semiannual indicator variable, then similar results obtain as shown in figure 5.
Of course, the R-squared of the model and the coefficient of the semi-years variable are products of the annual model.However, what has changed is the statistical sign, scale, and statistical significane of the indicator variable.previously it was positive;in the present model, it is negative.Previously it is of the order 10,000 barrels;presently it is of the order 300,000 barrels.Previously its t-statistics was a scant 0.04;presently its t0statistics is -1.26.Although the indic.ator variable is not statistically significant for any alpha less than 22%, the drastic change in the variable is important for us to consider.
Quarterly.The categorical variables for quarters are coded and the resulting multiple regression retains an of 92% and its value is All of these coefficients are highly statistically significant, with Q4 significant to the largest alpha value of 1.8%.The model suggests that the first quarter is the expected lowest sales and the highest sales are expected in the early summer (Q2), followed by slightly lower sales in the late summer (Q3), and continuing this decline to Q4 , still about 1/3 of a million barrels above first quarter sales. This model and the resulting multiple linear regression estimates are shown in figure 6.
We have seen that the annual model provided a very good overall estimate of annual increases in sales, but the semi-annual extension did not provide additional information.However, when further granulizing the data to quarterly the estimate was improved further and did provide information that the semi-annual forecast could not.This process is continued for monthly estimates below
Monthly.The categorical variables for months are coded and the resulting multiple regression containing the previously determined annual increase and quarterly changes is examined.Usually when modeling nested categorical variables , that one variable must always be “left out”.In our case, since variable Q2 contains the months April,may, and June, it is necessary in constructing the monthly variables to leave out one of these months.In the present model, the first variable of each quarter is left out and there are no monthly variables for January April,July, and October.The results from a monthly multiple regression are shown in table 4.
All of the remaining variables are statistically significant except for August and Novermber(shaded in table 4).A final estimation is considered after removing these two variables and the results are shown in table 5.each of the coefficients is statistically significant at leat at the 5% level.The R-squared of the model is 88.1% and standard error s 146,000 barrels Table 5 The monthly model is shown in figure 7.
The coefficient values found in the Table 5 provide additional insight.These coefficients are used to construct the seasonal regression equation itself.Not all of the model parameter coefficients are positive for the monthly seasonal models.However, the coefficients are relative to each other within each model.For the quarterly model, it is seen that the Q4(Oct, Nov, Dec) coefficient is lower than the coefficients for Q2 and Q3.This ia also true for the sep and dec coefficients as they are actually negative compared to the other monthly coefficients each of these parameters corresponds to the time frame of the early fall into Winter seasons.In turn, it could be tentatively concluded that some type of winter effect comes from what the coefficients denote within the regression model itself.Within regression models, positive coefficients move in unison with changes in the model parameter. In our case, the coefficient of the Q4 parameter is lower and that the Sep and Dec coefficients are negative when compared to the other coefficients in the monthly model therefore they provide a damping effect on their predictors.The lower and/or lower coefficients associated with the Q4, Sep, and Dec parameters are mostly likely attributable to the holiday lag and the temperature drop that occurs every year around Nov, Dec, and January, and Feb in the United States.It is well known that beer sales in United States lag during the colder months of each year and the holiday season due to consumers drinking other beverages, both alcoholic,non-alcholic , and consumers drinking other beverages, both alcoholic,non-alcholic and non-chilled Finally, if the annual time trend is pro-rated across the time periods(i.e.1999=1,2000=2, etc.) then the R-squared drops slightly to 88%.Whereas it is natural and very common for us to pro-rate the annual increase per month by using an indexing time variable, it is not required.
One advantage to employing Excel’s regression procedure is the case in interpreting the results of the regression analysis and understanding its “statistical quality”. To interpret the regression analysis we should begin by checking the values for three statistical measures: the R- Square () statistic, the F-statistic, and the tA·statistic. The value of provides an assessment of the forecast model`s accuracy. Specially, it can be interpreted as the proportion of the variance in Y attributable to the variance in the X variables. Generally, values above 0.7 provide a minimum threshold of accuracy for business models, while values above 0.8 are considered very good. Table 6 presents the values for each of the seasonal regression models, whereas Table 7 presents the F-statistics of each model. According to the analysis any of the proposed seasonal regression models are statistically significant and could be used to effectively develop forecasts for U.S. import beer sales. However, a good manager needs to know which model produces the “best” results. The next section illustrates how to construct the seasonal regression equation for the monthly model. Defines and describes error for each model, and discusses model efficacy via error coupled with the regression statistics. Table 6 Table 7
From a mathematical perspective, the coefficient values are easily inserted into the original regression model to yield the seasonal regression forecasting equation.The monthly seasonal regression equation can be written as For seasonal regression equation, a forecast for January 2008 will be created.Since the forecasting time period is January 2008, the YrIndicator=2008.Since January falls in the first quarter and is the first month of the year there are no quarterly or monthly indicators in the model and in turn Q2=0, Q3=0, Q4=0, Feb=0,Mar=0, May=0,Jun=0,Sep=0, and Dec=0 Therefore, the seasonal regression model produces the following result The forecast U.S import beer sales for January 2008 are 2.006 million Brls.Calculating the error associated with a forecasting models is cornerstone to determining a model’s performance.Coupling the error measurement with the regression statistics allows a forecastor to comment on model’s overall efficacy.A model that performs well on all statistical measures and carries relatively low error can be deemed adequate.Error, also referred to as deviation, is defined as the actual less predicted value.Excel can generate error terms for a regression model when prompted Figure 8 We can instruct Excel to automatically calculate the error terms or the residuals of a regression model by checking the residual box in the Regression Dialogue Box.When the regression model is computed via the Regression dialogue Box, the residual output is generated and returned below the regression output.
Figure 8 displays a partial part of the residual output for the monthly seasonal regression model within Excel. A standard measure of error in forecasting is mean absolute percentage error or MAPE and is calculated as follows: MAPE Table 8 Using the residual terminology from the Excel’s regression tool, the formula would resemble the following: MAD= To obtain MAPE for residual contained in figure 8, we first take the absolute value of each residual in the residual column, divide that absolute residual by the associated actual , and then take an average of those absolute percentage errors Forecasters generally compute error for multiple forecasting models and then compare across each model where the model with the lowest error is considered superior. The MAPE for each of the seasonal models is presented in Table 8. From Table 8, the yearly regression model has the lowest MAPE of the three models. However. it does not provide detail that a manager may need to make decisions in a shorter time frame. Therefore a manager most likely will use the yearly model for long range planning purposes and may use the monthly model for shorter range planning purposes. It is readily apparent from figure 7 that the monthly seasonal regression model fits the actual data very well by accounting for the seasonal trends in import beer sales over time.The figures also visually reinforces the calculated value R-squared(0.88) presented earlier.Based on the regression statistics, MAPE and the predicted versus Actual graph , it can be determined that the monthly seasonal model is doing an overall good job of forecasting U.S import beer Sales.
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