1. FORECASTING CH 1 PART 2 The Five Steps to Forecasting

2. Step 1: Problem definition Defining the problem carefully requires an understanding of: 1. the way the forecasts will be used, 2. who requires the forecasts, 3. and how the forecasting function fits within the organization requiring the forecasts. A forecaster needs to spend time talking to everyone who will be involved in collecting data, maintaining databases, and using the forecasts for future planning.

3. Step 1: Problem definition Consider the following statement by the manager of a paper products manufacturing company: We have a computerized inventory control system and we can get daily, weekly, and monthly reports at the drop of a hat. But our inventory situation is bad. We have too much inventory at the factories, in the warehouses, and in the pipeline. Can we get better forecasts of future production and demand so we can reduce our inventory and save storage costs?

4. Step 1: Problem definition A forecaster has a great deal of work to do to properly define the forecasting problem, before any answers can be provided. For example, we need to know exactly what products are stored, who uses them, how long it takes to produce each item, what level of unsatisfied demand the company is prepared to bear, and so on.

5. Step 2: Gathering information There are always at least two kinds of information required: (a) statistical data, and (b) the accumulated expertise of the people who collect the data and use the forecasts. Often, it will be difficult to obtain enough historical data to be able to fit a good statistical model. However, occasionally, very old data will be less useful due to changes in the system being forecast.

6. Step 2: Gathering information In the case of the paper products inventory, the data collected may consist of monthly demand and production for each item of interest over the previous three years. Other relevant data such as the timing and length of any significant production downtime due to equipment failure or industrial disputes may also need to be collected.

7. Step 3: Preliminary (exploratory) analysis Always start by graphing the data. 1. Are there consistent patterns? 2. Is there a significant trend? 3. Is seasonality important? 4. Is there evidence of the presence of business cycles? 5. Are there any outliers in the data that need to be explained by those with expert knowledge? 6. How strong are the relationships among the variables available for analysis?

8. Step 3: Preliminary (exploratory) analysis Then we compute some simple descriptive statistics (e.g., mean, standard deviation, minimum, maximum, percentiles) associated with each set of data. Where more than one series of historical data is available and relevant, we can produce scatter plots of each pair of series and related descriptive statistics (e.g., correlations). Another useful tool is decomposition analysis to check the relative strengths of trend, seasonality, cycles, and to identify unusual data points. Such preliminary analyses will help suggest a class of quantitative models that might be useful in the forecasting assignment.

9. Step 4: Choosing and fitting models This step involves choosing and fitting several quantitative forecasting models. The preliminary analysis (step 3, above) serves to limit the search for an appropriate forecasting model and we would pursue one or two leading contenders for subsequent analysis.

10. Step 4: Choosing and fitting models Each model is itself an artificial construct. It is based on a set of assumptions (explicit and implicit) and usually involves one or more parameters which must be “fitted” using the known historical data Note that when forecasting the long-term, a less formal approach is often better. This can involve identifying and extrapolating mega trends going back in time, using analogies, and constructing scenarios to consider future possibilities.

11. Step 5: Using and evaluating a forecasting model. Once a model has been selected judiciously and its parameters estimated appropriately, the model is to be used to make forecasts, and the users of the forecasts will be evaluating the pros and cons of the model as time progresses. A forecasting assignment is not complete when the model has been fitted to the known data. The performance of the model can only be properly evaluated after the data for the forecast period have become available.

12. Exercise You are asked to provide sales forecasts of several products for a large biscuit manufacturing company. Define the five steps of forecasting in the context of this project.

13. Exercise: Step 1: Problem definition This would involve understanding the nature of the individual product lines to be forecast. For example, are they high-demand products or specialty biscuits produced for individual clients?

14. Exercise: Step 1: Problem definition It is also important to learn who requires the forecasts and how they will be used. Are the forecasts to be used in scheduling production, or in inventory management, or for budgetary planning? Will the forecasts be studied by senior management, or by the production manager, or someone else? Have there been stock shortages so that demand has gone unsatisfied in the recent past? If so, would it be better to try to forecast demand rather than sales so that we can try to prevent this happening again in the future?

15. Exercise: Step 1: Problem definition The forecaster will also need to learn whether the company requires one-off forecasts or whether the company is planning on introducing a new forecasting system. If the latter, are they intending it to be managed by their own employees and, if so, what software facilities do they have available and what forecasting expertise do they have in-house?

16. Exercise: Step 2: Gathering information It will be necessary to collect historical data on each of the product lines we wish to forecast. The company may be interested in forecasting each of the product lines for individual selling points. If so, it is important to check that there are sufficient data to allow reasonable forecasts to be obtained. For each variable the company wishes to forecast, at least a few years of data will be needed.

17. Exercise: Step 2: Gathering information There may be other variables which impact the biscuit sales, such as economic fluctuations, advertising campaigns, introduction of new product lines by a competitor, advertising campaigns of competitors, production difficulties. This information is best obtained by key personnel within the company. It will be necessary to conduct a range of discussions with relevant people to try to build an understanding of the market forces. If there are any relevant explanatory variables, these will need to be collected.

18. Exercise: Step 3: Preliminary (exploratory) analysis Each series of interest should be graphed and its features studied. Try to identify consistent patterns such as trend and seasonality. Check for outliers. Can they be explained? Do any of the explanatory variables appear to be strongly related to biscuit sales?

19. Exercise: Step 4: Choosing and fitting models A range of models will be fitted. These models will be chosen on the basis of the analysis in Step 3.

20. Exercise: Step 5: Using and evaluating a forecasting model Forecasts of each product line will be made using the best forecasting model identified in Step 4. These forecasts will be compared with expert in-house opinion and monitored over the period for which forecasts have been made. There will be work to be done in explaining how the forecasting models work to company personnel. There may even be substantial resistance to the introduction of a mathematical approach to forecasting. Some people may feel threatened. A period of education will probably be necessary. A review of the forecasting models should be planned.

21. The statistical forecasting perspective The thing we are trying to forecast is unknown (or we wouldn’t be forecasting it), and so we can think of it as a random variable. In most forecasting situations, the variation associated with the thing we are forecasting will shrink as the event approaches. In other words, the further ahead we forecast, the more uncertain we are.

22. The statistical forecasting perspective When we obtain a forecast, we are estimating the middle of the range of possible values the random variable could take. Very often, a forecast is accompanied by a prediction interval giving a range of values the random variable could take with relatively high probability. For example, a 95% prediction interval contains a range of values which should include the actual future value with probability 95%.

23. Statistical perspective (cont.) A forecast is always based on some observations. Suppose we denote all the information we have observed as ℐ and we want to forecast y i. We then write y i | ℐ meaning “the random variable y i given what we know in ℐ ”. The set of values that this random variable could take, along with their relative probabilities, is known as the “probability distribution” of y i | ℐ. In forecasting, we call this the “forecast distribution”.

24. Statistical perspective (cont.) When we talk about the “forecast”, we usually mean the average value of the forecast distribution, and we put a “hat” over y to show this. Thus, we write the forecast of y i as ŷ i, meaning the average of the possible values that y i could take given everything we know. Occasionally, we will use ŷ i to refer to the median (or middle value) of the forecast distribution instead.

25. Statistical Perspective (cont.)