Finance 30210: Managerial Economics

1. Finance 30210: Managerial Economics Demand Forecasting

2. Suppose that you work for a local power company. You have been asked to forecast energy demand for the upcoming year. You have data over the previous 4 years:

3. First, let’s plot the data…what do you see? This data seems to have a linear trend

4. A linear trend takes the following form: Estimated value for time zero Estimated quarterly growth (in kilowatt hours) Forecasted value at time t(note: time periods are quarters and time zero is 2003:1) Time period: t = 0 is 2003:1 and periods are quarters

5. Lets forecast electricity usage at the mean time period (t = 8)

6. Here’s a plot of our regression line with our error bands…again, note that the forecast error will be lowest at the mean time period T = 8

7. We can use this linear trend model to predict as far out as we want, but note that the error involved gets worse! Sample

8. One method of evaluating a forecast is to calculate the root mean squared error Sum of squared forecast errors Number of Observations

9. Lets take another look at the data…it seems that there is a regular pattern… Q2 Q2 Q2 Q2 We are systematically under predicting usage in the second quarter

10. Average Ratios • Q1 = .87 • Q2 = 1.16 • Q3 = .91 • Q4 = 1.04 We can adjust for this seasonal component…

11. Now, we have a pretty good fit!!

12. Recall our prediction for period 76 ( Year 2022 Q4)

13. Recall, our trend line took the form… This parameter is measuring quarterly change in electricity demand in millions of kilowatt hours. Often times, its more realistic to assume that demand grows by a constant percentage rather that a constant quantity. For example, if we knew that electricity demand grew by g% per quarter, then our forecasting equation would take the form

14. If we wish to estimate this equation, we have a little work to do… Note: this growth rate is in decimal form If we convert our data to natural logs, we get the following linear relationship that can be estimated

15. Lets forecast electricity usage at the mean time period (t = 8) BE CAREFUL….THESE NUMBERS ARE LOGS !!!

16. The natural log of forecasted demand is 2.698. Therefore, to get the actual demand forecast, use the exponential function Likewise, with the error bands…a 95% confidence interval is +/- 2 SD

17. Again, here is a plot of our forecasts with the error bands T = 8

18. When plotted in logs, our period 76 ( year 2022 Q4) looks similar to the linear trend

19. Again, we need to convert back to levels for the forecast to be relevant!! Errors is growth rates compound quickly!!

20. There doesn’t seem to be any discernable trend here… Consider a new forecasting problem. You are asked to forecast a company’s market share for the 13th quarter.

21. Smoothing techniques are often used when data exhibits no trend or seasonal/cyclical component. They are used to filter out short term noise in the data. A moving average of length N is equal to the average value over the previous N periods

22. The longer the moving average, the smoother the forecasts are…

23. Calculating forecasts is straightforward… MA(3) MA(5) So, how do we choose N??

24. Total = 78.3534 Total = 62.48

25. Exponential smoothing involves a forecast equation that takes the following form Forecast for time t Forecast for time t+1 Actual value at time t Smoothing parameter Note: when w = 1, your forecast is equal to the previous value. When w = 0, your forecast is a constant.

26. For exponential smoothing, we need to choose a value for the weighting formula as well as an initial forecast Usually, the initial forecast is chosen to equal the sample average

27. As was mentioned earlier, the smaller w will produce a smoother forecast

28. Calculating forecasts is straightforward… W=3 W=5 So, how do we choose W??

29. Total = 87.19 Total = 101.5