A Quantitative Approach to Commercial Damages: Applying Statistics to the Measurement of Lost Profits, + Website

CHAPTER 16

Case Study 16—Determining Lost Sales Using Nonregression Trend Models

In the previous two chapters, we presented techniques for analyzing and then forecasting stationary time series data in which there was no significant trend in the data over time. However, simply because of inflation, it is usual for time series data, especially sales, to exhibit some type of upward trend over time. Trend is the long-term sweep or general direction of movement in a time series. It reflects the net influence of long-term factors that affect the time series in a fairly consistent and gradual way over time. In other words, the trend reflects changes in the data that occur with the passage of time.

When Averaging Techniques Are Not Appropriate

Because the moving average, weighted moving average, and exponential smoothing techniques use some average of the previous values to predict future values, they consistently underestimate the actual values if there is an upward trend in the data. For example, consider the time series data given by 2, 4, 6, 8, 10, 12, 14, 16, and 18. These data show a clear upward trend leading us to expect that the next value in the time series should be 20. But the forecasting techniques discussed in the previous two chapters would predict that the next value in the series would be less than or equal to 18 because no average or weighted average of the given data could exceed 18. In this chapter we consider several techniques that are appropriate for nonstationary ...