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

CHAPTER 15

Case Study 15—Determining Lost Sales with Stationary Time Series Data

As promised in the previous chapter, we now return to the Urban Food Store time series data and run through various forecasting techniques that are appropriate for random data that are stationary. This chapter uses time series forecasting methods that analyze the past behavior of the time series variable so that we can predict its future behavior.

As discussed in the introduction, in commercial damages cases this variable would always be sales, rather than lost profits. If we can uncover some sort of systematic behavior in past sales, we can model this behavior to assist us in forecasting future sales. Techniques that analyze past behavior of a time series variable to predict the future are sometimes called extrapolation models. All these models search for patterns in the historical series and then extrapolate these patterns into the future. The time-series regression models that we have previously introduced demonstrate extrapolation techniques.

Prediction Errors and Their Measurement

After we build a model, we test it to see if it fits the historical data well; that is, how well does it “track” the known values of the time series? Specifically, we calculate the one-period-ahead predictions from the model and compare these to the known values for each observation in the historical time period. We attempt to find a model that produces small prediction errors, that is, small differences between the ...