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LOS b: Discuss the factors that determine whether a linear or a log-linear trend should be used with a particular time series, and evaluate the limitations of trend models.

Dianne Hart, CFA, is considering the purchase of an equity position in Book World, Inc, a leading seller of books in the United States. Hart has obtained monthly sales data for the past seven years, and has plotted the data points on a graph. Which of the following statements regarding Hart’s analysis of the data time series of Book World’s sales is most accurate? Hart should utilize a:

A)	mean-reverting model to analyze the data because the time series pattern is covariance stationary.

B)	log-linear model to analyze the data because it is likely to exhibit a compound growth trend.

C)	linear model to analyze the data because the mean appears to be constant.

A log-linear model is more appropriate when analyzing data that is growing at a compound rate. Sales are a classic example of a type of data series that normally exhibits compound growth.

Trend models can be useful tools in the evaluation of a time series of data. However, there are limitations to their usage. Trend models are not appropriate when which of the following violations of the linear regression assumptions is present?

One of the primary assumptions of linear regression is that the residual terms are not correlated with each other. If serial correlation, also called autocorrelation, is present, then trend models are not an appropriate analysis tool.

Rhonda Wilson, CFA, is analyzing sales data for the TUV Corp, a current equity holding in her portfolio. She observes that sales for TUV Corp. have grown at a steadily increasing rate over the past ten years due to the successful introduction of some new products. Wilson anticipates that TUV will continue this pattern of success. Which of the following models is most appropriate in her analysis of sales for TUV Corp.?

A)	A linear tend model, because the data series is equally distributed above and below the line and the mean is constant.

B)	A log-linear trend model, because the data series exhibits a predictable, exponential growth trend.

C)	A log-linear trend model, because the data series can be graphed using a straight, upward-sloping line.

The log-linear trend model is the preferred method for a data series that exhibits a trend or for which the residuals are predictable. In this example, sales grew at an exponential, or increasing rate, rather than a steady rate.