Page 45 - FINAL CFA II SLIDES JUNE 2019 DAY 3

LOS 9.b: Describe factors that determine whether a linear or
a log-linear trend should be used with a particular time READING 9: TIME SERIES ANALYSIS
series and evaluate limitations of trend models.

FACTORS THAT DETERMINE WHICH MODEL IS BEST

A linear trend model : If the data points appear to be
equally distributed above and below the regression line
(e.g. Inflation rate data);

A log-linear trend model : If the data plots with a non-linear
(curved) (when the residuals from a linear trend model are
serially correlated). Financial data (e.g., stock indices and
stock prices) and company sales data are often best
modeled with log-linear models.

The bottom line:
Use linear model when the variable increases over time by a constant amount; and
Log-linear model when a variable grows at a constant rate.

Limitations of trend models

• Recall – autocorrelation? In this case, when the residuals persistently + or - for periods of time, we have serial correlation (a
significant limitation, hence model is inappropriate for the time series and thus should not be used to predict future values).

• Even with constant growth rate, a log-linear model is not appropriate if serial correlation is present (go autoregressive model).

• Recall Durbin Watson statistic (DW) is used to detect autocorrelation. For a time series model without serial correlation
DW = 2 . A DW significantly different from 2.0 suggests that the residual terms are correlated.