R² Measures for Time Series

Abstract

With time series data, the conventional regression R ² is a nebulous concept, as the explained variation consists in part of variation that can be attributed merely to past values of the dependent variable. Thus R ² is extremely sensitive to prefiltering operations such as first differencing. This article develops and illustrates an alternative R ² concept, which eliminates this ambiguity by measuring the explanatory power of a time series-regression model relative to that of the past values of the dependent variable alone. The variance to be explained by the model is thus taken to be the innovation variance of the dependent variable.

Key Words:

• Relationships, Measurement of
• Coherence
• Regression relations
• Time series regression
• Coefficient of determination