Chapter 14 - Error Correction, Spurious Regressions, and Cointegration

Abstract

The ARDL model may be reexpressed in “error correction” form, which separates out short-run effects from the discrepancy from long-run equilibrium—the error correction. This form is especially interesting when the variables entering the ARDL are allowed to be nonstationary. Regression of nonstationary time series is shown to be fraught with difficulties, and generally leads to the “spurious regression” problem. However, it is possible for nonstationary time series to “cointegrate,” where a linear combination of, say, I(1) processes is I(0) rather than I(1), as might be expected. Cointegration is shown to be intimately related to error correction and, if it exists, makes empirical modeling much simpler and interpretable. Tests for cointegration are therefore essential, as are methods for estimating the cointegration regressions that exist in its presence.