The Effects of Detrending in Granger Causality Tests

Nonstationary time series are frequently detrended in empirical investigations by regressing the
series on time or a function of time. The effects of the detrending on the tests for causal
relationships in the sense of Granger are investigated using quarterly U.S. data. The causal
relationships between nominal or real GNP and MI, inferred from the Granger-Sims tests, are
shown to depend very much on, among other factors, whether or not series are detrended.
Detrending tends to remove or weaken causal relationships, and conversely, failure to detrend
tends to introduce or enhance causal relationships. The study suggests that we need a more
robust test or a better definition of causality.
KEY WORDS: Nonstationarity; ARlMA analysis; Granger-Sims tests.

1. INTRODUCTIONMany economic time series are nonstationary and appear to have a deterministic trend. In empirical investigations, nonstationary time series are frequently "detrended" by regressing the series on time or a function of time. The purpose of this article is to investigate the effects of detrending in the tests for causal relationships of time series in the sense of Granger (1969). A time series XI is said to cause another series Y, if the future values of Y, can be better predicted when the information contained in the series XI is included than when that information is excluded.