On the seasonality of vector autoregression residuals

This letter suggests that the correlation matrix of innovations from different equations should be based on residual vectors without seasonal patterns. Such residuals, however, do not always result from regressions with seasonally-adjusted data. In particular, seasonality can result if variables seasonally adjusted by least squares are lagged as independent variables instead of including a full set of seasonal dummies in the regression or (equivalently) seasonally adjusting each lagged variable individually. An example is presented using U.S. macroeconomic data in which ‘seasonally adjusting and then lagging’ leads to seriously misleading estimates.