Many current seasonally adjusted level data are based on Census-X-11-type moving average filters applied to past and forecasted log-transformed observations, which is usually called the Census-X-11 ARIMA method. The forecasts are often generated from seasonal ARIMA models for the log-transformed...

This note gives a few practical guidelines for cointegration analysis. The focus is on testing the cointegration rank in a VAR model and on how an intercept and a trend should be incorporated in the model. Only two cases appear relevant for most economic data.

We propose methods to test for common deterministic seasonality, while allowing for possible seasonal unit roots. For this purpose, we consider panel methods, where we allow for individualand for common dynamics. To decide on the presence of seasonal unit roots, we introduce a decision-based...

We consider representation, estimation and inference on cointegration in a periodic vector autoregressive time series model (PVAR). We show that cointegration amounts to a restriction on a product of parameter matrices. We therefore use GMM to construct estimators of the long-run (cointegration)...