Scandinavian Working Papers in Economics

SSE/EFI Working Paper Series in Economics and Finance,
Stockholm School of Economics

No 0418: On seasonal error correction when the processes include different numbers of unit roots

Johan Lyhagen () and Mårten Löf ()
Additional contact information
Johan Lyhagen: Dept. of Economic Statistics, Stockholm School of Economics, Postal: Stockholm School of Economics, P.O. Box 6501, S-113 83 Stockholm, Sweden
Mårten Löf: Dept. of Economic Statistics, Stockholm School of Economics, Postal: Stockholm School of Economics, P.O. Box 6501, S-113 83 Stockholm, Sweden

Abstract: We propose a seasonal cointegration model [SECM] for quarterly data which includes variables with different numbers of unit roots and thus needs to be transformed in different ways in order to yield stationarity. A Monte Carlo simulation is carried out to investigate the consequences of specifying a SECM with all variables in annual diffrerences in this situation. The SECM in annual differences is compared to the correctly specified model. Pre-testing for unit roots using two different approaches, and where the models are specified according to the unit root test results, is also considered. The forecast mean squared error criterion and certain parameter estimation results indicate that, in practice, a cointegration model where all variables are transformed with the annual difference filter is more robust than one obtained by pre-testing for a smaller number of unit roots. The second best choice, when the true model is not known and when the aim is to forecast, is an ordinary VAR model, also in annual differences.

Keywords: Seasonal cointegration; forecasting

JEL-codes: C32; C53

17 pages, First version: December 13, 2000. Revised: March 15, 2001. Earlier revisions: March 15, 2001.

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