### Modeling the Import and Export System of the United States: Using the Error Correction Model Representation

#### Abstract

This paper deals with the analysis of integration and cointegration of all seasonal frequencies for the export and import system of the United States in aggregated quarterly data that cover the period 1980-2003 (96 quarters). The used procedures are HEGY for the integration and EGHL for the cointegration. The two time series are integrated at order 1 for all frequencies: and . The commercial balance series is integrated at order 1 of the frequencies 0 and and consequentely it becomes stationary while filtering it by . The cointegration analysis shows that these two time series are not cointegrated of the frequencies 0 and whereas they are cointegrated of the frequency (and ¾). Two cointegrating relations have been considered. The first relation (titled ) has a constant deterministic part. The second relation (titled ) has a deterministic part constituted of constant and three seasonal indicatory variables. For each of these two relations, we estimated the Error Correction Model (ECM) representation and we did some forecastings for the period 2002-2003 (8 quarters). The quality of the forecastings has been measured using the MAPE (Mean Absolute Percentage Error) criterion. The Chow test reveals a little structural change (at level 5 %) in the value of the parameters of the ECM representation using the cointegration relation . But if we choose a level of 1% then we accept the null hypothesis that shows a non- structural change in the model.

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