A comparison of forecasting performance between ECM and the difference ARX model¹

¹ The views expressed in this article are those of the author and not necessarily those of the Deutsche Bundesbank.

Abstract

Using Monte Carlo simulations, we compare the forecasting performance of the single equation error correction model (SEECM) with that of the (misspecified) difference autoregressive model with exogenous variables (ARX). The main result of the article is that the SEECM produces superior forecasts for short horizons, but not for long horizons, as shown analytically by Christoffersen and Diebold (1999).

¹ The views expressed in this article are those of the author and not necessarily those of the Deutsche Bundesbank.

Acknowledgements

Research support from the Alexander von Humboldt Foundation is gratefully acknowledged.

Notes

¹ The views expressed in this article are those of the author and not necessarily those of the Deutsche Bundesbank.

² Phillips and Hansen (1990) set σ = ±0.8, ± 0.4 and m = 0.8, 0.4, 0. The results of the various combinations of σ and m can be summarized in the two cases set out in (5).

³ The results from the higher orders of p and/or q are the same with respect to the main concern of the simulation.

⁴ In Engle and Yoo (1987), however, the relative efficiency ratio is greatest at the one-step forecasting horizon, whereas, in our result, it is almost 100 (100.04, precisely).