Abstract

Cointegration is a long-run property of some non-stationary time series where a linear combination of those time series is stationary. This behaviour has been studied in finance because cointegration restrictions often improve forecasting. The vector error correction model (VECM) is a well-known econometric technique that characterises short-run variations of a set of cointegrated time series incorporating long-run relationships as an error correction term. VECM has been broadly used with low frequency time series. We aimed to adapt VECM to be used in finance with high frequency stream data. Cointegration relations change in time and therefore VECM parameters must be updated when new data is available. We studied how forecasting performance is affected when VECM parameters and the length of historical data used change in time. We observed that the number of cointegration relationships varies with the length of historical data used. Moreover, parameters that increased these relationships in time led to better forecasting performance. Our proposal, called an Adaptive VECM (AVECM) is to make a parameters grid search that maximises the number of cointegration relationships in the near past. To ensure the search can be executed fast enough, we used a distributed environment. The methodology was tested using four 10-s frequency time series of the Foreign Exchange market. We compared our proposal with ARIMA and the naive forecast of the random walk model. Numerical experiments showed that on average AVECM performed better than ARIMA and random walk. Additionally, AVECM significantly improved execution times with respect to its serial version.