This paper uses a multivariate autoregressive conditional heteroscedasticity model to investigate the effect of British grain prices on their Irish equivalents. We find that in the long run the law of one price holds and in the short run the model captures the salient features of Irish grain prices. The model is used to compute rolling forecasts of the conditional means, variances and covariance of Irish grain prices one year ahead. We find that this model produces superior forecasts compared with those based on a commonly used approach of an autoregressive conditional mean model where the second moments are estimated using a fixed‐weight moving average.