Consistent covariance matrix estimation in probit models with autocorrelated errors

Some recent time-series applications use probit models to measure the forecasting power of a set of variables. Correct inferences about the significance of the variables requires a consistent estimator of the covariance matrix of the estimated model coefficients. A potential source of inconsistency in maximum likelihood standard errors is serial correlation in the underlying disturbances, which may arise, for example, from overlapping forecasts. We discuss several practical methods for constructing probit autocorrelation-consistent standard errors, drawing on the generalized method of moments techniques of Hansen (1982), Newey-West (1987) and others, and we provide simulation evidence that these methods can work well.