Lagged Regression with Unknown Lags

Summary The problem considered is that of determining the parameters in a lagged regression of one stationary time series on another when the lag is unknown and is not an integral multiple of the time interval between observations. The residual in the regression is also taken to be a stationary time series. The method of estimation is based on the maximization with respect to the lag of a form of autocorrelation between the two series. However, the autocorrelation is defined via the Fourier transformed data which enables non-integral lags to be considered and an optimal weighting of frequencies to be introduced. The estimation procedure's validity depends upon the satisfaction of an identification (aliasing) condition. Limit theorems are proved for the estimates and the method is extended to multivariate regressions. The method is applied to some economic and to some oceanographic data.