ROBUST RESIDUAL CROSS-CORRELATION TESTS FOR LAGGED RELATIONS IN TIME-SERIES
Testing for lagged relations between two time series is an important problem with many applications. Some examples include transfer function modelling and the well known Granger causality problem in econometrics. The usual tests based on residual cross correlations are not robust to even one or two outliers within the series. In this paper a robustified residual cross correlation is defined. The asymptotic distribution of the residual cross correlations based on this definition is obtained under very general conditions. From this result several robustified residual cross correlation tests for lagged relations are derived. These tests appear to be more resistant to outliers in terms of both size and power in simulation experiments.
residual cross correlations asymptotic distribution autoregressive moving average models causality tests residual autocovariance estimates