Robust estimation of crosscovariance function in the presence of outliers for large sample series

Abstract

This paper considers the effect of outliers on cross covariance as model identification and specification tool. We established that outliers in series significantly affect the mean of cross-covariance function (CCF). For large samples, the asymptotic convergence of cross-covariance function expectations are infested if the original series is classified as 2-dimensional random fields in the presence of outliers. Robust estimates of cross-covariance function that accommodate outliers are proposed. Analytically, the proposed Jacknife (JK) estimate reduced the bias in the conventional method (CM) of estimation by 50%. When the upper bound of the outlier infested part of JK estimate is constrained to the number of outliers in the series, the new Jacknife estimate (NJK) completely removes the outlier infested bias in CM. The empirical illustration with real-life data showed that NJK estimates have lowest standard errors compared with CM and JK and decay with increase in lag.