Estimating the Codifference function of Linear Time Series Models with Infinite Variance

Abstract

We consider the codifference and the normalized codifference function as dependence measures for stationary processes. Based on the empirical characteristic function, we propose estimators of the codifference and the normalized codifference function. We show consistency of the proposed estimators, where the underlying model is the ARMA with symmetric α-stable innovations, 0 < α ≤ 2. In addition, we derive their limiting distribution. We present a simulation study showing the dependence of the estimator on certain design parameters. Finally, we provide an empirical example using some stocks from Indonesia Stock Exchange.