A Nonlinear ARMA-GARCH Model With Johnson $S_u$ Innovations and Its Application to Sea Clutter Modeling

Abstract

In this paper, a novel time series heteroskedastic model is proposed for sea clutter modeling application. In the light of characteristics of the practical clutter at low grazing angle, the original generalized autoregressive conditional heteroskedasticity process, which has been widely used in various fields of economics, is extended from three aspects. First, the autoregressive moving-average terms are introduced for modeling the temporal correlation of both clutter returns and innovations. Second, the exponential of the conditional variance is generalized from one to arbitrary positive value, to capture the nonlinearity existing in the practical clutter. Third, the traditional Gaussian innovation is replaced by the Johnson $S_{u}$ random variable, which is a monotonic transformation of the Gaussian random variable and is capable of modeling the skewness and kurtosis. By systematically analyzing a large number of practical sea clutter data sets, we show that the proposed time series model fits the data better than some commonly used statistic-based distributions, such as the Weibull and compound Gaussian distributions.