We develop a new class of Continuous-time Auto-Regressive Fractionally Integrated Moving-Average (CARFIMA) models which are useful for modelling regularly-spaced and irregularly-spaced discrete-time long-memory data. We derive the autocovariance function of a stationary CARFIMA model, and study maximum likelihood estimation of a regression model with CARFIMA errors, based on discrete-time data ...

Joint time series of wave height, period and direction are essential input data to computational models which used simulate diachronic beach evolution in coastal engineering. However, it is often impractical collect a large amount the required due expense. Based on nearshore records offshore Littlehampton Southeast England over from 1 September 2003 30 June 2016, this paper presents statistical...

A general approach for modeling the volatility process in continuous-time is based on the convolution of a kernel with a non-decreasing Lévy process, which is non-negative if the kernel is non-negative. Within the framework of Continuous-time Auto-Regressive Moving-Average (CARMA) processes, we derive a necessary condition for the kernel to be non-negative, and propose a numerical method for ch...

Akaike’s criterion is often used to test composite hypotheses; for example to determine the order of a priori unknown Auto-Regressive and/or Moving Average models. Objections are formulated against Akaike’s criterion and some modifications are proposed. The application of the theory leads to a general technique for AR-model order estimation based on testing pairs of composite hypotheses. This t...

In our present study, GARCH family models are used for modeling and forecasting the rice yield of four provinces of Pakistan during the period of 1947-48 to 2008-09. Also Auto regressive, moving average and Autoregressive moving average models are described. Thus, the selected GARCH models for all provinces are also presented for forecasting purpose on the basis of two criteria AIC (Akaike info...

In this paper, we address the problem of online change detection of Markov-modulated time series models. For simplicity, we look at Auto-regressive time-series models the parameters of which are modulated by a nite-state homogeneous Markov chain. We propose a Cumulative Sum based statistical test to detect abrupt changes is such processes. Computation of average run length functions, in particu...