Ce document est publié dans l'intention de rendre accessibles les résultats préliminaires de la recherche effectuée au CIRANO, afin de susciter des échanges et des suggestions. Les idées et les opinions émises sont sous l'unique responsabilité des auteurs, et ne représentent pas nécessairement les positions du CIRANO ou de ses partenaires. This paper presents preliminary research carried out at...

Autoregressive fractional integrated moving average modeling strategy was used to model the daily average temperature (DAT) series of Sokoto metropolis for the period of 01/01/2003 to 03/04/2007. The time plot suggests that there is persistence dependence in the series. The order of fractional integration was found to be 0.6238841. The correct model for the daily average temperature data (DAT) ...

This paper proposes an easy test for independence between two stationary autoregressive fractionally integrated moving average (ARFIMA) processes via AR approximations. We prove that an ARFIMA (p, d, q) process, φ(L)(1 − L)yt = θ(L)et, d ∈ (0, 0.5), where et is a white noise, can be approximated well by an autoregressive (AR) model and establish the theoretical foundation of Haugh’s (1976) stat...

In this paper, we study ergodic properties of α-stable autoregressive fractionally integrated moving average (ARFIMA) processes which form a large class of anomalous diffusions. A crucial practical question is how long trajectories one needs to observe in an experiment in order to claim that the analyzed data are ergodic or not. This will be solved by checking the asymptotic convergence to 0 of...

We study the autocorrelation structure and the spectral density function of aggregates from a discrete-time process. The underlying discrete-time process is assumed to be a stationary AutoRegressive Fractionally Integrated MovingAverage (ARFIMA) process, after suitable number of differencing if necessary. We derive closed-form expressions for the limiting autocorrelation function and the normal...

In this paper, we study the dual long memory property of the Korean stock market. For this purpose, the ARFIMA–FIGARCH model is applied to two daily Korean stock price indices (KOSPI and KOSDAQ). Our empirical results indicate that long memory dynamics in the returns and volatility can be adequately estimated by the joint ARFIMA–FIGARCH model. We also found that the assumption of a skewed Stude...