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...

By design a wavelet’s strength rests in its ability to localize a process simultaneously in time-scale space. The wavelet’s ability to localize a time series in time-scale space directly leads to the computational efficiency of the wavelet representation of a N × N matrix operator by allowing the N largest elements of the wavelet represented operator to represent the matrix operator [Devore, et...

Aims: To model the concentration variation of PM2.5 and PM10 in selected locations Delhi.
 Study Design: ARFIMA-GARCH model.
 Place Duration Study: The study was conducted by using daily (24 hour interval) data from three air quality monitoring stations Delhi namely, Narela, Okhla Phase II Pusa.
 Methodology: ARFIMA is applied as mean GARCH variance Results: series are stationary...

In this work we study stationary linear time-series models, and construct analyse “score-matching” estimators based on the Hyvärinen scoring rule. We consider two scenarios: a single series of increasing length, an number independent fixed length. latter case there are variants, one full data, another sufficient statistic. empirical performance these in three special cases, autoregressive (AR),...

A new parametric minimum distance time-domain estimator for ARFIMA processes is introduced in this paper. The proposed estimator minimizes the sum of squared correlations of residuals obtained after filtering a series through ARFIMA parameters. The estimator is easy to compute and is consistent, asymptotically normally distributed and efficient for fractionally integrated (FI) processes with an...