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...

Autoregressive fractionally integrated moving average ARFIMA pro cesses are widely used for modeling time series exhibiting both long memory and short memory behavior Properties of Toeplitz matrices associated with the spectral density functions of Gaussian ARFIMA processes are used to compute di erential geometric quantities INTRODUCTION Time series data occurring in several areas such as geol...