data with high frequency have a particular type of none stationary that is called fractional none stationary. this property causes the emergence of long-term memory in financial time series with high frequency. the existence of long-term memory in cement industry time-series is studied in this paper at first and its presence will be confirmed in a high confidence level by two tests r/s and gph....

We develop an easy-to-implement method for forecasting a stationary autoregressive fractionally integrated moving average (ARFIMA) process subject to structural breaks with unknown break dates. We show that an ARFIMA process subject to a mean shift and a change in the long memory parameter can be well approximated by an autoregressive (AR) model and suggest using an information criterion (AIC o...

This paper analyses moment and near-epoch dependence properties for the general class of models in which the conditional variance is a linear function of squared lags of the process. It is shown how the properties of these processes depend independently on the sum and rate of convergence of the lag coefficients, the former controlling the existence of moments, and the latter the memory of the v...

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...

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...

One objective of this paper is to estimate the parameters p,d,q of an autoregressive fractionally integrated moving average ARFIMA(p,d,q) stochastic model by minimizing the squares of the residuals using a Bayesian global optimization techniques. We consider bilinear model, too because it is the simple extension of linear model, defined by adding a bilinear term to traditional ARMA model. There...

Jiang and and Tian (2010) have estimated an ARFIMA model for stock return volatility. We argue that this result does not imply actual 'long memory' in such time series -as any kind of instability in the population mean yields apparent fractional integration as a statistical artifact. Alternative high-pass filters for studying stock market volatility data are suggested.