The R/S test has been extensively used in testing the long memory of financial time series, but little attentions have been paid on its validity. The paper sets the chemical raw materials styrene price time series as an example, to test the stable of the price series. It indicates that we should give prudent explanation for the R/S test, and then establish the ARFIMA model to determine the data...

The maximum likelihood estimator (MLE) of the fractional difference parameter in the Gaussian ARFIMA(0, d, 0) model is well known to be asymptotically N(0, 6/π). This paper develops a second order asymptotic expansion to the distribution of this statistic. The correction term for the density is shown to be independent of d, so that the MLE is second order pivotal for d. This feature of the MLE ...

In this paper we examine the ̄nite-sample properties of the approximate maximum likelihood estimate (MLE) of the fractional di®erencing parameter d in an ARFIMA(p, d, q) model based on the wavelet coe±cients. Ignoring wavelet coe±cients of higher order of resolution, the remaining wavelet coe±cients approximate a sample of independently and identically distributed normal variates with homogeneo...

Currently the emergence of novel coronavirus (Sars-Cov-2), which causes COVID-19 pandemic and has become a serious health problem because high risk death. Therefore, fast appropriate action is needed to reduce spread pandemic. One way build prediction model so that it can be reference in taking steps overcome them. Because nature transmission this disease massive cause extreme data fluctuations...

In the last decade, several HRV based novel methodologies for describing and assessing heart rate dynamics have been proposed in the literature with the aim of risk assessment. Such methodologies attempt to describe the non-linear and complex characteristics of HRV, and hereby the focus is in two of these characteristics, namely long memory and heteroscedasticity with variance clustering. The A...

A key application of long memory time series models concerns innation. Long memory implies that shocks have a long-lasting eeect. It may however be that empirical evidence for long memory is caused by neglecting one or more level shifts. Since such level shifts are not unlikely for innation, where the shifts may be caused by sudden oil price shocks, we examine whether evidence for long memory (...

In this paper, taking about 7 years’ high-frequency data of the Shanghai Stock Exchange Composite Index (SSEC) as an example, we propose a daily volatility measure based on the multifractal spectrum of the high-frequency price variability within a trading day. An ARFIMA model is used to depict the dynamics of this multifractal volatility (MFV) measures. The one-day ahead volatility forecasting ...