Statistics for long-memory processes

By Jan Beran. 1994

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Citations in the corpus

Trend analysis of climate time series: A review of methods (2019, background): “In case of long-memory autocorrelation (Beran, 1994; Doukhan et al., 2003; Robinson, 2003), where the autocorrelation function decays hyperbolically (i.”
ESTIMATION OF PARAMETERS IN ARFIMA PROCESSES: A SIMULATION STUDY (2001, methodology): “For more details see (4), (23) and (6).”
Scaling and correlation in financial time series (2000, unknown): “Recently, Liu and his collaborators found that the amplitude of the returns, the absolute value or the square – closely related to what is referred to in economics as the volatility [84–88] – shows long-range correlations [42–46,82,83,89–91] with persistence [92] up to several months, Fig.”
Modelling and Forecasting Multivariate Realized Volatility (2011, methodology): “To get an initial idea of the degree of fractional integration, we run OLS regressions of log-autocorrelations on log-lags (see Beran, 1998, pp. 89–92) and obtain an estimate of 0.40 on average across the m series.”
Complexity–entropy analysis of daily stream flow time series in the continental United States (2014, background): “…parameter H, and other stream flow properties The Hurst parameter is a well-known index that measures the long range dependence of a process (e.g., Beran 1994), and characterizes important theoretical stochastic processes, such as fGn and the corresponding fBm. Bandt and Shiha (2007) showed that…”
The Distribution of Realized Exchange Rate Volatility (2001, unknown): “Then, as discussed by, Beran (1994) and Diebold and Lindner (1996), among others, if xt is fractionally integrated, the partial sums obey a scaling law, Var46xt 7h5 = c h 2d+ 10 (26) Of course, by de nition 6vardt7h vardt1h and 6varyt7h varyt1h , so the variance of the realized volatilities should…”
Stochasticity, nonlinearity and forecasting of streamflow processes (2006, methodology): “But in the presence of long-memory, Beran (1994) proved that the variance of the sample mean could be expressed by 2 2 var( ) H x cN − ≈ , where c>0 and H is the Hurst coefficient. Correspondingly, Beran (1994) suggested the following method for estimating the Hurst coefficient H.”
Robust estimation of the scale and of the autocovariance function of Gaussian short‐ and long‐range dependent processes (2009, methodology): “The data consists of yearly minimal water levels of the Nile river measured at the Roda gauge, near Cairo, for the years 622–1284 AD (663 observations); The units for the data as presented by Beran (1994) Figure 6.”
Limit theory for the sample autocorrelations and extremes of a GARCH (1,1) process (2000, background): “Despite the fact that there is no unique de nition of thephenomenon LRD, one way to characterise it is given by Ph j jXj(h)j =1; see for example Beran[4].”
Variations and Hurst index estimation for a Rosenblatt process using longer filters (2009, background): “Information on these various approaches, apart from wavelets, for fBm and other long-memory processes, can be found in the book of Beran [3].”
Whittle Pseudo-Maximum Likelihood Estimation for Nonstationary Time Series (2000, methodology): “For the short memory simulation of the exponential models we used the Davies and Harte (1987) algorithm, as programmed by Beran (1994), using the rst 50 autocovariances obtained by numerical integration of the sd. Non-tapered (p = 1) and tapered (with Zhurbenko taper of order p = 2) data were…”
Testing for homogeneity of variance in time series: Long memory, wavelets, and the Nile River (2002, unknown): “0 SY fð Þ CS fj ja ¼ 1 ð1Þ [Beran, 1994, p. 42].”
Nonparametric Regression with Correlated Errors (2001, background): “For a review of work in that direction, see Beran [8], [9].”
From Stationarity to Self-similarity, and Back: Variations on the Lamperti Transformation (2003, background): “, in [3], [30] or [34]), but rarely used and even discussed per se.”
VOLATILITY AND CORRELATION FORECASTING (2006, background): “, Beran (1994) for an introduction to models incorporating long-memory features.”