Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [long-range-dependence]

Used for time series with long memory. Could also arise in spatial data.

See https://en.wikipedia.org/wiki/Long-range_dependence

18 questions
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Predicting long-memory processes

I'm working with a two-state process with $x_t$ in $\{1, -1\}$ for $t = 1, 2, \ldots$ The autocorrelation function is indicative of a process with long-memory, i.e. it displays a power law decay with an exponent < 1. You can simulate a similar…
Chris Taylor
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Why can't ARIMA model large lags and/or long range dependence?

ARIMA cannot model large lags (obtained from autocorrelation plot) and long range dependency (hurst exponent $H > 0.5$). Why is it so?
Vaib
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Examining correlation and long range dependence in time series data with strong diurnal effects

I have data sets of network traffic that exhibit strong diurnal effects making them non-stationary. One of the analysis that I want to run is to show correlation between days. If we chopped up the time series into individual days, how would…
creatiwit
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Biased estimates of Hurst exponent in R/S analysis

I've used the standard R/S algorithm for estimating the Hurst exponent in Mathematica*, and tested it on fBm and fGn for $H\in\{0.05,0.1,\ldots,0.95\}$, generating 1000 time series for each $H$. The results, in form of violin plots, are as…
corey979
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How small is too small to fit a reasonable long memory model?

When looking at papers about long memory they tend to analyze data sets whose length is in the thousands, see http://www.math.canterbury.ac.nz/~m.reale/pub/Reaetal2011.pdf for an example. My question is to the long memory researchers and…
adunaic
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Verifying long-range dependency in multi-variate time series

I am fairly new to the area of time series and I am trying to understand the notion of long-range dependence in time series. My goal is to characterize the same in the case of multi-variate time series. The Wikipedia page on long-range dependence…
pikachuchameleon
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When is it reasonable to assume that a set of observations is from a strong-mixing process?

I am trying to apply OLS for time-series data that is clearly from a neither independent nor identically distributed process. The observations are hourly power system load values and the covariates include hourly temperature and historical power…
catcher
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How bad are short-term forecasts of ARIMA models of ARFIMA processes?

Suppose I have a set of economic time series that appear to be a unit root process. I difference them, and fit an ARMA model to the differenced series. Suppose however that the true data generating process is integrated not of order 1, but of order…
andrewH
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long-range dependence measure

Hurst exponent is a simple, powerful and widely used measure of a long-term memory of time series. What is are the disadvantages of this measure for checking long-range dependence in the series and what else could be used instead of Hurst…
ABK
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Can processes with long range dependence be classified as stationary/non-stationary?

If my process has long range dependence (hurst exponent > 0.5 ) can it be concluded that it is stationary/non-stationary? How? Is there any correlation between Long range dependence and Stationarity?
Vaib
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Simulating data with long range dependencies

I want to evaluate how well a recurrent neural network I've created captures long-range dependencies, and the effects altering the network have on this. I'm not entirely sure how I would go about doing this except by training it on data where I…
as646
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Extreme Value Theory and heavy (long) tailed distributions

I'm analyzing data about which I have a strong suspicion that it is self-similar (Hurst parameter ranging from 0.60 to 0.78 depending on estimation method and sample sequence). I also observe high realization values much more often (compared to…
moorray
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How do I test long memory in ARFIMA?

I've been wondering about measuring long-term memory in ARFIMA models - should I use ACF/PACF for it? Or maybe there are some different methods - and then is there anything I didn't know since my first thought was the above tests? Any functions in…
Fatafim
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Why the simulation of a FARIMA process using the autocovariance function should be better?

Let us consider a Fractional Autoregressive Moving Average process: $ (1 - L)^d y_t = \epsilon_t$ where $d \in (-0.5,0.5)$ and $\epsilon_t$ is a white noise sequence. Let $\gamma(k)$ be the autocovariance function of the above process at lag $k$. It…
Federico
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Compare long range dependence among non-stationary multivariate time series'

I have 5 non-stationary multivariate time series' and I need to compare the "strength" of long range dependence among them. I have found many papers on long range dependence estimation (parametric, semi parametric, Whittle, etc.), but as my…
Ijjz
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