# Questions tagged [long-range-dependence]

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

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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 ...
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1 vote
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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 ...
• 11
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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 ...
1 vote
80 views

### 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 ...
• 2,587
1 vote
29 views

### 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 ...
• 406
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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 ...
• 1,145
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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 ...
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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, ...
• 1
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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 ...
1 vote
70 views

### 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?
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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?
• 71
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### Aggregate variance function and Hurst parameter

What is the aggregate variance method for estimating the value of Hurst exponent? How does it measure long range dependence?
• 103
1 vote
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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 ...
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### ARFIMA covariance structure

I have a set of response processes (queue lengths in infinite server network). Using queue theory, I can numerically calculate response autocovariance structure, from the known service time ...
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1 vote
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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 ...
• 63
417 views

### Examining correlation and long range dependence in time series data with strong diurnal effects [closed]

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 ...
• 123
162 views

### Minimum number of observations to determine long range dependency

What is the minimum number of observations to be considered in order to determine long range dependency? I'm trying to estimate Hurst parameter using R/S method. I've used SELFIS as well as R. ...
• 257
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 ...