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This article studies the asymptotic properties of the discrete Fourier transforms (DFT) and the periodogram of a stationary long-memory time series over different epochs. The main theoretical result is a novel bound for the covariance of the DFT ordinates evaluated on two distinct epochs, which...
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Methods for parameter estimation in the presence of long-range dependence and heavy tails are scarce. Fractional autoregressive integrated moving average (FARIMA) time series for positive values of the fractional differencing exponent d can be used to model long-range dependence in the case of...
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Fractional Brownian motion is a mean-zero self-similar Gaussian process with stationary increments. Its covariance depends on two parameters, the self-similar parameter H and the variance C. Suppose that one wants to estimate optimally these parameters by using n equally spaced observations. How...
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