Estimation methods for stationary Gegenbauer processes

This paper reviews alternative methods for estimation for stationary Gegenbauer processes specifically, as distinct from the more general long memory models. A short set of Monte Carlo simulations is used to compare the accuracy of these methods. The conclusion found is that a Bayesian technique results in the highest accuracy. The paper is completed with an examination of the SILSO Sunspot Number series as collated by the Royal Observatory of Belgium.

True versus Spurious Long Memory in Cryptocurrencies

We test whether the selected cryptocurrencies exhibit long memory behavior in returns and volatility. We use data on five most traded cryptocurrencies: Bitcoin, Litecoin, Ethereum, Bitcoin Cash, and XRP. Using recent tests of long memory developed against persistent and nonlinear alternatives, this paper finds that long memory is mostly rejected in returns. The tests fail to reject the null hypothesis of long memory in most cases across different volatility proxies and cryptocurrencies. The estimated memory parameters show that volatility is persistent, and when volatility is measured by log range, it is borderline nonstationary.

Modified periodogram method for estimating the Hurst exponent of fractional Gaussian noise

Fractional Gaussian noise (fGn) is an important and widely used self-similar process, which is mainly parametrized by its Hurst exponent (H) . Many researchers have proposed methods for estimating the Hurst exponent of fGn. In this paper we put forward a modified periodogram method for estimating the Hurst exponent based on a refined approximation of the spectral density function. Generalizing the spectral exponent from a linear function to a piecewise polynomial, we obtained a closer approximation of the fGn's spectral density function. This procedure is significant because it reduced the bias in the estimation of H . Furthermore, the averaging technique that we used markedly reduced the variance of estimates. We also considered the asymptotical unbiasedness of the method and derived the upper bound of its variance and confidence interval. Monte Carlo simulations showed that the proposed estimator was superior to a wavelet maximum likelihood estimator in terms of mean-squared error and was comparable to Whittle's estimator. In addition, a real data set of Nile river minima was employed to evaluate the efficiency of our proposed method. These tests confirmed that our proposed method was computationally simpler and faster than Whittle's estimator.