Long-Range Dependence in Stationary Gaussian Time Series: An Application to Stock Trading Volume and Realized Volatility

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Authors
Arango Castillo, Lenin
Keyword
Long-Range Dependence , Stationary Gaussian Time Series , Stock Trading Volume , Realized Volatility
Abstract
In this thesis, we examine pure and mixed-spectra Gaussian long-range dependent time series. In chapter 2, we introduce background material that is used in subsequent chapters. In chapter 3, we propose a method to robustly estimate the variance of the sample mean for two Gaussian processes exhibiting long-range dependence (LRD): fractional Gaussian noise, fGn(H), and fractional integrated noise with Gaussian innovations, GFI(H). An important feature of the proposed method is a test statistic to differentiate between fGn(H) and GFI(H), which, under a correct decision, allows us to estimate the Hurst parameter H using the correct model specification. Theoretical properties of the test statistic are derived and numerical comparisons against existing estimators are presented. In chapter 4, we study time series characterized by hidden periodic components buried in stationary noise. We propose an approach to the problem of estimating H in processes with mixed spectra in the context of two Gaussian LRD processes: fGn(H) and GFI(H). We apply the method to synthetic periodic time series, and we show numerical results. We also examine a real data case on air quality indices based on particulate matter data from the United States and we show the effect of hidden periodic components on the estimation of H using the method. Lastly, in chapter 5, we use stock trading volume and stock realized volatility time series to illustrate the methods in chapters 3 and 4. We show the presence of hidden periodic components and, using the test statistic in chapter 3, we propose a modelling approach.
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