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Full-Text Articles in Social and Behavioral Sciences
Asymptotic Properties Of Least Squares Estimator In Local To Unity Processes With Fractional Gaussian Noises, Xiaohu Wang, Weilin Xiao, Jun Yu
Asymptotic Properties Of Least Squares Estimator In Local To Unity Processes With Fractional Gaussian Noises, Xiaohu Wang, Weilin Xiao, Jun Yu
Research Collection School Of Economics
This paper derives asymptotic properties of the least squares estimator of the autoregressive parameter in local to unity processes with errors being fractional Gaussian noises with the Hurst parameter H. It is shown that the estimator is consistent when H ∈ (0, 1). Moreover, the rate of convergence is n when H ∈ [0.5, 1). The rate of convergence is n2H when H ∈ (0, 0.5). Furthermore, the limit distribution of the centered least squares estimator depends on H. When H = 0.5, the limit distribution is the same as that obtained in Phillips (1987a) for the local to …
Persistent And Rough Volatility, Xiaobin Liu, Shuping Shi, Jun Yu
Persistent And Rough Volatility, Xiaobin Liu, Shuping Shi, Jun Yu
Research Collection School Of Economics
This paper contributes to an ongoing debate on volatility dynamics. We introduce a discrete-time fractional stochastic volatility (FSV) model based on the fractional Gaussian noise. The new model has the same limit as the fractional integrated stochastic volatility (FISV) model under the in-fill asymptotic scheme. We study the theoretical properties of both models and introduce a memory signature plot for a model-free initial assessment. A simulated maximum likelihood (SML) method, which maximizes the time-domain log-likelihoods obtained by the importance sampling technique, is employed to estimate the model parameters. Simulation studies suggest that the SML method can accurately estimate both models. …