Time Series Analysis : Nonstationary and Noninvertible Distribution Theory. - Tanaka, Katsuto (New York : John Wiley & Sons, Incorporated, 2017)
Chapter 13 Statistical Inference Associated with the Fractional Brownian Motion -- 13.1 Introduction -- 13.2 A Simple Continuous-Time Model Driven by the fBm -- 13.3 Quadratic Functionals of the Brownian Motion -- 13.4 Derivation of the c.f. -- 13.4.1 Stochastic Process Approach via Girsanov's Theorem -- 13.4.1.1 Case of H = 1/2 -- 13.4.1.2 Case of H &gt -- 1/2 -- 13.4.2 Fredholm Approach via the Fredholm Determinant -- 13.4.2.1 Case of H = 1/2 -- 13.4.2.2 Case of H &gt -- 1/2 -- 13.5 Martingale Approximation to the fBm -- 13.6 The Fractional Unit Root Distribution -- 13.6.1 The FD Associated with the Approximate Distribution -- 13.6.2 An Interesting Moment Property -- 13.7 The Unit Root Test Under the fBm Error -- Chapter 14 Maximum Likelihood Estimation for the Fractional Ornstein-Uhlenbeck Process -- 14.1 Introduction -- 14.2 Estimation of the Drift: Ergodic Case -- 14.2.1 Asymptotic Properties of the OLSEs -- 14.2.2 The MLE and MCE -- 14.3 Estimation of the Drift: Non-ergodic Case -- 14.3.1 Asymptotic Properties of the OLSE -- 14.3.2 The MLE -- 14.4 Estimation of the Drift: Boundary Case -- 14.4.1 Asymptotic Properties of the OLSEs -- 14.4.2 The MLE and MCE -- 14.5 Computation of Distributions and Moments of the MLE and MCE -- 14.6 The MLE-based Unit Root Test Under the fBm Error -- 14.7 Concluding Remarks -- Chapter 15 Solutions to Problems -- References -- Author Index -- Subject Index -- EULA.
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
Keywords: Time-series analysis; Electronic books