| Summary: | 碩士 === 國立中山大學 === 應用數學系研究所 === 99 === In this paper, we study the parameter estimation of the multiple linear time series
regression model with long memory stochastic regressors and innovations. Robinson and
Hidalgo (1997) and Hidalgo and Robinson (2002) proposed a class of frequency-domain
weighted least squares estimates. Their estimates are shown to achieve the Gauss-Markov
bound with standard convergence rate. In this study, we proposed a time-domain generalized LSE approach, in which the inverse autocovariance matrix of the innovations is estimated via autoregressive coefficients. Simulation studies are performed to compare the proposed estimates with Robinson and Hidalgo (1997) and Hidalgo and Robinson (2002). The results show the time-domain generalized LSE is comparable to Robinson and Hidalgo (1997) and Hidalgo and Robinson (2002) and attains higher efficiencies when the
autoregressive or moving average coefficients of the FARIMA models have larger values.
A variance reduction estimator, called TF estimator, based on linear combination of the
proposed estimator and Hidalgo and Robinson (2002)''s estimator is further proposed to
improve the efficiency. Bootstrap method is applied to estimate the weights of the linear combination. Simulation results show the TF estimator outperforms the frequency-domain as well as the time-domain approaches.
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