Essays on long memory time series and panel models - KE, Shuyao (Institutional Knowledge at Singapore Management University, 2022)
This dissertation studies different long memory models. The first chapter considers a time series regression model where both the regressors and error term are locally stationary long memory processes with time-varying memory parameters, and the regression coefficients are also allowed to be time-varying. We consider a frequency-domain least squares estimator with kernelized discrete Fourier transform and derive its pointwise asymptotic normality and uniform consistency. A specification test on the constancy of coefficients is provided. The second chapter studies a linear regression panel data model with interactive fixed effects where the regressors, factors and idiosyncratic error terms are all stationary but with potential long memory. The setup involves a new factor model formulation for which weakly dependent regressors, factors and innovations are embedded as a special case. Standard methods based on principal component decomposition and least squares estimation, as in Bai (2009), are found to suffer bias correction failure because the order of magnitude of the bias is determined in a complex manner by the memory parameters. To cope with this failure and to provide a simple implementable estimation procedure, frequency domain least squares estimation is proposed. The limit distribution of this frequency domain approach is established and a hybrid selection method is developed to determine the number of factors. The third chapter estimates the memory parameters and test them against spurious long memory of the latent factors in a linear regression model with interactive fixed effects, based on the estimated discrete Fourier transform of the factors. The same asymptotic properties hold as if we use the infeasible true factors for both the memory estimator and the test. This result illustrates how the frequency domain least squares estimator can be applied to further inference other than the regression coefficients.