Latent local-to-unity models

• Main Author: Yu, Jun
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2021
• Subjects: State-space; Local-to-unity; O-U process; Fractional O-U process; Fractional Brownian motion; Fractional integration; Instrumental variable; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_working_paper/3; https://ink.library.smu.edu.sg/cgi/viewcontent.cgi?article=1003&context=soe_working_paper
• Institution: Singapore Management University

This paper proposes a class of state-space models where the state equation is a local-to-unity process. The large sample theory is obtained for the least squares (LS) estimator of the autoregressive (AR) parameter in the AR representation of the model under two sets of conditions. In the first set of conditions, the error term in the observation equation is independent and identically distributed (iid), and the error term in the state equation is stationary and fractionally integrated with memory parameter H ϵ 2 (0; 1). It is shown that both the rate of convergence and the asymptotic distribution of the LS estimator depend on H. In the second set of conditions, the error term in the observation equation is independent but not necessarily identically distributed, and the error term in the state equation is strong mixing. When both error terms are iid, we also develop the asymptotic theory for an instrumental variable estimator. Special cases of our models are discussed.