The Stochastic Stationary Root Model

Andreas Hetland
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Andreas Hetland: Department of Economics, University of Copenhagen, 1353 Copenhagen K, Denmark

Econometrics, 2018, vol. 6, issue 3, 1-33

Abstract: We propose and study the stochastic stationary root model. The model resembles the cointegrated VAR model but is novel in that: (i) the stationary relations follow a random coefficient autoregressive process, i.e., exhibhits heavy-tailed dynamics, and (ii) the system is observed with measurement error. Unlike the cointegrated VAR model, estimation and inference for the SSR model is complicated by a lack of closed-form expressions for the likelihood function and its derivatives. To overcome this, we introduce particle filter-based approximations of the log-likelihood function, sample score, and observed Information matrix. These enable us to approximate the ML estimator via stochastic approximation and to conduct inference via the approximated observed Information matrix. We conjecture the asymptotic properties of the ML estimator and conduct a simulation study to investigate the validity of the conjecture. Model diagnostics to assess model fit are considered. Finally, we present an empirical application to the 10-year government bond rates in Germany and Greece during the period from January 1999 to February 2018.

Keywords: cointegration; particle filtering; random coefficient autoregressive model; state space model; stochastic approximation (search for similar items in EconPapers)
JEL-codes: B23 C C00 C01 C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Date: 2018
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