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Econometrics 2018, 6(3), 39; https://doi.org/10.3390/econometrics6030039

The Stochastic Stationary Root Model

Department of Economics, University of Copenhagen, 1353 Copenhagen K, Denmark
Received: 31 March 2018 / Revised: 27 July 2018 / Accepted: 13 August 2018 / Published: 21 August 2018
(This article belongs to the Special Issue Celebrated Econometricians: Katarina Juselius and Søren Johansen)
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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. View Full-Text
Keywords: cointegration; particle filtering; random coefficient autoregressive model; state space model; stochastic approximation cointegration; particle filtering; random coefficient autoregressive model; state space model; stochastic approximation
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Hetland, A. The Stochastic Stationary Root Model. Econometrics 2018, 6, 39.

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