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.
Highlights
IntroductionWe introduce the multivariate stochastic stationary root (SSR) model. The SSR model is a nonlinear state space model, which resembles the Granger-Johansen representation of the cointegrated vector autoregressive (CVAR) model, see inter alia Johansen (1996) and Juselius (2007)
In this paper, we introduce the multivariate stochastic stationary root (SSR) model
We appeal to the incomplete data framework and the simulation-based approach known as particle filtering to approximate the log-likelihood function, sample score and observed Information matrix
Summary
We introduce the multivariate stochastic stationary root (SSR) model. The SSR model is a nonlinear state space model, which resembles the Granger-Johansen representation of the cointegrated vector autoregressive (CVAR) model, see inter alia Johansen (1996) and Juselius (2007). We appeal to the incomplete data framework and the simulation-based approach known as particle filtering to approximate the log-likelihood function, sample score and observed Information matrix. Summarizing, the main contributions of this paper are to i ii introduce and study the SSR model, and propose a method for approximate frequentist estimation and inference. It is beyond the scope of this paper to provide a complete proof of the asymptotic properties of the ML estimator. We denote a sequence of n ∈ N+ real dz –dimensional vectors by z1:n ..= [ z10 . . . z0n ]0 ∈ Rn×dz
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