The Stochastic Stationary Root Model
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The Stochastic Stationary Root Model. / Hetland, Andreas.
In: Econometrics, Vol. 6, No. 3, 21.08.2018.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - The Stochastic Stationary Root Model
AU - Hetland, Andreas
PY - 2018/8/21
Y1 - 2018/8/21
N2 - 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.
AB - 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.
KW - Faculty of Social Sciences
KW - cointegration
KW - particle filtering
KW - random coefficient autoregressive model
KW - state space model
KW - stochastic approximation
U2 - 10.3390/econometrics6030039
DO - 10.3390/econometrics6030039
M3 - Journal article
VL - 6
JO - Econometrics
JF - Econometrics
SN - 2225-1146
IS - 3
ER -
ID: 222620162