Unit Root Vector Autoregression with Volatility Induced Stationarity

37 Pages Posted: 13 Jun 2012

See all articles by Anders Rahbek

Anders Rahbek

University of Copenhagen - Department of Statistics and Operations Research; University of Copenhagen - Department of Economics

Heino Bohn Nielsen

University of Copenhagen - Department of Economics

Date Written: June 8, 2012

Abstract

We propose a discrete-time multivariate model where lagged levels of the process enter both the conditional mean and the conditional variance. This way we allow for the empirically observed persistence in time series such as interest rates, often implying unit-roots, while at the same time maintain stationarity despite such unit-roots. Specifically, the model bridges vector autoregressions and multivariate ARCH models in which residuals are replaced by levels lagged. An empirical illustration using recent US term structure data is given in which the individual interest rates have unit roots, have no finite first-order moments, but remain strictly stationary and ergodic, while they co-move in the sense that their spread has no unit root. The model thus allows for volatility induced stationarity, and the paper shows conditions under which the multivariate process is strictly stationary and geometrically ergodic. Interestingly, these conditions include the case of unit roots and a reduced rank structure in the conditional mean, known from linear co-integration to imply non-stationarity. Asymptotic theory of the maximum likelihood estimators for a particular structured case (so-called self-exciting) is provided, and it is shown that √T−convergence to Gaussian distributions apply despite unit roots as well as absence of finite first and higher order moments. Monte Carlo simulations confirm the usefulness of the asymptotics in finite samples.

Keywords: vector autoregression, unit-root, reduced rank, volatility induced stationarity, term structure, double autoregression

JEL Classification: C32

Suggested Citation

Rahbek, Anders and Nielsen, Heino Bohn, Unit Root Vector Autoregression with Volatility Induced Stationarity (June 8, 2012). Univ. of Copenhagen Dept. of Economics Discussion Paper No. 12-02, Available at SSRN: https://ssrn.com/abstract=2083452 or http://dx.doi.org/10.2139/ssrn.2083452

Anders Rahbek (Contact Author)

University of Copenhagen - Department of Statistics and Operations Research

Universitetsparken 5
DK-2100
Denmark
+45 3532 0682 (Phone)

University of Copenhagen - Department of Economics

Øster Farimagsgade 5
Bygning 26
1353 Copenhagen K.
Denmark

Heino Bohn Nielsen

University of Copenhagen - Department of Economics ( email )

Øster Farimagsgade 5
Bygning 26
1353 Copenhagen K.
Denmark

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