The Joint Moment Generating Function of Quadratic Forms in Multivariate Autoregressive Series
- 1 October 1996
- journal article
- research article
- Published by Cambridge University Press (CUP) in Econometric Theory
- Vol. 12 (4) , 682-704
- https://doi.org/10.1017/s0266466600006988
Abstract
Let (X1) be a discrete multivariate Gaussian autoregressive process of order 1. The paper derives the exact finite-sample joint moment generating function (m.g.f.) of the three quadratic forms constituting the sufficient statistic of the process. The formula is then specialized to some cases of interest, including the m.g.f. of functional of multivariate Ornstein-Uhlenbeck processes that arise asymptotically from more general (X1) processes as well.Keywords
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This publication has 24 references indexed in Scilit:
- The Limiting Distribution of the t Ratio Under a Unit RootEconometric Theory, 1995
- The Limiting Distribution of the Autocorrelation Coefficient under a Unit RootThe Annals of Statistics, 1993
- On the Asymptotic Power of Unit Root TestsEconometric Theory, 1993
- An Alternative Approach to the Asymptotic Theory of Spurious Regression, Cointegration, and Near CointegrationEconometric Theory, 1993
- A Continuous Time Approximation to the Unstable First-Order Autoregressive Process: The Case Without an InterceptEconometrica, 1991
- Asymptotic Properties of Multivariate Nonstationary Processes with Applications to AutoregressionsThe Annals of Statistics, 1990
- Regression Theory for Near-Integrated Time SeriesEconometrica, 1988
- The Order of Differencing in ARIMA ModelsJournal of the American Statistical Association, 1984
- The Limiting Distribution of the Serial Correlation Coefficient in the Explosive Case IIThe Annals of Mathematical Statistics, 1959
- Inversion Formulae for the Distribution of RatiosThe Annals of Mathematical Statistics, 1948