ORDER DETERMINATION OF MULTIVARIATE AUTOREGRESSIVE TIME SERIES WITH UNIT ROOTS
- 1 March 1984
- journal article
- Published by Wiley in Journal of Time Series Analysis
- Vol. 5 (2) , 115-127
- https://doi.org/10.1111/j.1467-9892.1984.tb00381.x
Abstract
This paper deals with order determination of multivariate time series where roots of the characteristic equation are allowed to be equal to one. For estimation of parameters in such processes, least squares were used. For a familiar class of order determination criteria it is shown that results on weak consistency valid in the stationary case can be generalized to processes with unit roots in the characteristic equation. Then a discussion of the possibility of underestimating the order for finite samples is given for a particular model, and it is indicated that nonstationarity of this type decreases the probability of underestimating the order. Finally some Monte Carlo simulation results are given to supplement the theoretical results.Keywords
This publication has 9 references indexed in Scilit:
- Order Determination for a Multivariate AutoregressionJournal of the Royal Statistical Society Series B: Statistical Methodology, 1980
- The Determination of the Order of an AutoregressionJournal of the Royal Statistical Society Series B: Statistical Methodology, 1979
- Estimating the Dimension of a ModelThe Annals of Statistics, 1978
- Selection of the order of an autoregressive model by Akaike's information criterionBiometrika, 1976
- Selection of the Order of an Autoregressive Model by Akaike's Information CriterionBiometrika, 1976
- A new look at the statistical model identificationIEEE Transactions on Automatic Control, 1974
- Multiple Time SeriesWiley Series in Probability and Statistics, 1970
- Some Theorems on Matrix Differentiation with Special Reference to Kronecker Matrix ProductsJournal of the American Statistical Association, 1969
- Some Theorems on Matrix Differentiation with Special Reference to Kronecker Matrix ProductsJournal of the American Statistical Association, 1969