Sage Journals: Discover world-class research

Abstract

The index model and the reduced-rank model are two useful models which adopt different views to explore a vector autoregressive (VAR) model structure. However, we expect that there will be more information when the two models are implemented simultaneously. This paper combines these two models to propose a VAR model with constraints. The model extracts the leading index and explores the reduced-rank structures simultaneously. In this study, theoretical results are presented, which include a necessary and sufficient condition for a transformation for parsimonious parameterizations and model identification, the maximum likelihood estimations and the likelihood ratio test. The empirical results for the analysis of famous US hog data using the proposed model display the unification of several results in the literature, revealing that the novel model is reasonable and works quite well.

Keywords

index model reduced-rank model vector autoregressive model

Get full access to this article

View all access options for this article.

References

Ahn

Reinsel

(1988) Nested reduced-rank autoregressive models for multiple time series. Journal of the American Statistical Association, 83, 849–56.

Arbúes

(2008) An extended portmanteau test for VARMA models with mixing constraints. Journal of Time Series Analysis, 29, 741–61.

Box

GEP

Tiao

(1977) A canonical analysis of multiple time series. Biometrika, 64, 355–65.

Camba-Mendez

Kapetanios

Smith

Weale

(2003) Tests of rank in reduced rank regression models. Journal of Business & Economic Statistics, 21, 145–55.

Hannan

Deistler

(1988) The statistical theory of linear systems. New York: John Wiley and Sons.

(2011) Likelihood function and canonical correlation analysis of the Peña-Box model. Communication in Statistics–Theory and Methods, 40, 1453–67.

Chou

(2004) On the Peña-Box model. Journal of Time Series Analysis, 25, 811–30.

Kohn

(1979) Asymptotic estimation and hypothesis testing results for vector linear time series models. Econometrica, 47, 1005–30.

Quenouille

(1957) The analysis of multiple time series. London: Griffin.

10.

Reinsel

(1983) Some results on multivariate autoregressive index models. Biometrika, 70, 145–56.

11.

Sargent

Sims

(1977) Business cycle modeling without pretending to have too much a priori economic theory. New Methods in Business Cycle Research, Proceedings from a Conference. Minneapolis, Federal Reserve Bank of Minneapolis, pp. 45–110.

12.

Tiao

Tsay

(1989) Model specification in multivariate time series (with discussion). Journal of the Royal Statistical Society B, 51, 157–213.

13.

Velu

Reinsel

Wichern

(1986) Reduced rank models for multiple time series. Biometrika, 73, 105–18.

On the reduced-rank model with leading index

Abstract

Keywords

Get full access to this article

References