Takamitsu Kurita

An I(2) Cointegration Model with Piecewise Linear Trends: Likelihood Analysis and Application

This paper presents likelihood analysis of the I(2) cointegrated vector autoregression with piecewise linear deterministic terms. Limiting behavior of the maximum likelihood estimators are derived, which is used to further derive the limiting distribution of the likelihood ratio statistic for the cointegration ranks, extending the result for I(2) models with a linear trend in Nielsen and Rahbek (2007) and for I(1) models with piecewise linear trends in Johansen, Mosconi, and Nielsen (2000). The provided asymptotic theory extends also the results in Johansen, Juselius, Frydman, and Goldberg (2009) where asymptotic inference is discussed in detail for one of the cointegration parameters. To illustrate, an empirical analysis of US consumption, income and wealth, 1965 - 2008, is performed, emphasizing the importance of a change in nominal price trends after 1980.

An I(2) cointegration model with piecewise linear trends

This paper presents likelihood analysis of the I(2) cointegrated vector autoregression which allows for piecewise linear deterministic terms. Limiting behaviour of the maximum likelihood estimators are derived, which is used to further derive the limiting distribution of the likelihood ratio statistic for the cointegration ranks, extending Nielsen and Rahbek. The provided asymptotic theory extends also the results in Johansen et al. where asymptotic inference is discussed in detail for one of the cointegration parameters. An empirical analysis of US consumption, income and wealth, 1965–2008, is performed, emphasizing the importance of a change in nominal price trends after 1980.

A simulation analysis of conditional tests for parameter stability in cointegrated VAR models

This paper conducts a simulation study of parameter stability tests using conditional cointegrated vector autoregressive (CVAR) models. Monte Carlo simulation experiments show that, under the assumption of weak exogeneity, the parameter stability tests based on conditional CVAR models are more powerful than those based on a joint CVAR model. However, the reverse is observed in the experiments when the assumption fails to hold true. The overall assessment of the simulation study leads to the formulation of a practical procedure for testing the constancy of parameters in both conditional and joint CVAR models.

Exploring the Impact of Multivariate GARCH Innovations on Hypothesis Testing for Cointegrating Vectors

This article investigates the impact of multivariate generalized autoregressive conditional heteroskedastic (GARCH) errors on hypothesis testing for cointegrating vectors. The study reviews a cointegrated vector autoregressive model incorporating multivariate GARCH innovations and a regularity condition required for valid asymptotic inferences. Monte Carlo experiments are then conducted on a test statistic for a hypothesis on the cointegrating vectors. The experiments demonstrate that the regularity condition plays a critical role in rendering the hypothesis testing operational. It is also shown that Bartlett-type correction and wild bootstrap are useful in improving the small-sample size and power performance of the test statistic of interest.

MODELLING TIME SERIES DATA OF MONETARY AGGREGATES USING I(2) AND I(1) COINTEGRATION ANALYSIS

The objective of this paper is to consider methodology for modelling time series data of monetary aggregates such as monetary base and broad money. A brief review is made with regard to the likelihood‐based cointegration analysis of I(2) (integrated of order 2) data and I(2)‐to‐I(1) transformations. The paper then investigates procedures for econometric modelling of monetary aggregates, which are in general deemed to be I(2) variables analogous to price indices. It is shown that I(2)‐to‐I(1) transformations centering on a money multiplier play an important role in the modelling procedures. Finally, the study presents an empirical illustration of the proposed methodology using monetary aggregate data from Japan.

Likelihood-Based Inference for Weak Exogeneity in I(2) Cointegrated VAR Models

This article develops limit theory for likelihood analysis of weak exogeneity in I(2) cointegrated vector autoregressive (VAR) models incorporating deterministic terms. Conditions for weak exogeneity in I(2) VAR models are reviewed, and the asymptotic properties of conditional maximum likelihood estimators and a likelihood-based weak exogeneity test are then investigated. It is demonstrated that weak exogeneity in I(2) VAR models allows us to conduct asymptotic conditional inference based on mixed Gaussian distributions. It is then proved that a log-likelihood ratio test statistic for weak exogeneity in I(2) VAR models is asymptotically χ2 distributed. The article also presents an empirical illustration of the proposed test for weak exogeneity using Japans macroeconomic data.

Local Power of Likelihood-Based Tests for Cointegrating Rank: Comparative Analysis of Full and Partial Systems

This note investigates local power properties of likelihood‐based cointegrating rank tests for partial and full vector autoregressive systems. The asymptotic distributions of partial likelihood‐based tests under local alternatives are derived, depending on various specifications of deterministic terms. A simulation study is then performed using both the full and partial systems. It is demonstrated that the rank tests based on the partial system, if a required parametric condition is fulfilled, can be more powerful than those based on the full system. This finding encourages testing cointegrating rank using a partial system as well as a full system, in such circumstances as the parametric condition could be satisfied.

Original article: Long-run exclusion and the determination of cointegrating rank: Monte Carlo evidence

Abstract: This note investigates long-run exclusion in a cointegrated vector autoregressive (VAR) model from the viewpoint of finite-sample statistical inference. Monte Carlo experiments show that, in various circumstances, a mis-specified partial VAR model, which is justified by the existence of a long-run excluded variable, can lead to better finite-sample inference for cointegrating rank than a fully specified VAR model. Implications of long-run exclusion for econometric modelling are then considered based on the Monte Carlo study.

Effects of a signal-to-noise ratio on finite sample inference for cointegrating vectors

This paper investigates effects of a signal-to-noise ratio on finite sample inference for cointegrating vectors. The ratio is defined as a measure of the magnitude of a permanent shock relative to a transitory shock. According to Monte Carlo experiments conducted in this paper, a high signal-to-noise ratio tends to reduce size distortions of a likelihood-based test statistic for a hypothesis on cointegrating vectors; a low signal-to-noise ratio is, in contrast, prone to amplify the size distortions. The experiments demonstrate that the performance of a bootstrap method also depends on the volume of the signal-to-noise ratio. Finally, an empirical illustration is presented.