Yuzo Hosoya

Elimination of Third-series Effect and Defining Partial Measures of Causality

Using the one-way effect extraction method, this paper presents a set of partial causal measures which represents quantitatively the interdependence between a pair of vector-valued processes in the presence of a third process. Those measures are defined for stationary as well as for a class of non-stationary time series. In contrast to conventional conditioning methods, the partial concept defined in the paper would be mostly devoid of feedback distortion by the third process. The paper also discusses statistical inference on the proposed measures.

The quasi-likelihood approach to statistical inference on multiple time-series with long-range dependence☆

Abstract The paper gives a unified approach to dealing with multiple long-memory time-series possessing a variety of singularities in their spectrum, based on the quasi-likelihood function. It proposes quasi-maximum-likelihood estimation and the quasi-likelihood ratio test for statistical inference purposes. A large-sample theory is given by means of a bracketing function approach under very general conditions, without the usual assumptions of Gaussianity or exact martingale differences for innovation processes. The paper also discusses the particular characteristic of modelling long-memory time-series which influences the type of the quasi-likelihood function and produces distinct differences in the asymptotic properties of related statistics.

Harmonizable stable processes

SummaryThis paper examines properties of a class of complex-valued stable processes which have spectral representation by means of independent-increments processes. A representation is derived by an application of Schilders stochastic integral. Also, another construction of harmonizable stable processes by means of generalized stochastic processes is given, and its relation to the stochastic integral is shown. Some limit theorems of the Fourier transform of a sample from harmonizable stable processes are provided. Moreover, a linear prediction theory which pertains to those processes is suggested as an extension of that of second-order stationary processes.

Inference on one-way effect and evidence in Japanese macroeconomic data

This paper provides an approach to testing a variety of causal characteristics expressed in terms of the measures of one-way effect for cointegrated vector time series. For this purpose, we propose Wald tests and their computational algorithm by means of the measures of one-way effect, incorporating Johansens algorithm for the maximum likelihood estimates and the likelihood ratio tests. Using the Wald test statistics, the paper also provides a method of confidence-set construction for the causal measures. The approach proposed in the paper includes testing Grangers non-causality as an instance of its multiple applications. As an illustration, the paper presents a characterization of the causal structure of the recent Japanese macroeconomy on the basis of the proposed method and the derived evidence.

A Simultaneous Test in the Presence of Nested Alternative Hypotheses

This paper considers the generalized likelihood ratio (GLR) test or its modification dealing with nested models. The algorithm for evaluating the critical values and the error-rates for the canonical tests are provided; a table of critical values of a class of GLR tests is also given. The test proposed in the paper has applications in time-series model selection. This paper explores a generalization of the likelihood-ratio test in order to deal with testing a hypothesis against nested alternatives. Though such a testing situation is very common in the practice of time-series analysis (take for instance testing the hypothesis of white noise against the autoregressive hypotheses of various orders), there does not seem to be an established general method of dealing with it, except probably for the one which chooses the most complicated as the alternative, which is not necessarily a reasonable choice when a simpler alternative is true. The paper proposes a simultaneous use of several likelihood-ratio statistics which is termed a generalized likelihood ratio (GLR) test and a use of a transformation method of such statistics in cases where an algorithmic impasse with respect to the evaluation of simultaneous distribu- tion arises.

A numerical method for factorizing the rational spectral density matrix

Improving Rozanov (1967, Stationary Random Processes. San Francisco: Holden-day.)s algebraic-analytic solution to the canonical factorization problem of the rational spectral density matrix, this article presents a feasible computational procedure for the spectral factorization. We provide numerical comparisons of our procedure with the Bhansalis (1974, Journal of the Statistical Society, B36 , 61.) and Wilsons (1972 SIAM Journal on Applied Mathematics, 23 , 420) methods and illustrate its application in estimation of invertible MA representation. The proposed procedure is usefully applied to linear predictor construction, causality analysis and other problems where a canonical transfer function specification of a stationary process in question is required. Copyright Copyright 2010 Blackwell Publishing Ltd

Ancillarity and the Limited Information Maximum-Likelihood Estimation of a Structural Equation in a Simultaneous Equation System

The concepts of the curved exponential family of distributions and ancillarity are applied to estimation problems of a single structural equation in a simultaneous equation model, and the effect of conditioning on ancillary statistics on the limited information maximum-likelihood (LIML) estimator is investigated. The asymptotic conditional covariance matrix of the LIML estimator conditioned on the second-order asymptotic maximal ancillary statistic is shown to be efficiently estimated by Liu and Breens formula. The effect of conditioning on a second-order asymptotic ancillary statistic, i.e., the smallest characteristic root associated with the LIML estimation, is analyzed by means of an asymptotic expansion of the distribution as well as the exact distribution. The smallest root helps to give an intuitively appealing measure of precision of the LIML estimator.

Some limit theorems on stationary processes with long-range dependence

The paper provides central limit theorems on multivariate stationary processes with long-range dependence as a natural extension of the corresponding theory on short-range dependent processes. In order to establish those theorems, the paper imposes weak assumptions on conditional moments of innovation processes, dispensing with the usual assumptions of exact Martingale difference or the contemporaneously transformed Gaussianity.

INFORMATION AMOUNT AND HIGHER-ORDER EFFICIENCY IN ESTIMATION

By means of second-order asymptotic approximation, the paper clarifies the relationship between the Fisher information of first-order asymptotically efficient estimators and their decision-theoretic performance. It shows that if the estimators are modified so that they have the same asymptotic bias, the information amount can be connected with the risk based on convex loss functions in such a way that the greater information loss of an estimator implies its greater risk. The information loss of the maximum likelihood estimator is shown to be minimal in a general set-up. A multinomial model is used for illustration.

The Measures of One-Way Effect, Reciprocity, and Association

To characterize the interdependent structure of a pair of two jointly second-order stationary processes , this chapter introduces the (overall as well as frequency-wise) measures of one-way effect, reciprocity, and association. Section 2.2 defines the Granger and Sims non-causality and establishes their equivalence for a general class of (not necessarily stationary) second-order processes. Sections 2.3 and 2.4 define the overall and frequency-wise one-way effect measures and provide three ways of deriving the frequency-wise measure. One is based on direct canonical factorization of the spectral density matrix. The other two are based on distributed-lag representation and innovation orthogonalization, respectively. Each approach provides a different representation of the same quantity. Section 2.5 introduces the overall and the frequency-wise measures of reciprocity and association.