Koichi Maekawa

The sampling distributions of the predictor for an autoregressive model under misspecifications

Abstract Approximations to the sampling distributions of the predictor are given misspecifying the autoregressive moving average model as an autoregressive model. We deal with both conditional and unconditional distributions for the dependent and independent cases according to whether the sample data used in estimation and in prediction are dependent or not. The bias and mean squared error are easily obtained from these approximations.

Test for Parameter Change in ARIMA Models

ABSTRACT In this article we consider the problem of testing for parameter changes in ARIMA models based on the cusum test. The proposed test procedure is applicable to testing for the change from stationary models to non stationary models, and vice versa. The idea is to transform the time series via differencing to make the whole time series as a combination of stationary subseries. For this task, we propose a graphical method to identify the right order of differencing. Then the cusum test statistic proposed by Lee et al. (2003) is constructed based the differenced time series. Simulation study and real data analysis are provided for illustration.

Estimating break points in a time series regression with structural changes

In econometric literatures, a number of tests for unit roots have been proposed in the presence of structural changes in I(1) and I(0) model when the numbers of break points are or are not known (though their locations are unknown). Recently, Hatanaka and Yamada [A unit root test in the presence of structural changes in I(1) and I(0) models, in: R.F. Engle, H. White (Eds.), Cointegration, Causality, and Forecasting: A Festschrift in Honour of Clive W.J. Granger, Oxford University Press, Oxford, 1999 (Chapter 11)] proposed a unit root test consisted of two steps: estimating break points and testing a unit root, but their methods resulted in remarkable negative biases in the break points estimates. Our paper attempts to eliminate the negative biases by utilizing the weighted symmetric estimation.

Comparing the Wald, LR and LM tests for heteroscedasticity in a linear regression model

Abstract We compare the power of the Wald, likelihood ratio, and Lagrangian multiplier tests for heteroscedasticity between two sample regimes in a linear regression model through the asymptotic expansion of the non-null distribution for the three tests up to O 1 N , where n is the sample size. As a result, we see that the power of the three tests depends on both the nature of the explanatory variables and the direction of the alternative hypothesis and that no one statistic is uniformly superior to the others. However, if the moments of the explanatory variables are stable over the whole sample period, then the asymptotic power, up to O 1 N , is equivalent for the three tests.

Professor Michio Hatanaka

This interview with Michio Hatanaka is the first in this series given in the East, of which we are very proud. Hatanaka is a pioneer of econometrics in Japan. In the early 1950s he traveled to the United States to study as a graduate student at Vanderbilt University. That step was really unusual in the Japanese profession at that time. His stay in the States was extended to 1966, during which time he taught at Princeton and Rochester. His pathfinding behavior influenced and encouraged many Japanese scholars. Hatanaka started his academic career as a mathematical economist. This may partly explain why his research papers suggest deep economic thought as well as deep understanding of mathematics and statistics. His early contributions to econometrics are concerned with applying the spectral method to various economic problems. These contributions include the associate authorship of Spectral Analysis of Economic Time Series by C. W. J. Granger. His other contributions cover theoretical work on identification and estimation problems for dynamic econometric models, among which Hatanakas efficient two-step estimator is well known. His research also includes empirical work on the Japanese economy and economic policy, which is relatively less known to people outside of Japan. His attitude toward research has set a standard for Japanese econometricians. His research papers are always a product of deep and full thought, and imbued with his own originality.