Mototsugu Shintani

Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos

This paper derives the asymptotic distribution of the nonparametric neural network estimator of the Lyapunov exponent in a noisy system. Positivity of the Lyapunov exponent is an operational definition of chaos. We introduce a statistical framework for testing the chaotic hypothesis based on the estimated Lyapunov exponents and a consistent variance estimator. A simulation study to evaluate small sample performance is reported. We also apply our procedures to daily stock return data. In most cases, the hypothesis of chaos in the stock return series is rejected at the 1% level with an exception in some higher power transformed absolute returns.

Testing for a Unit Root Against Transitional Autoregressive Models

This article develops a novel test for a unit root in general transitional autoregressive models, which is based on the infimum of t‐ratios for the coefficient of a parametrized transition function. Our test allows for very flexible specifications of the transition function and short‐run dynamics and is significantly more powerful than all the other existing tests. Moreover, we develop a large sample theory general enough to deal with randomly drifting parameter spaces, which is essential to properly test for a unit root against stationary transitional models. An empirical application of our test to the exchange rate data is also provided.

No evidence of chaos but some evidence of dependence in the US stock market

Abstract This paper uses recent advances in the field of applied econometrics and tools from dynamical systems theory to test for random walks and chaos in the US stock market, using daily observations on the Dow Jones Industrial Average (from January 3, 1928 to October 18, 2000––a total of 18,490 observations). In doing so, we follow the recent contribution by Whang and Linton [J Econometr 91 (1999) 1] and construct the standard error for the Nychka et al. [J Roy Statist Soc B 54 (1992) 399] dominant Lyapunov exponent, thereby providing a statistical test of chaos. We find statistically significant evidence against low-dimensional chaos and point to the use of stochastic models and statistical inference in the modeling of asset markets.

A Simple Cointegrating Rank Test Without Vector Autoregression

This paper proposes a fully nonparametric test for cointegrating rank which does not require estimation of a vector autoregressive model. The test exploits the fact that the degeneracy in the moment matrix of the variables with mixed integration order corresponds to the notion of cointegration. With an appropriate standardization, the test statistics are shown to have a nuisance parameter free limiting distribution and to be consistent under reasonable conditions. Monte Carlo experiments also suggest that the performance of the test is satisfactory with a moderate sample size. The proposed tests are applied to the stochastic growth model using the U.S. aggregate data.

Nonlinear Forecasting Analysis Using Diffusion Indexes: An Application to Japan

This paper extends the diffusion index (DI) forecast approach of Stock and Watson (1998, 2002) to the case of possibly nonlinear dynamic factor models. When the number of series is large, a two-step procedure based onthe method of principal components is useful since it allows wide variety of nonlinearity in the factors. The factors extracted from a large Japanese data suggest some evidence of nonlinear structure. Furthermore, both the linear and nonlinear DI forecasts in Japan outperform traditional time series forecasts, while the linear DI forecast, in most cases, performs as well as the nonlinear DI forecast.

Testing for a unit root against transitional autoregressive models

This article develops a novel test for a unit root in general transitional autoregressive models, which is based on the infimum of t‐ratios for the coefficient of a parametrized transition function. Our test allows for very flexible specifications of the transition function and short‐run dynamics and is significantly more powerful than all the other existing tests. Moreover, we develop a large sample theory general enough to deal with randomly drifting parameter spaces, which is essential to properly test for a unit root against stationary transitional models. An empirical application of our test to the exchange rate data is also provided.

The Inf‐T Test for a Unit Root Against Asymmetric Exponential Smooth Transition Autoregressive Models

This paper proposes a new test for a unit root against an alternative of asymmetric exponential smooth transition autoregressive models, by extending the infimum test developed by Park and Shintani. Simulation results suggest that the test performs reasonably well in finite samples. The proposed test is also applied to real exchange rates to examine their asymmetric and nonlinear mean-reverting properties.

Measuring international business cycles by saving for a rainy day

Macroeconomics inevitably begins with a trend-cycle decomposition of a nations output. We propose a decomposition in which consumption is the trend component and savings is the cycle component. Using data from the G-7 plus Australia, we show that this decomposition identifies international business cycles that are: (i) more volatile, (ii) of longer mean duration and (iii) less correlated across countries than the cycle component from the Hodrick-Prescott filter. We argue that this difference stems from the fact that our method imposes a basic theoretical restriction arising from the permanent income hypothesis similar to the restriction used in Cochranes ( ) decomposition.

Asymptotic Inference for Dynamic Panel Estimators of Infinite Order Autoregressive Processes

In this paper we consider the estimation of a dynamic panel autoregressive (AR) process of possibly infinite order in the presence of individual effects. We employ double asymptotics under which both the cross-sectional sample size and the length of time series tend to infinity and utilize the sieve AR approximation with its lag order increasing with the sample size. We establish the consistency and asymptotic normality of the fixed effects estimator and propose a bias-corrected fixed effects estimator based on a theoretical asymptotic bias term. Monte Carlo simulations demonstrate the usefulness of bias correction. As an illustration, the proposed methods are applied to dynamic panel estimation of the law of one price deviations among US cities.

Improving the Finite Sample Performance of Autoregression Estimators in Dynamic Factor Models: A Bootstrap Approach

ABSTRACT We investigate the finite sample properties of the estimator of a persistence parameter of an unobservable common factor when the factor is estimated by the principal components method. When the number of cross-sectional observations is not sufficiently large, relative to the number of time series observations, the autoregressive coefficient estimator of a positively autocorrelated factor is biased downward, and the bias becomes larger for a more persistent factor. Based on theoretical and simulation analyses, we show that bootstrap procedures are effective in reducing the bias, and bootstrap confidence intervals outperform naive asymptotic confidence intervals in terms of the coverage probability.