• Journal of the Korean Statistical Society
• /
• v.36 no.1
• /
• pp.149-156
• /
• 2007

This study suggests a new method for testing seasonal unit roots in a momentum threshold autoregressive (MTAR) process. This sign test is robust against heteroscedastic or heavy tailed errors and is invariant to monotone data transformation. The proposed test is a seasonal extension of the sign test of Park and Shin (2006). In the case of partial seasonal unit root in an MTAR model, a Monte-Carlo study shows that the proposed test has better power than the seasonal sign test developed for AR model.

• Journal of the Korean Statistical Society
• /
• v.27 no.1
• /
• pp.57-66
• /
• 1998

In the analysis of time series it is an important issue to determine whether a time series under study is stationary. For the test of the stationary of the time series the Dickey-Fuller (DF) type tests have been mainly used. In this paper, we consider the regular unit root tests and seasonal unit root tests based on the generalized Durbin-Watson (DW) statistics when the errors are independent. The limiting distributions of the proposed DW-type test statistics are the functionals of standard Brownian motions. We also obtain the finite distributions and powers of the DW-type test statistics and compare the performances with the DF-type tests. It is observed that the DW-type test statistics have good behaviors against the DF-type test statistics especially in the nonzero (seasonal) mean model.

• Journal of the Korean Statistical Society
• /
• v.36 no.4
• /
• pp.447-456
• /
• 2007

On the basis of marginal likelihood of the residual vector which is free of nuisance mean parameters, we propose new Lagrange Multiplier seasonal unit root tests in seasonal autoregressive process. The limiting null distribution of the tests is the standardized ${\chi}^2-distribution$. A Monte-Carlo simulation shows the new tests are more powerful than the tests based on the ordinary least squares (OLS) estimator, especially for large number of seasons and short time spans.

• Communications for Statistical Applications and Methods
• /
• v.15 no.5
• /
• pp.719-726
• /
• 2008

In this paper we consider a joint test for seasonal cointegrating(CI) ranks that enables us to simultaneously model cointegrated structures across seasonal unit roots in seasonal cointegration. A CI rank test for a single seasonal unit root is constructed and extended to a joint test for multiple seasonal unit roots. Their asymptotic distributions and selected critical values for the joint test are obtained. Through a small Monte Carlo simulation study, we evaluate performances of the tests.

• Journal of the Korean Statistical Society
• /
• v.33 no.2
• /
• pp.149-157
• /
• 2004

The stationarity is one of the most important properties of a time series. We propose robust sign tests for seasonal autoregressive processes to determine whether or not a time series is stationary. The proposed tests are robust to the outliers and the heteroscedastic errors, and they have an exact binomial null distribution regardless of the period of seasonality and types of median adjustments. A Monte-Carlo simulation shows that the sign test is locally more powerful than the tests based on ordinary least squares estimator (OLSE) for heavy-tailed and/or heteroscedastic error distributions.

• Proceedings of the Korean Statistical Society Conference
• /
• 2003.05a
• /
• pp.281-286
• /
• 2003

The stationarity is one of the most important properties of a time series. We propose robust sign tests for seasonal autoregressive process to determine whether or not a time series is stationary. The tests have an exact binomial null distribution and are robust to the outliers and the heteroscedastic errors. Monte-Carlo simulation shows that the sign test is locally more powerful than the OLSE-based tests for heavy-tailed and/or heteroscedastic error distributions.

• Journal of the Korean Statistical Society
• /
• v.30 no.4
• /
• pp.597-612
• /
• 2001

We have developed a \

• Journal of the Korean Statistical Society
• /
• v.24 no.1
• /
• pp.77-90
• /
• 1995

The Lagrange multiplier test statistics for seasonal unit roots are derived and the asymptotic distributions of the derived statistics are obtained. The relationship between the derived LM test statistics and the "DHF" type regression t statistics are shown.are shown.

• Communications for Statistical Applications and Methods
• /
• v.2 no.2
• /
• pp.101-114
• /
• 1995

In this paper we consider the multiple unit root tests both for the regular and seasonal unit roots based on the Lagrange Multiplier(LM) principle. Unlike Li(1991)'s method, by plugging the restricted maximum likelihood estimates of the nuisance parameters in the model, we propose a Lagrange multiplier test which does not depend on the existence of the nuisance parameters. The asymptotic distribution of the proposed statistic is derived and empirical percentiles of the test statistic for selected seasonal periods are provided. The power and size of the test statistic for examined for finite samples through a Monte Carlo simularion.

• The Korean Journal of Applied Statistics
• /
• v.21 no.5
• /
• pp.783-789
• /
• 2008

We investigate the effects of the misspecification of cointegrating(CI) ranks at other frequencies on the inference of seasonal models at the frequency of interest; our study includes tests for CI ranks and estimation of CI vectors. Earlier studies focused mostly on a single frequency corresponding to one seasonal root at a time, ignoring possible cointegration at the remaining frequencies. We investigate the effects of the mis-specification, especially in finite samples, by adopting Gaussian reduced rank(GRR) estimation by Ahn and Reinsel (1994) that considers cointegration at all frequencies of seasonal unit roots simultaneously. It is observed that the identification of the seasonal CI rank at the frequency of interest is sensitive to the mis-prespecification of the CI ranks at other frequencies, mainly when the CI ranks at the remaining frequencies are underspecified.