국면전환 임계 자기회귀 분석을 위한 베이지안 방법 비교연구 = A Comparison Study of Bayesian Methods for a Threshold Autoregressive Model with Regime-Switching

국문 초록 (Abstract)

자기회귀 모형(autoregressive model)은 일변량(univaraite) 시계열자료의 분석에서 널리 사용되는 방법 중 하나이다. 그러나 이 방법은 자료에 일정한 추세가 있다고 가정하기 때문에 자료에 분절(structural break)이 존재할 때 적절하지 않을 수 있다. 이러한 문제점을 해결하기 위한 방법으로 국면전환(regime-switching) 모형인 임계자기회귀 모형(threshold autoregressive model)이 제안되었는데 최근 지연 모수(delay parameter)을 포함한 이 국면전환(two regime-switching) 모형으로 확장되어 많은 연구가 활발히 진행되고 있다. 본 논문에서는 이 국면전환 임계자기회귀 모형을 베이지안(Bayesian) 관점에서 살펴본다. 베이지안 분석을 위해 모수적 임계자기 회귀 모형 뿐만 아니라 디리슐레 과정(Dirichlet Process) 사전분포를 이용하는 비모수적 임계자기 회귀 모형을 고려하도록 한다. 두 가지 베이지안 임계자기 회귀 모형을 바탕으로 사후분포를 유도하고 마코프 체인 몬테 카를로(Markov chain Monte Carlo) 방법을 통해 사후추론을 실시한다. 모형 간의 성능을 비교하기 위해 모의실험을 통한 자료 분석을 고려하고, 더 나아가 한국과 미국의 국내 총생산(Gross Domestic Product)에 대한 실증적 자료 분석을 실시한다.

다국어 초록 (Multilingual Abstract)

Autoregressive models are used to analyze an univariate time series data; however, these methods can be inappropriate when a structural break appears in a time series since they assume that a trend is consistent. Threshold autoregressive models (popular regime-switching models) have been proposed to address this problem. Recently, the models have been extended to two regime-switching models with delay parameter. We discuss two regime-switching threshold autoregressive models from a Bayesian point of view. For a Bayesian analysis, we consider a parametric threshold autoregressive model and a nonparametric threshold autoregressive model using Dirichlet process prior. The posterior distributions are derived and the posterior inferences is performed via Markov chain Monte Carlo method and based on two Bayesian threshold autoregressive models. We present a simulation study to compare the performance of the models. We also apply models to gross domestic product data of U.S.A and South Korea.

참고문헌 (Reference)

1 Tang, M. A., "Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions" Springer 1998

2 Tong, H., "Threshold autoregressions, limit cycles, and data" 42 : 245-292, 1980

3 Sargan, J. D., "The estimation of economic relationships using instrumental variables" 26 : 397-415, 1958

4 Chow, G. C., "Tests of equality between sets of coefficients in two linear regressions" 28 : 591-605, 1960

5 Geman, S., "Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images" 6 : 721-741, 1984

6 Lee, R. H., "Regime switching research of GDP for Korea and the United States using Baysian analysis" 25-26, 2014

7 Tong, H., "Pattern Recognition and Signal Processing" Sijthoff and Noordhoff 101-141, 1978

8 Barrientos, A. F., "On the support of MacEachern’s dependent Dirichlet processes and extensions" 7 : 277-309, 2012

9 Müller, P., "Nonparametric Bayesian inference" 9 : 2013

10 Tong, H., "Non-linear Time Series: A Dynamical System Approach" Oxford University Press 1990

11 Hastings, W. K., "Monte Carlo sampling methods using Markov chains and their applications" 57 : 97-109, 1970

12 Burns, A., "Measuring Business Cycles" NBER 1946

13 Koop, G., "Impulse response analysis in nonlinear multivariate models" 74 : 119-147, 1996

14 Ishwaran, H., "Gibbs sampling methods for stick-breaking priors" 96 : 161-173, 2001

15 Metropolis, N., "Equation of state calculations by fast computing machines" 21 : 1087-1092, 1953

16 Koop, G., "Dynamic asymmetries in US unemployment" 17 : 298-312, 1999

17 MacEachern, S. N., "Dependent nonparametric process" 50-55, 1999

18 MacEachern, S. N., "Dependent Dirichlet processes, Technical Paper" Department of Statistics, Ohio State University 2000

19 Terasvirta, T., "Characterizing nonlinearities in business cycle using smooth transition autoregressive models" 7 : S119-S136, 1992

20 Geweke, J. F., "Bayesian threshold autoregressive models for nonlinear time series" 14 : 441-454, 1993

21 Hjort, N. L., "Bayesian nonparametrics" Cambridge University Press 2010

22 De I, M., "Bayesian nonparametric nonproportional hazards survival modeling" 65 : 762-771, 2009

23 Chen, C. W. S., "Bayesian inference of threshold autoregressive models" 16 : 483-492, 1995

24 Rodriguez, A., "Bayesian dynamic density estimation" 3 : 339-365, 2008

25 Koop, G., "Bayesian Econometric Methods" Cambridge University Press 2007

26 Gelman, A., "Bayesian Data Analysis, Third Edition" CRC press 2014

27 McCulloch, R. E., "Bayesian Analysis of Threshold Autoregressive Processes with a Random Number of Regimes" Interface Foundation of North America 253-262, 1993

28 Potter, S. M., "A nonlinear approach to US GNP" 10 : 109-126, 1995

29 Hamilton, J. D., "A new approach to the economic analysis of nonstationary time series and the business cycle" 57 : 357-384, 1989

30 Sethuraman, J., "A constructive definition of Dirichlet priors" 4 : 639-650, 1994

31 Di Lucca, M, A., "A Simple class of Bayesian nonparametric autoregression models" 8 : 63-88, 2013

32 Ferguson, T. S., "A Bayesian analysis of some nonparametric problems" 1 : 209-230, 1973