Non-Markovian Regime-Switching Models

김창진,김재호 한국계량경제학회 2023 JOURNAL OF ECONOMIC THEORY AND ECONOMETRICS Vol.34 No.4

To date, almost all extensions and applications of Hamilton’s (1989) regime switching model have been based on the assumption that the latent regimeindicator variable follows a Markovian switching process. This paper doubts the universal validity of this assumption and develops an MCMC algorithm for estimation of the non-Markovian regime switching model which employs an autoregressive continuous latent variable in specifying the dynamics of the discrete latent regime-indicator variable within the Probit specification. We show that, in spite of the non-Markovian nature of the discrete regime indicator variable, the Markovian property of this continuous latent variable allows us to successfully estimate the model. Our empirical results suggest that, for modeling volatility of the stock return, the non-Markovian switching model is strongly preferred to the Markovian switching model. However, for modeling the regime-switching nature of the business cycle based on real GDP, the convention of assuming Markovian switching seems to be valid.

KOSPI 200을 이용한 국면전환 연속시간 확률 변동성 모형의 추정

최승문 한국계량경제학회 2019 계량경제학보 Vol.30 No.1

This article estimates regime-switching continuous-time stochastic volatility models using daily KOSPI 200. We consider single regime Heston, GARCH, and CEV stochastic volatility models and 6 regime-switching stochastic volatility models which have two different regimes L and H. We employ Hamilton algorithm (Hamilton (1989)) to compute the log-likelihood and to apply MLE. Because the true transition probability density functions (TPDFs) of our stochastic volatility models are unknown, we use Ait-Sahalia (2008) and Choi (2015b) to obtain closed-form approximate TPDF. The regime-switching CEV model where the transition probability is allowed to vary over time has been found to be the best to explain the movements of KOSPI 200. Regime L has a stronger leverage effect than regime H. Comparing to regime L, the volatility variable tends to revert to its long-run mean level more rapidly, the volatility of volatility variable is greater, the probability of staying in the same regime H in the next period is bigger in regime H. And the transition probability varies with time depending on the stock price rather than the volatility. When the probabilities of regime H are high we could identify various economic and political events between South Korea and North Korea or inside or outside South Korea that could have affected Korean stock market. 이 논문에서는 KOSPI 200 일별 자료를 이용해 국면전환 (regime-switching) 연속시간 (continuous-time) 확률 변동성 (stochastic volatility) 모형들을 추정한다. 단일국면 Heston, GARCH, 그리고 CEV 확률 변동성 모형들과 두 가지 다른 국면 L과 H이 있는 6개의 국면전환 확률 변동성 모형들을 고려한다. 추정 방법은 해밀턴 알고리즘 (Hamilton (1989))을 이용해 우도 함수의 값을 계산하고 최우추정법을 이용한다. 우리의 확률 변동성 모형들의 전이 확률밀도 함수들을 알지 못하기에 Ait-Sahalia (2008)와 Choi (2015b)를 이용해 근사적이고 구체적인 식으로 구한다. 전이 확률이 시간에 따라 변하는 경우의 국면전환 CEV 모형이 KOSPI 200 자료를 가장 잘 설명한다는 추정 결과를 얻었다. L국면이 H국면보다 레버리지 효과가 더 컸다. 그리고 국면 L과 비교해 국면 H에서 변동성 변수가 장기적인 평균 수준으로 더 빨리 돌아오는 경향이 있었고, 변동성 변수의 변동성도 더 컸으며, 국면 H에 있을 때 다음 기에 같은 국면에 있을 확률이 더 컸고, 전이확률이 변동성 변수 보다는 주가에 의존하며 시간에 따라 변한다는 결과를 얻었다. 국면 H에 있을 확률이 높았던 시기에는 남북 관계나 대내외적으로 한국 주식 시장에 영향을 줄 수 있는 정치, 경제적인 여러 사건들이 있는 경우가 많았다.

국면전환모형을 이용한 제조업 경기변동 분석

박성근,김정현,최용옥 산업연구원 2023 산업연구(JIET) Vol.7 No.1

This study analyzes the business cycles of the manufacturing, chemical, steel, and semiconductor industries in Korea using an endogenous regime- switching model. We extract the cyclical component from the seasonally adjusted production index and apply the endogenous regime-switching model to the extracted cyclical component. We then compare and analyze the results obtained from the endogenous regime-switching model with those obtained using traditional methods, and draw implications. The empirical analysis reveals that the chemical and semiconductor industries show results similar to those obtained by traditional methods, with the regime determined based on a zero cyclical component. In contrast, the manufacturing and steel industries, which experienced relatively large declines in business cycles, the model determines the low regime parsimoniously compared to the traditional method. This indicates that the endogenous regime-switching model can be useful in detecting and analyzing relatively severe crises. The fact that the troughs of the extracted latent factors preceded the troughs of the cyclical components indicates that the endogenous regime-switching model can provide useful information for determining and predicting business cycle regimes.

Regime-Switching GARCH모형을 이용한 주택시장 변동성 구조 및 예측에 관한 실증분석

김종하(Kim, Jong Ha) 한국지역개발학회 2017 韓國地域開發學會誌 Vol.29 No.4

For the forecast of fluctuation in housing market, whose importance is growing, the present study compared GARCH model, which is generally used for the forecast of fluctuation, and RS-GARCH model, which considers business regime switching. In the result of analysis, when the profit rate of housing market was analyzed using GARCH model, the GARCH effect was found to be significant. However, it was confirmed that the analysis had the problem of overmeasuring fluctuation. On the contrary, when it was analyzed using RS-GARCH model, the existence of regimes was found to be significant and two regimes were analyzed to have different characteristics. Therefore, it was confirmed that there was the effect of regime-switching in domestic housing market and that more accurate analysis results could be deduced if the regimes are considered when analyzing housing market. When the variables that affect house profit rate were analyzed, the effect of variables was found to be different by regime. Loan rate was found to have positive effect in regime 1 (expansion) and negative effect in regime 2(contraction).

Bayesian Regime-switching Analysis via Stochastic Approximation Monte Carlo

전수영,이희찬 한국자료분석학회 2011 Journal of the Korean Data Analysis Society Vol.13 No.2

Monte Carlo methods have received much attention in the recent literature of the regime- switching analysis. However, the conventional Markov chain Monte Carlo (MCMC) algorithms, such as Metropolis-Hastings, tend to get trapped in a local mode in simulating from the posterior distribution of regime-switching time-series, rendering the inference ineffective. In this paper, we focus on the finding the best likelihood value in Bayesian nonlinear time-series model (Kim and Cheon, 2010) and the detection of multiple regime-switching in monthly simple returns and quarterly unemployment rate via the stochastic approximation Monte Carlo algorithm (Liang et al., 2007). The numerical results indicate that our method outperforms MCMC significantly for the regime-switching identification, and provide 3 and 5 regime switchings in monthly simple returns and quarterly unemployment rate, respectively.

Modeling the Dynamics between Stock Price and Dividend: An Endogenous Regime Switching Approach

( Heejoon Han ),( Na Kyeong Lee ) 한국경제학회 2018 The Korean Economic Review Vol.34 No.2

This study considers a new error correction model (ECM) for stock price and dividend, which accommodates nonlinearities in both long- and short-run relationships. First, timevarying coefficient cointegration is adopted to explain the nonlinear long-run relationship between stock price and dividend. Second, the model allows for endogenous regime switching to describe the short-run relationship. The empirical application on the S&P 500 Index and dividend shows that our model fits the data significantly better than existing models and provides estimates with meaningful interpretations. In addition, the linear cointegration is unsuitable to describe the long-run relationship, and the ECM with endogenous regime switching better explains the data than that with conventional Markov switching. An extract latent factor specifically reveals the periods for each regime, and the periods of high-volatility regime include the NBER recession periods and certain periods of financial crisis.

Return Predictability using an Endogenous Regime Switching Model

정민수(Minsoo Jeong),Chang Sik Kim,Nayul Kim 한국계량경제학회 2022 JOURNAL OF ECONOMIC THEORY AND ECONOMETRICS Vol.33 No.1

This paper examines whether stock excess return predictability is dependent upon the stock market volatility. The paper introduces a two-state regime switching model with endogenous feedback effect for the stock return predictability test. To model regime switching, this paper adopted a new approach proposed by Chang et al. (2017), allowing an endogenous feedback effect channel through which the underlying time series affect the next period volatility regime. This paper shows that modeling such a channel is important in the return predictability context to incorporate the leverage effect. Monte Carlo simulation results demonstrated that additional power gain and bias improvement could be achieved in the endogenous regime swithcing (ERS) model, compared to the conventional Markov switching model. The empirical test results using the ERS model indicate that none of the tested predictors have significant predictive power when stock returns are highly volatile. However, the dividend-price ratio and macro variables such as T-bill rate and term spread had significant predictability, at least in the low volatility regime.

내생적 국면 전환을 이용한 실현 변동성 모형

김세정,한희준 한국계량경제학회 2016 계량경제학보 Vol.27 No.4

This paper introduces and analyzes a new model for realized volatility that accommodates endogenous regime switching. The model is based on the heterogeneous autoregressive model and allows for two-state regime switching. Importantly, a current shock to the realized volatility affects the regime switching in the next period. We apply the model to the realized volatility of the daily S&P 500 Index return series. The estimation result shows that the short-term volatility component is the most influential in the high volatility regime while the long-term volatility component is dominant in the low volatility regime. Moreover, the model significantly outperforms existing models in within-sample fitting. 본 논문은 금융 시계열의 실현 변동성을 설명하기 위해 내생적 국면 전환을 도입한 새로운 모형을 제안하고 분석하고 있다. 모형은 이질적 자기회귀(hetorogenous autoregressive) 모형을 기반으로 한 두 국면(two-state) 전환 모형이다. 모형에서 가장 중요한 특징은 현재 기의 실현 변동성에 대한 충격이 다음 기 국면 전환에 영향을 미치는 내생적 국면 전환 구조를 도입한 점이다. 본 모형을 일별 S&P 500 지수 수익률의 실현 변동성에 적용한 결과, 변동성이 높은 국면에서는 단기 변동성 요인이 다음 기 변동성에 지배적인 영향을 미치는 반면 변동성이 낮은 국면에서는 장기 변동성 요인이 지배적인 영향을 미치는 것으로 나타났다. 또한 내생적 국면 전환을 도입함에 따라 기존 모형들에 비해 표본기간 내 설명력이 유의하게 개선되는 것으로 나타났다.

Investment under Ambiguity and Regime-Switching Environment

U Jin Choi,Kwangmoon Kim,Minsuk Kwak 한국재무학회 2009 한국재무학회 학술대회 Vol.2009 No.05

We consider all or nothing investment problem with a finite time horizon when the investment opportunity set is changing stochastically over time, especially under Markovian regime-switching environment, and a decision maker faces ambiguity of parameters governing prot ow dynamics of the investment. We apply a-Maxmin Expected Utility(a-MEU) preferences to re ect the ambiguity seeking attitude of de- cision maker and provide semi-explicit formulas for the expected value of investment and the critical present value of the profit fow. Numerical results show that the crit- ical present value of the profit fow depends on the business cycle and the tendency of ambiguity seeking is mitigated in case of project whose profit fow is dependent on regime-switching environment.

대외적 변동성충격에 대한 국면별 주택시장의 비대칭적 반응 연구

정재호(Chung, Jae-Ho),김종하(Kim, Jong-Ha) 한국부동산정책학회 2018 不動産政策硏究 Vol.19 No.1

The objective of this study was to empirically analyze the asymmetric response of the housing market to the volatility shocks. Two regimes were assumed for the analysis and the analysis period was from January 2004 to December 2017. The analysis results of the study implied that, first of all, the housing market revealed volatility clustering. In other words, it showed considerable variations over a substantially long period and maintained a relatively stable period alternately. Moreover, the results of this study confirmed that there was a GARCH effect within each regime. Secondly, the variables affecting the housing price earning rate varied by regime. The exchange rate was the main variable of this study and it was more influential in regime 2 than in regime 1. Therefore, it would be important to manage the interest rate politically when an external shock occurs. Thirdly, the mortgage interest rate had different effects on the housing market in regime 1 and regime 2. It adversely affected the housing price agreeing with the theoretical basis during regime 1. However, it had positive effects on the housing price during the regime 2, accompanying with abrupt volatility. In other words, if a volatility shock occurs in the South Korean housing market, the volume of the mortgage loan will increase even though the price is rising.