비선형 GARCH모형을 이용한 일중 변동성의 베이지언 예측

박수남 ( Soo Nam Park ),김영재 ( Young Jae Kim ) 한국경제통상학회 2012 경제연구 Vol.30 No.4

The purpose of this paper is to apply a Bayesian method to simulate the modified nonlinear GARCH models. In addition, the paper specifies the forecast performances on several GARCH models. The main findings and implications are as follows: First, forecast performances on most of GARCH models are not significantly different across the experiments with different sample sizes, however, the performances are different across forecast points. This finding indicates that if one has enough observations then she needs not extend observation to forecast intraday volatilities. Second, the forecast power of all models is different across forecast time points, which represents that the forecast power of the GARCH models are not stable. The price volatility in UHF data is non-stationary so that a proper forecast model may depend on the forecast time points. Third, the more complicated model, the more required computing time. However, the difference of computing time across models is not significant so that t-distribution models can be applied to the forecast of intraday volatility.

Forecasting Volatility of Asymmetric and Nonlinear GARCH Models on Chinese Commodity Futures Prices

정상국 한국무역통상학회 2009 무역통상학회지 Vol.9 No.1

This article provided evidence of linkages between the news shock and volatility with regard to the daily price return in futures market of China. Some asymmetric and nonlinear generalized autoregressive conditional heteroskedasticity (GARCH) models are applied to verify the possibility of forecasting volatility of commodity futures in China, in terms of copper, aluminum and soybean. And some comparisons of performances with regard to these models are also evaluated through some test across all forecast horizons. The findings of this study are in order. First, through the parameter estimate for all models except exponential GARCH model, negative shocks have a larger effect on conditional volatility than positive shocks of the same magnitude. Second, according to the out-of-sample forecasting performance aimed at evaluating the nonlinear GARCH models, it is seen that GJR-GARCH and QGARCH models do better in describing the properties of the specific data on all four criteria across all forecast horizons. This article provided evidence of linkages between the news shock and volatility with regard to the daily price return in futures market of China. Some asymmetric and nonlinear generalized autoregressive conditional heteroskedasticity (GARCH) models are applied to verify the possibility of forecasting volatility of commodity futures in China, in terms of copper, aluminum and soybean. And some comparisons of performances with regard to these models are also evaluated through some test across all forecast horizons. The findings of this study are in order. First, through the parameter estimate for all models except exponential GARCH model, negative shocks have a larger effect on conditional volatility than positive shocks of the same magnitude. Second, according to the out-of-sample forecasting performance aimed at evaluating the nonlinear GARCH models, it is seen that GJR-GARCH and QGARCH models do better in describing the properties of the specific data on all four criteria across all forecast horizons.

ON STRICT STATIONARITY OF NONLINEAR ARMA PROCESSES WITH NONLINEAR GARCH INNOVATIONS

Lee, O. The Korean Statistical Society 2007 Journal of the Korean Statistical Society Vol.36 No.2

We consider a nonlinear autoregressive moving average model with nonlinear GARCH errors, and find sufficient conditions for the existence of a strictly stationary solution of three related time series equations. We also consider a geometric ergodicity and functional central limit theorem for a nonlinear autoregressive model with nonlinear ARCH errors. The given model includes broad classes of nonlinear models. New results are obtained, and known results are shown to emerge as special cases.

On Strict Stationarity of Nonlinear ARMA Processeswith Nonlinear GARCH Innovations

이외숙 한국통계학회 2007 Journal of the Korean Statistical Society Vol.36 No.3

We consider a nonlinear autoregressive moving average model with non-linear GARCH errors, and nd sucient conditions for the existence of astrictly stationary solution of three related time series equations. We alsoconsider a geometric ergodicity and functional central limit theorem for anonlinear autoregressive model with nonlinear ARCH errors. The givenmodel includes broad classes of nonlinear models. New results are obtained,and known results are shown to emerge as special cases.

Copula parameter change test for nonlinear AR models with nonlinear GARCH errors

Lee, S.,Kim, B. Elsevier BV 2015 Statistical methodology Vol.25 No.-

In this paper, we study the problem of testing for a copula parameter change in nonlinear autoregressive (AR) models with nonlinear generalized autoregressive conditional heteroskedasticity (GARCH) errors. To perform a test, we propose the cusum test based on pseudo maximum likelihood estimates of copula parameters. We derive its limiting null distribution under regularity conditions. For illustration, we conduct a simulation study with an emphasis on STAR-STGARCH models. A real data analysis applied to the S&P 500 index and IBM stock price is also considered.

On the Origins of Conditional Heteroscedasticity in Time Series

( Richard Ashley ) 한국경제학회 2012 The Korean Economic Review Vol.28 No.1

The volatility clustering frequently observed in financial/economic time series is often ascribed to GARCH and/or stochastic volatility models. This paper demonstrates the usefulness of reconceptualizing the usual definition of conditional heteroscedasticity as the (h = 1) special case of h-step-ahead conditional heteroscedasticity, where the conditional volatility in period t depends on observable variables up through period t - h. Here it is shown that, for h > 1, h-stepahead conditional heteroscedasticity arises - necessarily and endogenously - from nonlinear serial dependence in a time series; whereas one-step-ahead conditional heteroscedasticity (i.e., h = 1) requires multiple and heterogeneously-skedastic innovation terms. Consequently, the best response to observed volatility clustering may often be to model the nonlinear serial dependence which is likely causing it, rather than ``tacking on`` an ad hoc volatility model. Even where such nonlinear modeling is infeasible - or where volatility is quantified using, say, a model-free implied volatility measure rather than squared returns - these results suggest a re-consideration of the usefulness of lag-one terms in volatility models. An application to observed daily stock returns is given.

PARAMETER CHANGE TEST FOR NONLINEAR TIME SERIES MODELS WITH GARCH TYPE ERRORS

Lee, Jiyeon,Lee, Sangyeol Korean Mathematical Society 2015 대한수학회지 Vol.52 No.3

In this paper, we consider the problem of testing for a parameter change in nonlinear time series models with GARCH type errors. We introduce two types of cumulative sum (CUSUM) tests: estimates-based and residual-based tests. It is shown that under regularity conditions, their limiting null distributions are the sup of independent Brownian bridges. A simulation study is conducted for illustration.

PARAMETER CHANGE TEST FOR NONLINEAR TIME SERIES MODELS WITH GARCH TYPE ERRORS

이지연,이상열 대한수학회 2015 대한수학회지 Vol.52 No.3

In this paper, we consider the problem of testing for a param- eter change in nonlinear time series models with GARCH type errors. We introduce two types of cumulative sum (CUSUM) tests: estimates-based and residual-based tests. It is shown that under regularity conditions, their limiting null distributions are the sup of independent Brownian bridges. A simulation study is conducted for illustration.

채소류가격의 비선형동학적 특성

강태훈 ( Kang Tae Hun ) 한국농업경제학회 2004 農業經濟硏究 Vol.45 No.1

N/A This paper shows the nonlinear dynamics of weekly price changes of vegetables such as cabbage, radish, garlic, onions, red pepper, carrot, and green onions, which are under vegetable supply stabilization program As for the weekly rate of change, mere observations are found at the center and at both tails of the distribution than normal distribution which implies the data are better explained by student distribution. Vegetable prices show volatility clustering that they are sometimes volatile but sometimes tranquil. Volatilities follow a fairly strong seasonal pattern. Conditional volatilities are estimated using GARCH(1,1)-t model. Results show that past shocks remain in the conditional volatility persistently in all of the vegetable prices under consideration except red popper, In case of red pepper, the shock of one period ahead explains most of current conditional volatility and disappears fast.

GARCH with omitted persistent covariate

한희준,박준용 Elsevier 2014 economics letters Vol.1240 No.20140