Smooth Transition GARCH Models Research Articles

The smooth transition GARCH model for simulation of highly nonstationary earthquake ground motions

The aim of this paper is to extend a stochastic model for simulation of highly nonstationary ground motions (GMs). In this model, the dual-tree complex discrete wavelet transform (DT-CDWT) is applied to a recorded ground motion to extract its wavelet coefficients and then the Smooth Transition Generalized Autoregressive Conditional Heteroscedastic (ST-GARCH) model is used to simulate these coefficients. This model simulates nonstationary features of real GMs greatly, because the conditional variance estimated by this model changes compatibly with the amplitude nonstationary features of real GMs. Because of having asymmetric structure, this model also estimates sudden changes in the amplitude of ground motions. Some of the special capabilities of this model are the simulation of multiple increasing–decreasing cycles in the temporal amplitude of GMs, prediction of several peaks in the frequency spectrum of GMs, estimation of steps of their energy curve, and simultaneous simulation of all shocks of a GM sequence. Also, this model simulates the time–frequency energy distribution of both wide-frequency and narrow-frequency bandwidth GMs.

Asymmetric volatility in cryptocurrency markets: New evidence from smooth transition GARCH models

This paper investigates the presence of asymmetric volatility dynamics in Bitcoin, Ethereum, Ripple, and Litecoin. Asymmetric effects between good and bad news are traditionally modeled using threshold GARCH models that allow only for two possible variance regimes. We experiment a slightly flexible specification for the conditional variance by using a Smooth Transition GARCH (ST-GARCH) model, where a continuum of intermediate states is allowed between the two extreme volatility regimes. We feature an inverted asymmetric reaction for the majority of cryptocurrencies. The presence of positive return-volatility relationship, which is different from other traditional assets, supports the safe-haven hypothesis in cryptocurrencies.

Markov switching asymmetric GARCH model: stability and forecasting

A new Markov switching asymmetric GARCH model is proposed where each state follows the smooth transition GARCH model, represented by Lubrano (Recherches Economiques de Louvain 67:257–287, 2001), that follows a logistic smooth transition structure between effects of positive and negative shocks. This consideration provides better forecasts than GARCH, Markov switching GARCH and smooth transition GARCH models, in many financial time series. The asymptotic finiteness of the second moment is investigated. The parameters of the model are estimated by applying MCMC methods through Gibbs and griddy Gibbs sampling. Applying the log return of some part of $$ S \& P\ 500$$ indices, we show the competing performance of in sample fit and out of sample forecast volatility and value at risk of the proposed model. The Diebold–Mariano test shows that the presented model outperforms all competing models in forecast volatility.

Pair trading based on quantile forecasting of smooth transition GARCH models

Pair trading is a statistical arbitrage strategy used on similar assets with dissimilar valuations. We utilize smooth transition heteroskedastic models with a second-order logistic function to generate trading entry and exit signals and suggest two pair trading strategies: the first uses the upper and lower threshold values in the proposed model as trading entry and exit signals, while the second strategy instead takes one-step-ahead quantile forecasts obtained from the same model. We employ Bayesian Markov chain Monte Carlo sampling methods for updating the estimates and quantile forecasts. As an illustration, we conduct a simulation study and empirical analysis of the daily stock returns of 36 stocks from U.S. stock markets. We use the minimum square distance method to select ten stock pairs, choose additional five pairs consisting of two companies in the same industrial sector, and then finally consider pair trading profits for two out-of-sample periods in 2014 within a six-month time frame as well as for the entire year. The proposed strategies yield average annualized returns of at least 35.5% without a transaction cost and at least 18.4% with a transaction cost.

Smooth Transition GARCH Models in Forecasting Non-Linear Economic Time Series Data

The need to capture the heterogeneous and volatility nature of both financial and economic time series theory and modeling their behavior in practical work have stimulated interest in the empirical modeling of variances which forms the basis for this study. In the study we augmented GARCH models with smooth transition model by dropping the assumption of autoregression of the model; necessary theoretical frame work was derived and properties of the new model established and illustrated with foreign exchange rate data from Federal Republic of Nigeria (Naira), Great Britain (Pound), Botswana (Pula) and Japanese (Yen) against United States of America (Dollar). The smooth transition GARCH model is better than the classical GARCH model as there were reduction in the variances of the augmented model; this claim is confirmed by the empirical illustration with foreign exchange data. Within the group of smooth transition GARCH model, Logistic Smooth Transition is adjudged the best as it produced the least variance.

Non‐linear GARCH models for highly persistent volatility

Summary In this paper we study a new class of nonlinear GARCH models. Special interest is devoted to models that are similar to previously introduced smooth transition GARCH models except for the novel feature that a lagged value of conditional variance is used as the transition variable. This choice of the transition variable is mainly motivated by the desire to find useful models for highly persistent volatility. The underlying idea is that high persistence in conditional variance is related to relatively infrequent changes in regime, which can be captured by a suitable specification of the new model. Using the theory of Markov chains, we provide sufficient conditions for the stationarity and existence of moments of various smooth transition GARCH models and even more general nonlinear GARCH models. An empirical application to an exchange rate return series demonstrates the differences between the new model and conventional GARCH models.

Modeling the volatility of the US SαP 500 index using an LSTGARCH model

Modélisation de la volatilité de l’indice américain SαP 500 par un modèle LSTGARCH Cet article propose une modélisation empirique de la volatilité de l’indice SαP 500 américain à l’aide de modèles GARCH à transition douce. Dans ces modèles, la volatilité est décrite par des changements de régimes à l’aide de variables dont la dynamique gouverne des effets de seuil. Nous appliquons un test permettant de discriminer entre des effets GARCH habituels et des effets GARCH avec des dynamiques variables au cours du temps. Une comparaison avec d’autres modèles montre une prédominance des modèles à seuil.

Bayesian estimation of smooth transition GARCH model using Gibbs sampling

Research into time series models of changing variance and covariance, which is often called volatility model, has exploded in the last 10 years. Financial series are characterized by periods of large volatility followed by periods of relative quietness. This type of clustering led to the idea that volatility is predictable. The ARCH and GARCH models were quite successful in predicting volatility compared to more traditional methods. But better predictions are obtained when asymmetries and nonlinearities in the response of volatility to news arriving in the market are taken into account. In this paper we propose a new kind of asymmetric GARCH in which the conditional variance obeys two different regimes with a smooth transition function. In this model, the conditional variance reacts differently to negative and positive shocks and its magnitude on shocks have separate effects. As financial data have very often a high frequency of observation, smooth transition seems a priori better than an abrupt transition. The change of regime occurs when the residuals cross the threshold zero. This threshold GARCH models can be generalized using a smooth transition function F T( η, s t ) taking continuous values between zero and one. We treat the joint point t * and the speed of adjustment η to be two unknown parameters.

Nonlinear GARCH Models for Highly Persistent Volatility

In this paper we study new nonlinear GARCH models mainly designed for time series with highly persistent volatility. For such series, conventional GARCH models have often proved unsatisfactory because they tend to exaggerate volatility persistence and exhibit poor forecasting ability. Our main emphasis is on models that are similar to previously introduced smooth transition GARCH models except for the novel feature that a lagged value of conditional variance is used as the transition variable. This choice of the transition variable corresponds to the idea that high persistence in conditional variance is related to relatively infrequent changes in regime. Using the theory of Markov chains we provide sufficient conditions for the stationarity and existence of moments of the considered smooth transition GARCH models and even some more general nonlinear GARCH models. Empirical applications to two exchange rate return series show that the new models can be superior to conventional GARCH models especially in longer term forecasting.

Bayesian option pricing using asymmetric GARCH models

This paper shows how one can compute option prices from a Bayesian inference viewpoint, using a GARCH model for the dynamics of the volatility of the underlying asset. The proposed evaluation of an option is the predictive expectation of its payoff function. The predictive distribution of this function provides a natural metric, provided it is neutralised with respect to risk, for gauging the predictive option price or other option evaluations. The proposed method is compared to the Black and Scholes evaluation, in which a marginal mean volatility is plugged, but which does not provide a natural metric. The methods are illustrated using symmetric, asymmetric and smooth transition GARCH models with data on a stock index in Brussels.

Smooth Transition Garch Models: a Bayesian Perspective

SummaryThis paper proposes a new kind of asymmetric GARCH where the conditional variance obeys two different regimes with a smooth transition function. In one formulation, the conditional variance reacts differently to negative and positive shocks while in a second formulation, small and big shocks have separate effects. The introduction of a threshold allows for a mixed effect. A Bayesian strategy, based on the comparison between posterior and predictive Bayesian residuals, is built for detecting the presence and the shape of non-linearities. The method is applied to the Brussels and Tokyo stock indexes. The attractiveness of an alternative parameterisation of the GARCH model is emphasised as a potential solution to some numerical problems.