HYGARCH Models Research Articles

ANALYSIS OF WEAK-FORM EFFICIENCY WITH STRUCTURAL FRACTURE LONG MEMORY MODELS IN BIST MAIN SECTOR INDEXES

Hisse senetlerinde uzun hafızanın varlığı, piyasanın zayıf formda etkin olmadığını göstermekte ve piyasa katılımcılarını hisse senedi piyasasının hareketlerini tahmin etmeye yöneltmektedir. Bu çalışmada Borsa İstanbul sektör endekslerinin getiri serilerinin varyansında (mali, sınai, hizmet ve teknoloji) uzun hafızanın varlığı 30.07.2000-12.03.2021 dönemi için günlük veriler dikkate alınarak araştırılmıştır. Bu amaçla Borsa İstanbul’un dört endeksine FIGARCH, FIEGARCH, FIAPARCH ve HYGARCH modelleri uygulanmıştır. Elde edilen sonuçlar, ele alınan dört endeksin uzun hafıza özelliği taşıdığını, diğer bir ifade ile endekslerin zayıf formda etkin olmadığını ortaya koymuştur. Ayrıca tüm endekslerde pozitif şokların volatilite üzerinde negatif şoklardan daha güçlü etkiye sahip olduğu tespit edilmiştir. Elde edilen sonuçlar mevcut veya potansiyel yatırımcılara, portföy yöneticilerine ve politika yapıcılara borsadaki uzun hafızanın dinamik doğasını anlamada yardımcı olacaktır.

KRİPTOPARA PİYASA VOLATİLİTESİNİN MODELLENMESİ, TAHMİNİ VE BİTCOİN’İN RİSKE MARUZ DEĞER DİNAMİKLERİ

Bitcoin volatility was investigated with various symmetric and asymmetric models in the study. In addition, value at risk (VaR) was calculated by using the Kupiec LR test and the error prediction performances of the models were compared. As a result of the work, the long memory of volatility in Bitcoin returns was found. It means the cryptocurrency market is not efficient. According to the FIAPARCH asymmetric model, it was determined that positive information shocks reaching the Bitcoin market increased volatility more than negative information shocks. Comparing the error prediction performance of the models by calculating VaR, the HYGARCH model prediction results were found to be superior to other models included in the study. Thus, it was determined that the most suitable model in predicting the volatility, namely the risk of Bitcoin in short and long positions for those who consider investing in Bitcoin, is the asymmetric model HYGARCH.

Stock-return volatility persistence over short and long range horizons: Some empirical evidences

In this paper, we account for memory failure or otherwise in the daily evolution of stock return and volatility within the purview of short and long ranges based on the arrival of fundamental news. This accounts for the return on assets in the current period to be a function of returns realized in the pasts. To achieve this objective, we estimated ARMA, ARFIMA, GARCH, FIGARCH and HYGARCH models. After implementing maximum likelihood estimation technique, we found out that the ARMA coefficients were not significant, the GARCH coefficients were significant and the memory coefficients in terms of ARFIMA, FIGARCH and HYGARCH were statistically significant. In the light of these, we propose the rejection of efficient hypothesis in the long range and document a single memory in volatility in the short range. The study recommends that ARFIMA and HYGARCH are the best forecasting models for return and volatility respectively in the Nigerian stock market.

Smooth Transition HYGARCH Model: Stability and Testing

HYGARCH process is commonly used for modeling long memory volatility. Many financial time series are characterized by transition between different levels of volatilities. Smooth transition HYGARCH (ST-HYGARCH) model is proposed to model smooth transition between components of HYGARCH process. The behavior of the conditional variance in the ST-HYGARCH are allowed to change smoothly over time. The asymptotic finiteness of the second moment is studied. A score test is developed to check the smooth transition property. The performance of the new proposed model and the score test are examined by some simulations. Applying the log returns of some part of S&P500 and Dow Jones industrial average indexes, we show the competing performance of the ST-HYGARCH model in comparison to HYGARCH and ST-GARCH models in forecasting volatility and value-at-risk.

Volatility forecasting, downside risk, and diversification benefits of Bitcoin and oil and international commodity markets: A comparative analysis with yellow metal

This study examines the diversification and hedging properties of Bitcoin (BTC) and gold assets for oil and S&P GSCI investors. We model and forecast the volatility performance of the pairs BTC–oil, gold–oil, BTC–S&P GSCI, and gold–GSCI using five bivariate DCC-GARCH family models, two popular forecasting measures (MSE and MAE), the Diebold and Mariano (1995) test, and different risk measures (value-at-risk, expected shortfall, semivariance, and regret) for different portfolios. We find that BTC and gold provide diversification benefits for oil and S&P GSCI. Moreover, by comparing the fitting and forecast performances of the five GARCH models, we find that the standard GARCH model is the best for the gold–oil and BTC–S&P GSCI pairs, while the HYGARCH model is the best for the BTC–oil and gold–S&P GSCI pairs regardless of the time horizon. Finally, we find strong evidence of hedging effectiveness and downside risk reductions, confirming the importance of BTC and gold in oil and S&P GSCI portfolio management.

Markov switch smooth transition HYGARCH model: Stability and estimation

HYGARCH model is basically used to model long-range dependence in volatility. We propose Markov switch smooth-transition HYGARCH model, where the volatility in each state is a time-dependent convex combination of GARCH and FIGARCH. This model provides a flexible structure to capture different levels of volatilities and also short and long memory effects. The necessary and sufficient condition for the asymptotic stability is derived. Forecast of conditional variance is studied by using all past information through a parsimonious way. Bayesian estimations based on Gibbs sampling are provided. A simulation study has been given to evaluate the estimations and model stability. The competitive performance of the proposed model is shown by comparing it with the HYGARCH and smooth-transition HYGARCH models for some period of the S&P500 and Dow Jones industrial average indices based on volatility and value-at-risk forecasts.

Modeling High Frequency Data with Long Memory and Structural Change: A-HYEGARCH Model

In this paper, we propose an Adaptive Hyperbolic EGARCH (A-HYEGARCH) model to estimate the long memory of high frequency time series with potential structural breaks. Based on the original HYGARCH model, we use the logarithm transformation to ensure the positivity of conditional variance. The structural change is further allowed via a flexible time-dependent intercept in the conditional variance equation. To demonstrate its effectiveness, we perform a range of Monte Carlo studies considering various data generating processes with and without structural changes. Empirical testing of the A-HYEGARCH model is also conducted using high frequency returns of S&P 500, FTSE 100, ASX 200 and Nikkei 225. Our simulation and empirical evidence demonstrate that the proposed A-HYEGARCH model outperforms various competing specifications and can effectively control for structural breaks. Therefore, our model may provide more reliable estimates of long memory and could be a widely useful tool for modelling financial volatility in other contexts.

A new hyperbolic GARCH model

There are two commonly used hyperbolic GARCH processes, the FIGARCH and HYGARCH processes, in modeling the long-range dependence in volatility. However, the FIGARCH process always has infinite variance, and the HYGARCH model has a more complicated form. This paper builds a simple bridge between a common GARCH model and an integrated GARCH model, and hence a new hyperbolic GARCH model along the lines of FIGARCH models. The new model remedies the drawback of FIGARCH processes by allowing the existence of finite variance as in HYGARCH models, while it has a form nearly as simple as the FIGARCH model. Two inference tools, including the Gaussian QMLE and a portmanteau test for the adequacy of the fitted model, are derived, and an easily implemented test for hyperbolic memory is also constructed. Their finite sample performances are evaluated by simulation experiments, and an empirical example gives further support to our new model.

Functional central limit theorems for augmented GARCH([formula omitted]) and FIGARCH processes

In this paper, we study the functional central limit theorem(FCLT) for the augmented GARCH process introduced by Duan (1997). We prove under proper moment assumptions that the process is geometrically L2-NED and then the FCLT holds. The fractional FCLT for FIGARCH processes is also considered. We examine the FCLT for the APGARCH, EGARCH and HYGARCH models as examples.

On the estimation and diagnostic checking of the ARFIMA–HYGARCH model

The estimation and diagnostic checking of the fractional autoregressive integrated moving average with hyperbolic generalized autoregressive conditional heteroscedasticity (ARFIMA–HYGARCH) model is considered. The ARFIMA–HYGARCH model is a long-memory model for the conditional mean that also allows for long memory in the conditional variance, the latter given by an HYGARCH model that nests both the GARCH and integrated GARCH models. It is therefore important to provide a thorough treatment of its statistical inference. Asymptotic properties of the maximum likelihood estimators under the Student’s t distribution are established, and the asymptotic normality of the Gaussian quasi-maximum likelihood estimation is also derived. Two portmanteau test statistics based on the residual autocorrelations and squared residual autocorrelations are defined and their asymptotic distributions are derived. These tests will be useful in model diagnostic checking. Simulation results show that the tests have reasonable empirical size and power.

Dual long memory property in returns and volatility: Evidence from the CEE countries' stock markets

This paper investigates the presence of long memory in the eight Central and Eastern European (CEE) countries' stock market, using the ARFIMA, GPH, FIGARCH and HYGARCH models. The data set consists of daily returns, and long memory tests are carried out both for the returns and volatilities of these series. The results of the ARFIMA and GPH models indicate the existence of long memory in five of eight return series. The results also suggest that long memory dynamics in the returns and volatility might be modeled by using the ARFIMA–FIGARCH and ARFIMA–HYGARCH models. The results of these models indicate strong evidence of long memory both in conditional mean and conditional variance. Moreover, the ARFIMA–FIGARCH model provides the better out-of-sample forecast for the sampled stock markets.

Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model

This article analyses the statistical properties of that general class of conditional heteroscedasticity models in which the conditional variance is a linear function of squared lags of the process. GARCH, IGARCH, FIGARCH, and a newly proposed generalization, the HYGARCH model, belong to this class. Conditions are derived for the existence of second and fourth moments, and for the limited memory condition of near-epoch dependence. The HYGARCH model is applied to 10 daily dollar exchange rates, and also to data for Asian exchange rates over the 1997 crisis period. In the latter case, the model exhibits notable stability across the pre-crisis and post-crisis periods.