Asymmetric Power GARCH Research Articles

A Zero-Inflated Poisson Asymmetric Power GARCH Model for $$\mathbb {Z}$$-valued Time Series

A Zero-Inflated Poisson Asymmetric Power GARCH Model for $$\mathbb {Z}$$-valued Time Series

Forecasting BDI Sea Freight Shipment Cost, VIX Investor Sentiment and MSCI Global Stock Market Indicator Indices: LSTAR-GARCH and LSTAR-APGARCH Models

Prediction of the economy in global markets is of crucial importance for individuals, decisionmakers, and policies. To this end, effectiveness in modeling and forecasting the directions of such leading indicators is of crucial importance. For this purpose, we analyzed the Baltic Dry Index (BDI), Investor Sentiment Index (VIX), and Global Stock Market Indicator (MSCI) for their distributional characteristics leading to proposed econometric methods. Among these, the BDI is an economic indicator based on shipment of dry cargo costs, the VIX is a measure of investor fear, and the MSCI represents an emerging and developed county stock market indicator. By utilizing daily data for a sample covering 1 November 2007–30 May 2022, the BDI, VIX, and MSCI indices are investigated with various methods for nonlinearity, chaos, and regime-switching volatility. The BDS independence test confirmed dependence and nonlinearity in all three series; Lyapunov exponent, Shannon, and Kolmogorov entropy tests suggest that series follow chaotic processes. Smooth transition autoregressive (STAR) type nonlinearity tests favored two-regime GARCH and Asymmetric Power GARCH (APGARCH) nonlinear conditional volatility models where regime changes are governed by smooth logistic transitions. Nonlinear LSTAR-GARCH and LSTAR-APGARCH models, in addition to their single-regime variants, are estimated and evaluated for in-sample and out-of-sample forecasts. The findings determined significant prediction and forecast improvement of LSTAR-APGARCH, closely followed by LSTAR-GARCH models. Overall results confirm the necessity of models integrating nonlinearity and volatility dynamics to utilize the BDI, VIX, and MSCI indices as effective leading economic indicators for investors and policymakers to predict the direction of the global economy.

Estimation of multivariate asymmetric power GARCH models

We suggest a new class of multivariate power transformed asymmetric models. It includes several functional forms of multivariate GARCH models which are of great interest in financial modeling and time series literature. We provide an explicit necessary and sufficient condition to establish the strict stationarity of the model. The asymptotic properties of the quasi-maximum likelihood estimator of the parameters are established. The asymptotic results are illustrated by Monte Carlo experiments and an application to real financial data is studied.

Portmanteau test for a class of multivariate asymmetric power GARCH model

We establish the asymptotic behaviour of the sum of squared residuals autocovariances and autocorrelations for the class of multi‐variate power transformed asymmetric models. We then derive a portmanteau test. We establish the asymptotic distribution of the proposed statistics. These asymptotic results are illustrated by Monte Carlo experiments. An application to a bivariate real financial data is also proposed.

Portmanteau test for the asymmetric power GARCH model when the power is unknown

It is now widely accepted that, to model the dynamics of daily financial returns, volatility models have to incorporate the so-called leverage effect. We derive the asymptotic behaviour of the squared residuals autocovariances for the class of asymmetric power GARCH model when the power is unknown and is jointly estimated with the model’s parameters. We then deduce a portmanteau adequacy test based on the autocovariances of the squared residuals. These asymptotic results are illustrated by Monte Carlo experiments. An application to real financial data is also proposed.

The impact of COVID-19 on S&P500 sector indices and FATANG stocks volatility: An expanded APARCH model

In this paper we hypothesize that not all stocks and sectors are affected equally by COVID-19 in terms of return volatility. Specifically, we hypothesize that at least some sectors (Information Technology, Consumer Discretionary, Telecom Services, Consumer Staples and Energy) must show statistically significant differences. We analyze eleven SP500 sectors and FATANG stocks, estimating an Asymmetric Power GARCH model including a dummy variable to account for the outbreak. Results reveal an exacerbation of volatility after February 2020 and validate our hypothesis with few exceptions. Based on a likelihood ratio test, the null hypothesis is rejected in most cases in favor of our APARCH(1, 1).

Hybrid quantile estimation for asymmetric power GARCH models

Asymmetric power GARCH models have been widely used to study the higher order moments of financial returns, while their quantile estimation has been rarely investigated. This paper introduces a simple monotonic transformation on its conditional quantile function to make the quantile regression tractable. The asymptotic normality of the resulting quantile estimators is established under either stationarity or non-stationarity. Moreover, based on the estimation procedure, new tests for strict stationarity and asymmetry are also constructed. This is the first try of the quantile estimation for non-stationary ARCH-type models in the literature. The usefulness of the proposed methodology is illustrated by simulation results and real data analysis.

COVID-19’s disasters are perilous than Global Financial Crisis: A rumor or fact?

This investigation employed the Asymmetric Power GARCH model and found that COVID-19 substantially harms the US and Japan's market returns. Moreover, COVID-19 has influenced the variance of the US, Germany, and Italy's stock markets more than the Global Financial Crises (GFC). However, GFC indicated a more significant impact on the financial volatility of the Nikkei 225 index and SSEC than COVID-19. The study confirmed the leverage effect for the S&P 500, Nasdaq Composite Index, DAX 30, Nikkei 225, FTSE MIB, and SSEC. The analysis authenticated that the health crisis that befell due to COVID-19 have imperatively originated the financial crisis globally; however, the Asian markets still make available better prospects for portfolio optimization.

Forecasting of the Nigeria Stock Returns Volatility Using GARCH Models with Structural Breaks

This study examines the stock returns series using Symmetric and Asymmetric GARCH models with structural breaks in the presence of some varying distribution assumptions. Volatility models of Symmetric GARCH (1,1), Asymmetric Power GARCH (1,1) and GJR-GARCH(1,1) models were considered in estimating and measuring shock persistence, leverage effects and mean reversion rate with structural breaks considering dummy variable for these structural changes and varying distributions . The skewed student-t distribution is considered best distribution for the models; moreover findings showed the high persistence of shock in returns series for the estimated models. However, when structural breaks were incorporated in the estimated models by including dummy variable in the conditional variance equations of all the models, there was significant reduction of shock persistence parameter and mean reversion rate. The study found the GJR-GARCH (1,1) with skewed student-t distribution best fit the series. The volatility was forecasted for 12 months period using GJR-GARCH (1,1) model and the values are compared with the actual values and the results indicates a continuous increase in unconditional variance.

Bayesian analysis of periodic asymmetric power GARCH models

Abstract In this paper, we set up a generalized periodic asymmetric power GARCH (PAP-GARCH) model whose coefficients, power, and innovation distribution are periodic over time. We first study its properties, such as periodic ergodicity, finiteness of moments and tail behavior of the marginal distributions. Then, we develop an MCMC algorithm, based on the Griddy-Gibbs sampler, under various distributions of the innovation term (Gaussian, Student-t, mixed Gaussian-Student-t). To assess our estimation method we conduct volatility and Value-at-Risk forecasting. Our model is compared against other competing models via the Deviance Information Criterion (DIC). The proposed methodology is applied to simulated and real data.

TEPCO’s (Tokyo Electric Power Co Holdings) Stock Behaviour in the Long Run

Noting the huge impact of the Fukushima accident on TEPCO’s (Tokyo Electric Power Co Holdings) activity and stock price, this study investigates the long-run patterns of returns and volatility of its stock, relative to the main return and volatility features of the Nikkei 225 over the past 30 years. The best fitting volatility for both series comes from an asymmetric power GARCH model; the standard deviation of volatility does not depend primarily on large innovations. For the Nikkei, large negative changes are not more clustered than positive changes. A regime-switching correlation model with three states reveals that a high correlation regime is the most frequent for TEPCO, with low switching probability, whereas the regime associated with the Fukushima crisis is less persistent. A strong interaction arises between the less common regimes, but the stable, low volatility regime appears mostly independent. In two regimes, the Nikkei returns have significant and negative effects on TEPCO returns, but the reverse is not true. The Fukushima environmental and industrial crisis thus could spark a new energetic era in Japan, including a real transition toward more environmentally friendly electric power.

Generalized quasi-maximum likelihood inference for periodic conditionally heteroskedastic models

This paper establishes consistency and asymptotic normality of the generalized quasi-maximum likelihood estimate (GQMLE) for a general class of periodic conditionally heteroskedastic time series models (PCH). In this class of models, the volatility is expressed as a measurable function of the infinite past of the observed process with periodically time-varying parameters, while the innovation is an independent and periodically distributed sequence. In contrast with the aperiodic case, the proposed GQMLE is rather based on S instrumental density functions where S is the period of the model while the corresponding asymptotic variance is in a “sandwich” form. Application to the periodic asymmetric power GARCH model is given. Moreover, we also discuss how to apply the GQMLE to the prediction of power problem in a one-step framework and to PCH models with complex periodic patterns such as high frequency seasonality and non-integer seasonality.

Volatility in High-Frequency Intensive Care Mortality Time Series: Application of Univariate and Multivariate GARCH Models

Mortality time series display time-varying volatility. The utility of statistical estimators from the financial time-series paradigm, which account for this characteristic, has not been addressed for high-frequency mortality series. Using daily mean-mortality series of an exemplar intensive care unit (ICU) from the Australian and New Zealand Intensive Care Society adult patient database, joint estimation of a mean and conditional variance (volatility) model for a stationary series was undertaken via univariate autoregressive moving average (ARMA, lags (p, q)), GARCH (Generalised Autoregressive Conditional Heteroscedasticity, lags (p, q)). The temporal dynamics of the conditional variance and correlations of multiple provider series, from rural/ regional, metropolitan, tertiary and private ICUs, were estimated utilising multivariate GARCH models. For the stationary first differenced series, an asymmetric power GARCH model (lags (1, 1)) with t distribution (degrees-of- freedom, 11.6) and ARMA (7,0) for the mean-model, was the best-fitting. The four multivariate component series demonstrated varying trend mortality decline and persistent autocorrelation. Within each MGARCH series no model specification dominated. The conditional correlations were surprisingly low (<0.1) between tertiary series and substantial (0.4 - 0.6) between rural-regional and private series. The conditional-variances of both the univariate and multivariate series demonstrated a slow rate of time decline from periods of early volatility and volatility spikes.

Markov Switching Artificial Neural Networks for Modelling and Forecasting Volatility: An Application to Gold Market

Abstract The study analyses the family of regime switching GARCH neural network models, which allow the generalization of MS type RS-GARCH models to MS-GARCH-NN models by incorporating with neural network architectures. Proposed models differ in terms of both the dynamics of the conditional volatility process and the forecasting capabilities compared to a family of GARCH models. Gray (1996) RS-GARCH model allows regime dependent heteroscedasticity structure following the markov switching methodology of Hamilton (1989). The MS-GARCH-NN model family differ in the sense that, they allow regime switching between GARCH-NN processes. Single regime GARCH-NN models are developed by Donaldson and Kamstra (1996) and further extended by Bildirici and Ersin (2009). Further, the proposed models incorporate a variety of neural network architectures. MS-GARCH-MLP and MS-GARCH-Hybrid-MLP models by Bildirici and Ersin(2014) are augmented with fractional integration (FI) and asymmetric power GARCH variants. And they developed models are MS-FIGARCH-Hybrid-MLP, MS-APGARCH-Hybrid-MLP and MS-FIAPGARCH-Hybrid-MLP models. In this paper, these models were used to test volatility of gold return. Tests are evaluated with MAE, MSE and RMSE criteria and equal forecast accuracy is tested with modified Diebold-Mariano tests. An empirical application is provided for forecasting daily returns in gold market. The results suggest that the proposed approach performs well in modeling and forecasting volatility in daily returns of international gold market.

Causality between inflation and inflation uncertainty in South Africa: Evidence from a Markov-switching vector autoregressive model

Abstract This study investigates the asymmetric and time-varying causalities between inflation and inflation uncertainty in South Africa within a conditional Gaussian Markov switching vector autoregressive (MS-VAR) model framework. The MS-VAR model is capable of determining both the sign and direction of causality. We account for the nonlinear, long memory and seasonal features of the inflation series simultaneously by measuring inflation uncertainty as the conditional variance of inflation generated by recursive estimation of a Seasonal Fractionally Integrated Smooth Transition Autoregressive Asymmetric Power GARCH (SEA-FISTAR-APGARCH) model using monthly data for the period 1921:01 to 2012:12. The recursive, rather than full-sample, estimation allows us to obtain a time-varying measure of uncertainty and better mimics the real-time scenario faced by economic agents and/or policy makers. The inferred probabilities from the four-state MS-VAR model show evidence of a time-varying relationship. The conditional (i.e. lead–lag) and regime-prediction Granger causality provide evidence in favor of Friedman's hypothesis. This implies that past information on inflation can help improve the one-step-ahead prediction of inflation uncertainty but not vice versa. Our results have some important policy implications.

Estimating Value at Risk for Sukuk Market Using Generalized Auto Regressive Conditional Heteroskedasticity Models

In this paper, we compare the forecasting ability of different GARCH models to estimate value at risk in sukuk market. A wide extensive list of both symmetric and asymmetric GARCH models (including GARCH, EGARCH, GJR-GARCH, IGARCH and Asymmetric power GARCH) were considered in modeling the volatility in the sukuk market. All VaR estimations are carried out by “rugarch” package in “R” software. The performance of these models is compared by both in-sample and out-of-sample analysis. We found that the performance of asymmetric models in estimating value at risk are superior in both in-sample and out-of-sample evaluation. We also found that in most cases the student-t distribution is more preferable than normal or generalized error distribution (GED).

Modeling Markov Switching ARMA-GARCH Neural Networks Models and an Application to Forecasting Stock Returns

The study proposes and a family of regime switching GARCH neural network models to model volatility. The proposed MS-ARMA-GARCH-NN models allow MS type regime switching in both the conditional mean and conditional variance for time series and further augmented with artificial neural networks to achieve improvement in forecasting capabilities. Gray (1996) RS-GARCH model allows within regime heteroskedasticity with markov switching of Hamilton (1989). Firstly, models are extended to fractional integration and asymmetric power GARCH and MS-ARMA-FIGARCH, MS-ARMA-APGARCH, MS-ARMA-FIAPGARCH models are evaluated and discussed. Secondly, in addition to regime swiching type nonlinearity, neural networks based augmentated models are evaluated and discussed. In this respect, MS-ARMA-GARCH models are augmented with Multi Layer Perceptron (MLP), Radial Basis Function (RBF), Elman type Recurrent NN (Elman RNN), Time lag (delay) Recurrent NN (RNN) and Hybrid MLP models. Therefore, the second model group includes MS-ARMA-GARCH-MLP, MS-ARMA-GARCH-RBF, MS-ARMA-GARCH-ElmanRNN, MS-ARMA-GARCH-RNN and MS-ARMA-GARCH-HybridMLP. Thirdly, fractional integrated versions are augmented with neural networks and denoted as MS-ARMA-FIGARCH-MLP, MS-ARMA-FIGARCH-RBF, MS-ARMA-FIGARCH-ElmanRNN, MS-ARMA-FIGARCH-RNN and MS-ARMA-FIGARCH-HybridMLP. Fourth, by allowing asymmetric power transformations, models are further extended to GARCH models. These models are MS-ARMA-APGARCH-RBF, MS-ARMA-APGARCH-ElmanRNN, MS-ARMA-APGARCH-RNN and MS-ARMA-FIGARCH-HybridMLP. Therefore, a total of four group of GARCH models are proposed and evaluated in the study. In the empirical application section, daily stock returns in ISE100 Istanbul Stock Index are modeled and forecasted. Forecast success is evaluated with MAE, MSE and RMSE criteria. Equal forecast accuracy is tested with modified Diebold-Mariano tests. Accordingly, fractional integration and asymmetric power transformation perform better in modeling the daily returns in IMKB100 stock index compared to the simple GARCH and RS-GARCH model of Gray. Hybrid MLP and time lag recurrent architectures (MS-ARMA-FIAPGARCH-HybridMLP and MS-ARMA-FIAPGARCH-RNN) provided the best forecast and modeling performance. In conclusion, the newly proposed GARCH models have significant forecasting improvement and therefore are promising in various economic applications.

V-uniform ergodicity of a continuous time asymmetric power GARCH(1,1) model

Abstract A continuous time asymmetric power GARCH(1,1) model is presented and the V-uniform ergodicity and β -mixing property of the process with exponential decay rate are proved. The V-uniform ergodicity of the COGARCH(1,1) model is obtained as a special case.

Modeling and Explaining the Dynamics of European Union Allowance Prices at High-Frequency

In this paper we model the adjustment process of European Union Allowance (EUA) prices to the releases of announcements at high-frequency controlling for intraday periodicity, volatility clustering and volatility persistence. We find that the high-frequency EUA price dynamics are very well captured by a fractionally integrated asymmetric power GARCH process. The decisions of the European Commission on second National Allocation Plans have a strong and immediate impact on EUA prices. On the other hand, our results suggest that EUA prices are only weakly connected to indicators about the future economic development as well as the current economic activity.

Modeling and explaining the dynamics of European Union Allowance prices at high-frequency

In this paper we model the adjustment process of European Union Allowance (EUA) prices to the releases of announcements at high-frequency controlling for intraday periodicity, volatility clustering and volatility persistence. We find that the high-frequency EUA price dynamics are very well captured by a fractionally integrated asymmetric power GARCH process. The decisions of the European Commission on second National Allocation Plans have a strong and immediate impact on EUA prices. On the other hand, our results suggest that EUA prices are only weakly connected to indicators about the future economic development as well as the current economic activity.