Asymmetric Power GARCH Model Research Articles

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.

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.

Asymmetric Volatility in Emerging and Mature Markets

In his Nobel Laureate lecture Engle notes that asymmetric volatility has a significant impact on risk. In this article equity market volatility is estimated using an asymmetric power-GARCH model which nests many other popular models. We estimate the magnitude of asymmetric volatility for several emerging and mature markets for three sub-periods. Many mature markets exhibit large magnitudes of asymmetric volatility and several emerging markets do so as well. The magnitude of asymmetry varies by sub-period and is consistent with the suggestion in Campbell and Hentschel (1992) that asymmetry is greater when markets are more volatile.

On Valuing Participating Life Insurance Contracts with Conditional Heteroscedasticity

In this paper, we consider a novel approach for the fair valuation of a participating life insurance policy when the dynamics of the reference portfolio underlying the policy are governed by an Asymmetric Power GARCH (APGARCH) model with innovations having a general parametric distribution. The APGARCH model provides a flexible way to incorporate the effect of conditional heteroscedasticity or time-varying conditional volatility and nests a number of important symmetric or asymmetric ARCH-type models in the literature. It also provides a flexible way to capture both the memory effect of the conditional volatility and the asymmetric effects of past positive and negative returns on the current conditional volatility, called the leverage effect. The key valuation tool here is the conditional Esscher transform of Buhlmann et al. (1996, 1998). The conditional Esscher transform provides a convenient and flexible way for the fair valuation under different specifications of the conditional heteroscedastic models. We illustrate the practical implementation of the model using the S&P 500 index as a proxy for the reference portfolio. We also conduct sensitivity analysis of the fair value of the policy with respect to the parameters in the APGARCH model to document the impacts of different conditional volatility models nested in the APGARCH model and the leverage effect on the fair value. The results of the analysis reveal that the memory effect of the conditional volatility has more significant impact on the fair value of the policy than the leverage effect.

A power GARCH examination of the gold market

This paper investigates macroeconomic influences on gold using the asymmetric power GARCH model (APGARCH) of [Ding, Z., Granger, C.W.J., Engle, R.F, 1993. Long memory property of stock market returns and a new model. J. Empirical Finance 1, 83–106]. In this model the power term is estimated within the model rather than specified by the authors. This paper examines both cash and futures prices of gold and significant economic variables over the 1983–2003 period, with special focus on two periods, around the 1987 and 2001 equity market crashes. As specified in [Ding, Z., Granger, C.W.J., Engle, R.F., 1993. Long memory property of stock market returns and a new model. J. Empirical Finance 1, 83–106] a number of autoregressive conditional heteroskedasticity (ARCH) and GARCH models are nested within the APGARCH model. To estimate the goodness of fit of each model, likelihood ratio tests are used to assess the significance of each model and provide the best fit for the data. The results suggest that APGARCH model provides the most adequate description for the data, with the inclusion of a GARCH term, free power term and unrestricted leverage effect term. This paper is the first of its kind to undertake an APGARCH investigation of the gold price. The role of the dollar in gold is confirmed but few other macroeconomic variables have an impact.

An analysis of the flexibility of Asymmetric Power GARCH models

The Asymmetric Power GARCH (APGARCH) model allows a wider class of power transformations than simply taking the absolute value or squaring the data as in classical heteroscedastic models. A dynamic estimation is used to compare the three GARCH families and examine their forecasting performances in a value-at-risk setting. The results suggest that the optimal power transformation obtained with the APGARCH model is virtually never statistically different from 1 or 2. Moreover, although some indices switch between these two values over the time, the measures of accuracy and efficiency used to assess the performance of VaR forecasts indicate that the additional flexibility brought by the APGARCH model provides little, if any, improvements for risk management.

Stock market dynamics in a regime-switching asymmetric power GARCH model

This paper analyzes the dynamics of Asian stock index returns through a Regime-Switching Asymmetric Power GARCH model (RS-APGARCH). The model confirms some stylized facts already discussed in former studies but also highlights interesting new characteristics of stock market returns and volatilities. Mainly, it improves the traditional regime-switching GARCH models by including an asymmetric response to news and, above all, by allowing the power transformations of the heteroskedasticity equations to be estimated directly from the data. Several mixture models are compared where a first-order Markov process governs the switching between regimes.

An APGARCH Investigation of the Main Influences on the Gold Price

The paper investigates whether the asymmetric power GARCH model (APGARCH) introduced by Ding, Granger and Engle (1993) captures the dynamics of the gold market. This paper examines both the cash and futures price of gold and significant economic variables identified during two periods: the 1987 crisis and the 2001 crisis. As specified in Ding et al. (1993) a number of ARCH and GARCH models are nested within the APGARCH model. To estimate the goodness of fit of each model, likelihood ratio tests are used. The results suggest that APGARCH model provides the most adequate description for the data. This paper is the first of its kind to undertake a significant GARCH model of the main influencers on the gold price. While further investigation is required, it has unearthed interesting results.

Strict stationarity and mixing properties of asymmetric power GARCH models allowing a signed volatility

A nonlinear asymmetric power GARCH (p, q) model which allows a signed volatility is considered. Sufficient conditions for strict stationarity, existence of higher order moments and β-mixing with exponential decay rates are provided.