It seems plausible that an increase in stock market volatility raises required stock returns, and thus lowers stock prices. We develop a formal model of this volatility feedback effect using a simple model of changing variance (a quadratic generalized autoregressive conditionally heteroskedastic, or QGARCH, model). Our model is asymmetric and helps to explain the negative skewness and excess kurtosis of U.S. monthly and daily stock returns over the period 1926–1988. We find that volatility feedback normally has little effect on returns, but it can be important during periods of high volatility.; Economics

In this paper we consider a model with stochastic trend, seasonal and transitory components with the disturbances of the trend and transitory disturbances specified as QGARCH models. We propose to use the differences between the autocorrelations of squares and the squared autocorrelations of the auxiliary residuals to identify which component is heteroscedastic. The finite sample performance of these differences is analysed by means of Monte Carlo experiments. We show that conditional heteroscedasticity truly present in the data can be rejected when looking at the correlations of observations or of standardized residuals while the autocorrelations of auxiliary residuals allow us to detect adequately whether there is heteroscedasticity and which is the heteroscedastic component. We also analyse the finite sample behaviour of a QML estimator of the parameters of the model. Finally, we use auxiliary residuals to detect conditional heteroscedasticity in monthly series of inflation of eight OECD countries. We conclude that, for most of these series, the conditional heteroscedasticity affects the transitory component while the long-run and seasonal components are homoscedastic. Furthermore, in the countries where there is a significant relationship between the volatility and the level of inflation...

In this paper, we compare the statistical properties of some of the most popular GARCH models with leverage e?ect when their parameters satisfy the positivity, stationarity and nite fourth order moment restrictions. We show that the EGARCH speci cation is the most exible while the GJR model may have important limitations when restricted to have nite kurtosis. On the other hand, we show empirically that the conditional standard deviations estimated by the TGARCH and EGARCH models are almost identical and very similar to those estimated by the APARCH model. However, the estimates of the QGARCH and GJR models di?er among them and with respect to the other three speci cations.

This article shows that the relationship between kurtosis, persistence of shocks to volatility, and first-order autocorrelation of squares is different in GARCH and ARSV models. This difference can explain why, when these models are fitted to the same series, the persistence estimated is usually higher in GARCH than in ARSV models, and, why gaussian ARSV models seem to be adequate, whereas GARCH models often require leptokurtic conditional distributions. We also show that introducing the asymmetric response of volatility to positive and negative returns does not change the conclusions. These results are illustrated with the analysis of daily financial returns.

In this paper we propose a model for monthly inflation with stochastic trend, seasonal and transitory components with QGARCH disturbances. This model distinguishes whether the long-run or short-run components are heteroscedastic. Furthermore, the uncertainty associated with these components may increase with the level of inflation as postulated by Friedman. We propose to use the differences between the autocorrelations of squares and the squared autocorrelations of the auxiliary residuals to identify heteroscedastic components. We show that conditional heteroscedasticity truly present in the data can be rejected when looking at the correlations of standardized residuals while the autocorrelations of auxiliary residuals have more power to detect conditional heteroscedasticity. Furthermore, the proposed statistics can help to decide which component is heteroscedastic. Their finite sample performance is compared with that of a Lagrange Multiplier test by means of Monte Carlo experiments. Finally, we use auxiliary residuals to detect conditional heteroscedasticity in ten monthly inflation series.

In this paper we propose a model for monthly inflation with stochastic trend, seasonal and transitory components with QGARCH disturbances. This model distinguishes whether the long-run or short-run components are heteroscedastic. Furthermore, the uncertainty associated with these components may increase with the level of inflation as postulated by Friedman. We propose to use the differences between the autocorrelations of squares and the squared autocorrelations of the auxiliary residuals to identify heteroscedastic components. We show that conditional heteroscedasticity truly present in the data can be rejected when looking at the correlations of standardized residuals while the autocorrelations of auxiliary residuals have more power to detect conditional heteroscedasticity. Furthermore, the proposed statistics can help to decide which component is heteroscedastic. Their finite sample performance is compared with that of a Lagrange Multiplier test by means of Monte Carlo experiments. Finally, we use auxiliary residuals to detect conditional heteroscedasticity in monthly inflation series of eight OECD countries.

El objetivo de esta tesis es analizar y comparar la capacidad de algunos de los modelos habituales de series temporales para representar la volatilidad de las series financieras y sus características más importantes. En concreto, una de las principales consiste en que las series suelen presentan mayor número de observaciones extremas que las esperadas bajo Gausianidad. Además, las observaciones se agrupan de tal manera que tras movimientos grandes siguen movimientos grandes, mientras que por el contrario, cuando los movimientos comienzan a ser pequeños siguen siéndolo durante cierto tiempo. Este agrupamiento de volatilidad se refleja a través de la autocorrelación de cuadrados que suele ser significativa, positiva y presenta decaimiento exponencial. Finalmente, otra característica extensamente observada y propuesta por Black (1976) es la respuesta asimétrica de la volatilidad ante rendimientos positivos o negativos y conocida como leverage effect. En concreto, el incremento en la volatilidad es mayor cuando los retornos anteriores son negativos que cuando éstos son de la misma magnitud pero positivos. La presencia de este tipo de comportamiento se detecta en las correlaciones cruzadas entre rendimientos y rendimientos futuros al cuadrado...

We perform the Bayesian inference of a GARCH model by the Metropolis-Hastings algorithm with an adaptive proposal density. The adaptive proposal density is assumed to be the Student's t-distribution and the distribution parameters are evaluated by using the data sampled during the simulation. We apply the method for the QGARCH model which is one of asymmetric GARCH models and make empirical studies for for Nikkei 225, DAX and Hang indexes. We find that autocorrelation times from our method are very small, thus the method is very efficient for generating uncorrelated Monte Carlo data. The results from the QGARCH model show that all the three indexes show the leverage effect, i.e. the volatility is high after negative observations.

We study the performance of the adaptive construction scheme for a Bayesian inference on the Quadratic GARCH model which introduces the asymmetry in time series dynamics. In the adaptive construction scheme a proposal density in the Metropolis-Hastings algorithm is constructed adaptively by changing the parameters of the density to fit the posterior density. Using artificial QGARCH data we infer the QGARCH parameters by applying the adaptive construction scheme to the Bayesian inference of QGARCH model. We find that the adaptive construction scheme samples QGARCH parameters effectively, i.e. correlations between the sampled data are very small. We conclude that the adaptive construction scheme is an efficient method to the Bayesian estimation of the QGARCH model.; Comment: ICIS2009

Descripció del recurs: 16 de gener de 2011; 1. En el primer capítulo “Impact of oil prices on international financial markets” se analiza el impacto de cambios en el precio de petróleo (barril WTI) y su volatilidad en los principales mercados de renta variable: DJIA, S&P500, FTSE100, DAX y NIKKEI225. Se investiga la relación lineal y no-lineal. Se usan los precios diarios del periodo 1984 – 2005. Se observa que los cambios en el precio de petróleo afectan negativamente a los mercados americanos (DJIA, S&P500) y DAX, este impacto es negativo y representa un tercio del retorno diario. No se observa ni un efecto de retraso en esta relación ni de asimetría. Los mercados americanos reaccionan positivamente a la alta volatilidad de los precios del petróleo en el entorno de bajada del precio que se explica por menor factor de coste para las empresas. No se detecta relación entre los retornos de las bolsas y las transformaciones no-lineales del precio del petróleo. Se observa la transmisión de los shocks del precio del petróleo a la volatilidad de las bolsas analizadas. 2. En el segundo capítulo “Changes in correlations between CEE stock markets and European stock markets” se detecta el cambio estructural en la correlación entre las bolsas de los países de Europa Central y de Este (bolsas de Varsovia...