Unobserved component models with asymmetric conditional variances.

In this paper, unobserved component models with GARCH disturbances are extended to allow for asymmetric responses of conditional variances to positive and negative shocks. The asymmetric conditional variance is represented by a member of the QARCH class of models. The proposed model allows to distinguish whether the possibly asymmetric conditional heteroscedasticity affects the short run or the long-run disturbances or both. We analyse the statistical properties of the new model and derive the asymptotic and finite sample properties of a QML estimator of the parameters. We propose to identify the conditional heteroscedasticity using the correlogram of the squared auxiliary residuals. Its finite sample properties are also analysed. Finally, we ilustrate the results fitting the model to represent the dynamic evolution of daily series of financial returns and gold prices, as well as of monthly series of inflation. The behaviour of volatility in both types of series is different. The conditional heteroscedasticity mainly affects the short run component in financial returns while in the inflation series, the heteroscedastic ity appears in the long-run component. We find asymmetric effects in both types of variables

Unobserved component models with asymmetric conditional variances

Unobserved component models with GARCH disturbances are extended to allow for asymmetric responses of conditional variances to positive and negative shocks. The asymmetric conditional variance is represented by a member of the QARCH class of models. The proposed model allows to distinguish whether the possibly asymmetric conditional heteroscedasticity affects the short-run or the long-run disturbances or both. Statistical properties of the new model and the finite sample properties of a QML estimator of the parameters are analyzed. The correlogram of squared auxiliary residuals is shown to be useful to identify the conditional heteroscedasticity. Finite sample properties of squared auxiliary residuals are also analysed. Finally, the results are illustrated by fitting the model to daily series of financial and gold prices, as well as to monthly series of inflation. The behavior of volatility in both types of series is different. The conditional heteroscedasticity mainly affects the short-run component in financial prices while in the inflation series, the heteroscedasticity appears in the long-run component. Asymmetric effects are found in both types of variables.Publicad

Estimation methods for stochastic volatility models: a survey

The empirical application of Stochastic Volatility (SV) models has been limited due to the difficulties involved in the evaluation of the likelihood function. However, recently there has been fundamental progress in this area due to the proposal of several new estimation methods that try to overcome this problem, being at the same time, empirically feasible. As a consequence, several extensions of the SV models have been proposed and their empirical implementation is increasing. In this paper, we review the main estimators of the parameters and the volatility of univariate SV models proposed in the literature. We describe the main advantages and limitations of each of the methods both from the theoretical and empirical point of view. We complete the survey with an application of the most important procedures to the S and P 500 stock price index

Using auxiliary residuals to detect conditional heteroscedasticity in inflation

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, this relation is positive, supporting the Friedman hypothesis

Estimation methods for stochastic volatility models: a survey

Although stochastic volatility (SV) models have an intuitive appeal, their empirical application has been limited mainly due to difficulties involved in their estimation. The main problem is that the likelihood function is hard to evaluate. However, recently, several new estimation methods have been introduced and the literature on SV models has grown substantially. In this article, we review this literature. We describe the main estimators of the parameters and the underlying volatilities focusing on their advantages and limitations both from the theoretical and empirical point of view. We complete the survey with an application of the most important procedures to the S&P 500 stock price index.Publicad

USING AUXILIARY RESIDUALS TO DETECT CONDITIONAL HETEROSCEDASTICITY IN INFLATION

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, this relation is positive, supporting the Friedman hypothesis.

ESTIMATION METHODS FOR STOCHASTIC VOLATILITY MODELS: A SURVEY

The empirical application of Stochastic Volatility (SV) models has been limited due to the difficulties involved in the evaluation of the likelihood function. However, recently there has been fundamental progress in this area due to the proposal of several new estimation methods that try to overcome this problem, being at the same time, empirically feasible. As a consequence, several extensions of the SV models have been proposed and their empirical implementation is increasing. In this paper, we review the main estimators of the parameters and the volatility of univariate SV models proposed in the literature. We describe the main advantages and limitations of each of the methods both from the theoretical and empirical point of view. We complete the survey with an application of the most important procedures to the S&P 500 stock price index.

Flexible inflation targets, forex interventions and exchange rate volatility in emerging countries

Emerging economies with inflation targets (IT) face a dilemma between fulflling the theoretical conditions of "strict IT", which implies a fully flexible exchange rate, or applying a "flexible IT", which entails a de facto managed floating exchange rate with forex interventions to moderate exchange rate volatility. Using a panel data model for 37 countries we find that, although IT lead to higher exchange rate instability than alternative regimes, forex interventions in some IT countries have been more effective in reducing volatility than in non-IT countries, which may justify the use of "flexible IT" by policymakers.inflation targeting; exchange rate volatility; foreign exchange interventions; emerging economies

Testing for conditional heteroscedasticity in the components of inflation

Incluye bibliografíaIn 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 countrie