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We present a novel GARCH model that accounts for time varying, state dependent, persistence in the volatility dynamics. The proposed model generalizes the component GARCH model of Ding and Granger (1996). The volatility is modelled as a convex combination of unobserved GARCH components where the combination weights are time varying as a function of appropriately chosen state variables. In order to make inference on the model parameters, we develop a Gibbs sampling algorithm. Adopting a fully Bayesian approach allows to easily obtain medium and long term predictions of relevant risk measures such as value at risk. Finally we discuss the results of an application to a series of daily returns on the S&P500.

We reconsider the issue of the (non-)equivalence of period and continuous time analysis in macroeconomic theory and its implications for the existence of chaotic dynamics in empirical macroeconomics. We start from the methodological precept that period and continuous time representations of the same macrostructure should give rise to the same qualitative outcome, i.e. in particular, that the results of period analysis should not depend on the length of the period chosen. A simple example where this is fulfilled is given by the Solow growth model, while all chaotic dynamics in period models of dimension less than 3 are in conflict with this precept. We discuss a typical example from the recent literature, where chaos results from an asymptotically stable continuous-time macroeconomic model when it is reformulated as a discrete-time model with a sufficiently long period length.

The existing literature shows that income inequality plays an important role in growth process, and such a relationship is better characterized as nonlinearity. The paper revisits the issue by employing the threshold regressions with instrumental variables approach. Using the initial level of economic development as a threshold variable, we find strong evidence in support of a nonlinear income threshold in the relationship. In particular, the data show that an increase in inequality would hinder growth in low-income countries but accelerate growth in high-income ones. The results therefore suggest that redistributive policy that alleviates inequality can foster economic growth in low-income countries, while policymakers confront a tradeoff between inequality and growth in high-income countries.

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.

This paper discuses the application of mixture models for analyzing data with hidden structure. More specifically, we are interested in situations where the structure is due to some unobserved factors. Detecting the latent structures in data is not trivial. On the other hand, since such structures could obscure the effect of the observed variables, ignoring them (e.g., using simple linear models) could result in wrong inference. To address this issue, we propose to use Dirichlet process mixtures. In this approach, the mixture identifier (i.e., the latent variable that assigns each component to a data point) acts as a surrogate for possible missing factors and provides insight into possible hidden structure in the data. An illustrative example is provided to show the usefulness of this approach. We also discuss the application of our method for analyzing time series processes that are subject to regime changes where there is no specific economic theory about the structure of the model.

In this paper we provide simulation and theoretical results concerning the finite sample theory of QML estimators in ARCH models when we include an exogenous variable in the conditional variance equation. In this setting, we find theoretical and simulation support to suggest that if we consider two exogenous variables with the same variance, the one that has the larger sample mean is more likely to produce a larger bias in the QML estimators, in such a way that can be quite misleading in practical applications. We warn about the existence of important biases and potentially low power of the t-tests in these cases. We also propose ways to deal with them. Finally, we generalize the Lumsdaine (1995) invariance properties for the biases in these situations. An empirical application shows the usefulness of our theoretical results.