Volume 9, Issue 4

This paper investigates if component GARCH models introduced by Engle and Lee(1999) and Ding and Granger(1996) can capture the long-range dependence observed in measures of time-series volatility. Long-range dependence is assessed through the sample autocorrelations, two popular semiparametric estimators of the long-memory parameter, and the parametric fractionally integrated GARCH (FIGARCH) model. Monte Carlo methods are used to characterize the finite sample distributions of these statistics when data are generated from GARCH(1,1), component GARCH and FIGARCH models. For several daily financial return series we find that a two-component GARCH model captures the shape of the autocorrelation function of volatility, and is consistent with long-memory based on semiparametric and parametric estimates. Therefore, GARCH models can in some circumstances account for the long-range dependence found in financial market volatility.

We analyze the post-float real exchange rates for a group of OECD countries using the newly developed threshold test and tests for unit roots against stationary but nonlinear alternative by Caner and Hansen ( 2001). These tools help us disentangle the nonlinearity from the nonstationarity rigorously for the first time in the literature. After applying the threshold test and unit root tests: we find evidence for non-linearity of exchange rates. Specifically real exchange rates behave like a unit root in a band and when the depreciation or appreciation of the currency against $US exceeds the boundaries of the band , the real exchange rates are mean-reverting. The threshold value is treated as unknown and estimated in the model.

Detecting nonlinearity in financial time series is a key point when the main interest is to understand the generating process. One of the main tests for testing linearity in time series is the Hinich Bispectrum Nonlinearity Test (HINBIN). Although this test has been succesfully applied to a vast number of time series, further improvement in the size power of the test is possible. A new method that combines the bispectrum and the surrogate method and bootstrap is then presented for detecting nonlinearity, gaussianity and time reversibility. Simulated and real data examples are given to demonstrate the efficacy of the new tests.

In this article, we formulate a time-scale decomposition of an international version of the CAPM that accounts for both market and exchange rate risk. In addition, we derive an analytical formula for time-scale value at risk (VaR) and time-scale marginal VaR of a portfolio. We apply our methodology to stock indices of seven emerging economies belonging to Latin America and Asia, for the sample period 1990-2004. Our main conclusions are the following. First, the estimation results hinge upon the choice of the world market portfolio. In particular, the stock markets of the sampled countries appear to be more integrated with other emerging countries than with developed ones. Second, value at risk depends on the investor’s time horizon. In the short run, potential losses are greater than in the long run. Third, additional exposure to some specific stock indices will increase value at risk to a greater extent, depending on the investment horizon. Our results go in line with recent research in asset pricing that stresses the importance of heterogeneous investors.

This paper analyzes the inflation dynamics of several countries belonging to the European Monetary Union and of the UK. We estimate the two main parameters driving the degree of persistence in inflation and its uncertainty using a dual long memory process. We also investigate the possible existence of heterogeneity in inflation dynamics across Euro area countries and examine the link between nominal uncertainty and macroeconomic performance measured by the inflation and output growth rates. Strong evidence is provided for the hypothesis that increased inflation raises nominal uncertainty in all countries. However, we find that uncertainty surrounding future inflation has a mixed impact on output growth. This result brings out an important asymmetry in the transmission mechanism of monetary policy in Europe in addition to the difference in the economic sizes of the countries. We also investigate whether one can find a correlation between central bank independence and inflation policy. Our conclusion is that the most independent central banks are in countries where inflation falls in response to increased uncertainty.

In this paper we compare a set of different standard GARCH models with a group of Markov Regime-Switching GARCH (MRS-GARCH) in terms of their ability to forecast the US stock market volatility at horizons that range from one day to one month. To take into account the excessive persistence usually found in GARCH models that implies too smooth and too high volatility forecasts, in the MRS-GARCH models all parameters switch between a low and a high volatility regime. Both gaussian and fat-tailed conditional distributions for the residuals are assumed, and the degrees of freedom can also be state-dependent to capture possible time-varying kurtosis. The forecasting performances of the competing models are evaluated both with statistical and risk-management loss functions. Under statistical losses, we use both tests of equal predictive ability of the Diebold-Mariano-type and test of superior predictive ability. Under risk-management losses, we use a two-step selection procedure where we first check which models pass the tests of correct unconditional or conditional coverage and then we compare the best models under two subjective VaR-based loss functions. The empirical analysis demonstrates that MRS-GARCH models do really outperform all standard GARCH models in forecasting volatility at horizons shorter than one week under both statistical and VaR-based risk-management loss functions. In particular, all tests reject the presence of a better model than the MRS-GARCH with normal innovations. However, at forecast horizons longer than one week, standard asymmetric GARCH models tend to be superior.