Some Exact Formulae for the Constant Correlation and Diagonal M - Garch Models

The purpose of this paper is to examine the covariance structure of multivariate GARCH (M-GARCH) models that have been introduced in the literature the last fifteen years, and have been greatly favoured by time series analysts and econometricians. In particular, we analyze the second moments of the constant conditional correlation M-GARCH model introduced by Bollerslev (1990) and the diagonal M-GARCH model introduced by Bollerslev, Engle and Wooldridge (1988).Autocovariance Generating Function; ARMA representations; Diagonal Multivariate GARCH.

Negative volatility spillovers in the unrestricted ECCC-GARCH model

Copyright @ 2010 Cambridge University Press.This paper considers a formulation of the extended constant or time-varying conditional correlation GARCH model that allows for volatility feedback of either the positive or negative sign. In the previous literature, negative volatility spillovers were ruled out by the assumption that all the parameters of the model are nonnegative, which is a sufficient condition for ensuring the positive definiteness of the conditional covariance matrix. In order to allow for negative feedback, we show that the positive definiteness of the conditional covariance matrix can be guaranteed even if some of the parameters are negative. Thus, we extend the results of Nelson and Cao (1992) and Tsai and Chan (2008) to a multivariate setting. For the bivariate case of order one, we look into the consequences of adopting these less severe restrictions and find that the flexibility of the process is substantially increased. Our results are helpful for the model-builder, who can consider the unrestricted formulation as a tool for testing various economic theories

Growth, volatility and political instability: Non-linear time-series evidence for Argentina, 1896-2000

What is the relationship between economic growth and its volatility? Does political instability affect growth directly or indirectly, through volatility? This paper tries to answer such questions using a power-ARCH framework with annual time series data for Argentina from 1896 to 2000. We show that while assassinations and strikes (what we call “informal” political instability) have a direct negative effect on economic growth, “formal” political instability (constitutional and legislative changes) has an indirect (through volatility) negative impact. We also find preliminary support for the idea that while the effects of “formal” instability are stronger in the long-run, those of “informal” instability are stronger in the short-run

Moments of the ARMA-EGARCH Model

This paper considers the moment structure of the ARMA(r,s)-EGARCH(p,q) model. In particular, we provide the autocorrelation function and any arbitrary moment of the conditional variance/squared errors. In addition, we derive the cross correlations between the process and the conditional variance/squared errors. We also explain our general results using the MA(1)-EGARCH(3,3)\ and the MA(1)-EGARCH(1,4) models as examples. Finally, the practical implications of the results are illustrated empirically using daily data on four East Asia Stock Indices.Autocorrelations; Exponential GARCH; Stock Returns.

Modeling Volatility Spillovers between the Variabilities of US Inflation and Output: the UECCC GARCH Model

This paper employs the unrestricted extended constant conditional correlation GARCH specification proposed in Conrad and Karanasos (2008) to examine the intertemporal relationship between the uncertainties of inflation and output growth in the US. We find that inflation uncertainty effects output variability positively, while output variability has a negative effect on inflation uncertainty.Bivariate GARCH process, negative volatility feedback, inflation uncertainty, output variability

Alternative GARCH in Mean Models: An Application to the Korean Stock Market

The purpose of this paper is the theoretical and empirical comparison of alternative GARCH-in-mean models. We examine three GARCH specifications: Bollerslev's (1986) GARCH model, Taylor (1986) - Schwert's (1989) GARCH model, and Nelson's (1991) Exponential GARCH model. In addition, we employ four of the most common forms in which the time-varying variance enters the specification of the mean to determine the risk premium: the quadratic, the linear, the logarithmic and the square root one. For all the aforementioned models we give the auto/cross correlations of the process and its conditional variance. The practical implications of the results are illustrated empirically using daily data on the Korean Stock Price Index (KOSPI).

Growth, Volatility & Political Instability: Non Linear Time Series Evidence for Argentina 1896-2000

What is the relationship between economic growth and its volatility? Does political instability affect growth directly or indirectly, through volatility? This paper tries to answer such questions using a power-ARCH framework with annual time series data for Argentina from 1896 to 2000. We show that while assassinations and strikes (what we call “informal” political instability) have a direct negative effect on economic growth, “formal” political instability (constitutional and legislative changes) has an indirect (through volatility) negative impact. We also find preliminary support for the idea that while the effects of “formal” instability are stronger in the long-run, those of “informal” instability are stronger in the short-run.economic growth, volatility, political instability, power-ARCH