No abstract

SUMMARYMultivariate GARCH specifications are typically determined by means of practical considerations such as the ease of estimation, which often results in a serious loss of generality. A new type of multivariate GARCH model is proposed, in which potentially large covariance matrices can be parameterized with a fairly large degree of freedom while estimation of the parameters remains feasible. The model can be seen as a natural generalization of the O-GARCH model, while it is nested in the more general BEKK model. In order to avoid convergence difficulties of estimation algorithms, we propose to exploit unconditional information first, so that the number of parameters that need to be estimated by means of conditional information is more than halved. Both artificial and empirical examples are included to illustrate the model.

The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.

This paper considers a simple Continuous Beliefs System (CBS) to investigate the effects on price dynamics of several behavioral assumptions: (i) herd behaviour; (ii) a-synchronous updating of beliefs; and (iii) heterogeneity in time horizons (memory) among agents. The recently introduced concept of a CBS allows one to model the co-evolution of prices and the beliefs distribution explicitly, while keeping track of the unpredictable nature of individual preferences (Diks and van der Weide, 2003). As a benchmark model we take a simple CBS, which in a market with many traders exhibits a random walk driven by news. Using the explicit nature of the dynamics of the CBS we show that the introduction of herding modifies the random walk to an ARIMA(0, 1, 1) process, which is observationally equivalent to a reduction of the number of market participants. In terms of returns the model predicts MA(1) structure with a negative coeffient. Asynchronous updating leads to an MA(1) model for returns with GARCH(1, 1) innovations, and predicts a relation between the ARCH and GARCH coefficients. Heterogeneity in memory leads to long-range dependence in returns. In the empirical section we perform a modest 'reality check' concerning the predicted sign of the MA coefficient and the relation between the ARCH and GARCH coefficients for exchange rate data.

Nonlinear dynamics, Simulation software, Heterogeneous agents, C60, E37, G10,