Forecasting Financial Crises and Contagion in Asia using Dynamic Factor Analysis

prediction of the currency market turbulence. Another diffusion index is the one constructed
by Chauvet and Dong (2004) who develop a factor model with Markov regime switching
dynamics in order to produce in sample and out-of-sample prediction of nominal exchange
rates in a number of the East Asian countries.

3 Empirical methodology

In this section we describe the Dynamic Factor model (see Stock and Watson, 2002) which
allows to pool the whole set of information provided by the different vulnerability indicators
in each country. We will show, first, how the DF model can be used to predict currency
crisis events by building a vulnerability indicator common to the whole East Asian region.
We will also assess the contribution of group of variables to the DF model performance in
forecasting the EMP index. Finally we will describe how to obtain probability forecasts
using different competing models.

3.1 Model specification for a large dataset

The interdependence among the different variables in the system is described by the following
Dynamic Factor model:

xt = Γft + ξt                                       (1)

where xt is an n × 1 vector of (stationary) variables observed at time t; ft is an r dimen-
sional vector of factors (latent variables), with r much smaller than n; Γ is an n × r matrix
of factor loadings and ξt is an n × 1 idiosyncratic shock component. In the first stage of the
analysis, each series is de-meaned and divided by the corresponding sample standard devia-
tion. The set of common factors ft and the idiosyncratic component ξt (treated as iid in this
study) are assumed to be orthogonal to each other. Then, we apply principal component
analysis to the standardised T × n panel x_t. The factor estimates are given by TWW, where
the matrix W is T × r , and it has, on the columns, the eigenvectors corresponding to the
first r largest eigenvalues of the sample covariance matrix Ω for x. The use of estimated
factors instead of true ones in futher econometric analysis may pose a generated regressor
problem. However, as long at n is sufficiently large compared to T this is not an issue.
In particular, Bai (2003) has shown that, when estimated factors are used in a regression
context, no generated regressor problem arises,as long as T∕∕→ → 0.

Following Forni et al. (2005), the dynamics of the factors are described by:

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