Forecasting Financial Crises and Contagion in Asia using Dynamic Factor Analysis

3.4 Probit model

We also use the principal components as regressors of a Probit model which is estimated by
maximising the log-likelihood:

where I(.) is an indicator function taking value 1 when a crisis event is observed (e.g. when
the EMP index at time t+ 1 exceeds a threshold), Φ is the cumulative Gaussian distribution
function and the γ⁰s are coefficients to be estimated by using Maximum Likelihood, ML. The
number of factors is selected by the one associated with the highest maximised log-likelihood
value. The estimates for γ_i are then used to produce probability forecasts as discussed in
the next subsection

3.5 Out-of-sample probability forecast and forecast accuracy eval-
uation

In this section we describe how to obtain probability forecasts from the density forecast of
EM P produced by the ARDL model and the competing model or from the estimated Probit
model. The crisis events are defined by the observations of the EMP index taking values of
either 1.5 standard or two standard deviation above the mean. When 1.5 standard deviations
are used as the threshold, the realisations of the EMP index which suggest a crisis event
are: a) semesters 1998:1 and 1998:2 for Indonesia; b) semester 1998:1 for Malaysia and for
the Philippines; c) semesters 1998:1 and 2001:2 for Korea; d) semesters 1997:2 and 1998:2 for
Thailand. When two standard deviations are used as the threshold, the realisations of the
EMP index which suggest a crisis event are: a) semesters 1998:1 and 1998:2 for Indonesia
and b) semester 1998:1 for Malaysia, Philippines, Korea, and Thailand.We now describe how
to obtain the probability forecasts.

We consider as a forecast evaluation period the one given by the last 20 periods (i.e.,. 10
years) in the sample. This is the period 1994:2 to 2004:1. It is important to observe that
the coefficient estimates for the model specifications given by equations (??),(??), (??), (??)
are obtained using recursive OLS, so as to avoid using future information in the forecasting
exercise. In particular, we use data available up to and including the first semester of 1994
and we use the estimated model to produce the second semester of 1994 probability forecast.
Then we add to the previous sample the information corresponding to the second semester of
1994, re-estimate the model and we produce the first semester of 1995 probability forecast.

10

<<   8   9   10   11   12   13   14   >>

More intriguing information