0306E - Faculty of Social Sciences - Université d'Ottawa

7 Appendix B
In this appendix, we present the models estimated for each of the series for
forecasting evaluation. All equations present the following statistics and diagnostic
tests. The R 2 is the coe¢cient of determination measuring the …t
of the data. The F-statistic tests the null hypothesis that all coe¢cients of
the regression are null (exception of the intercept). The DW is the Durbin-
Watson statistic testing for the presence of …rst-order autocorrelation, see
Durbin and Watson (1951). The e¾ is the estimated standard deviation of
the regression. The AIC is the Akaike information criteria. The BIC is
the Bayesian information criteria. The LJB is the statistic testing for nonnormal
residuals proposed by Doornik and Hansen (1994), which considers
a small sample correction based on the original statistic proposed by Jarque
and Bera (1987). The LM AR (p) is a Lagrange Multiplier statistic testing
for the presence of correlation of order p in the residuals of the regression,
see Harvey (1990). The F ARCH is an F-statistic testing for the presence
of autoregressive conditional hereroskedasticity, see Engle (1982). The RE-
SET statistic test for misspeci…cation in the estimated equation, see Ramsey
(1969). In the case of the PAR models, two more statistics are presented.
The F PER is an F-statistic testing for periodicity in the coe¢cients of the
estimated PAR models where the null hypothesis is constancy of the coe¢cients,
see Franses (1996). The LR ¿=0 statistic tests for the null hypothesis
of constancy of the coe¢cients associated to the time trend. The Q(i; j)
is the statistic of Ljung and Box (1978) based on the …rst i residuals autocorrelations.
The value PEV is the prediction error variance of one step
ahead predictor errors. Further we included seasonal dummy variables and
outlier dummy variables in some of our regressions. The seasonal dummies
are de…ned as D t;s = 1 if s = t and 0 otherwise. An example of an outlier
dummy used for all series for obvious reason is D2001 : 09 representing
September, 2001. Values in parenthesis below coe¢cient estimates are the
standard errors.
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