A good model is the one that has minimum aic among

A good model is the one that has minimum AIC among all the other models. The Schwarz
Criterion (SC) (Schwarz, 1978) considers both, the closeness of fit of the points to the model
and the number of parameters used by the model. Using this criterion, the best model is the
one with the lowest SC.
Table 1
Analysis of results in GARCH models
Model Model parameters
Parameters
significance
Akaike info criterion Schwarz criterion
GARCH (1.1)
=0.000433
=0.465281
=0.128459
0.0000
0.0000
0.0303
-4.314630 -4.264637
GARCH (2,1)
=0.000434
=0.459434
=0.208128
=-0.073937
0.0000
0.0000
0.0273
0.1361
-4.314609 -4.252118
EGARCH
=-3.428093
=0.215611
=0.483839
=0.553491
0.0000
0.0005
0.0000
0.0000
-4.403681 -4.341190
The results in Table 1 show that the EGARCH model has the minimum AIC and minimum
SC. However, the parameter is negative, then the assumption of positivity is not met.
Therefore, the best model that met the criterion s is the GARCH (1, 1).

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To estimate the parameters of the SV models, the Metropolis Hasting algorithm (Metro-
polis et al. 1953; Hasting, 1970) is used. Monte Carlo standard error (MCSE) is a standard
deviation around the posterior mean of the samples. The acceptable size of the MCSE de-
pends on the acceptable uncertainty, then when we compare models, a lower MCSE is better
(Flegal et al. 2008).
Table 2
Analysis of results in SV models
Model Model parameters
Montecarlo standard
error parameters
Max Efficiency MCMC
SV (1)
=0.0009798
=0.2209891
0.00097
0.00169
0.1342
SV (2)
=0.0007921
=0.183780
=0.172050
0.00001
0.00215
0.00209
0.1032
Table 2 presents the resulting parameters of stochastic models. The Monte Carlo standard
error shows that the parameter is better in the second model, but the rest of the parameters
are more significant in the first model. The efficiency MCMC demonstrates that SV1 is the
best model with 13.42%.
Comparison of models
In this section, the GARCH (1, 1) and the SV (1) models are compared in the forecast for the
next seven periods. It is observable that the following period which corresponds to November
2018 is a period of high volatility, while the fourth period which corresponds to February
2019 shows low volatility. We use and that were calculated previously on dependent
variables. To calculate and analyze the errors in forecasting, we use the Mean Absolute De-
viation (MAD), the Root Mean Squared Error (RMSE) and the Mean Absolute Percentage
Error (MAPE) methods (Franses, 2016; Khair et al. 2017). The results are in Table 3.
The error indicators show that the SV1 model minimizes the error for forecasting in periods
of instability (high or low volatility). It is observable that it minimizes the absolute error in
all periods except for the last two. The squared error is small in the stochastic model for most
periods, except in periods five and six.

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The global results in MAD, RMSE, and MAPE are smaller in the SV1 model than in the
GARCH (1.1) model. Therefore, the SV1 model is considered as the best model to predict
the variability in the exchange rate of the outside sample.