 # A good model is the one that has minimum aic among

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A good model is the one that has minimum AIC among all the other models. The SchwarzCriterion (SC) (Schwarz, 1978) considers both, the closeness of fit of the points to the modeland the number of parameters used by the model. Using this criterion, the best model is theone with the lowest SC.Table 1Analysis of results in GARCH modelsModelModel parametersParameterssignificanceAkaike info criterionSchwarz criterionGARCH (1.1)=0.000433=0.465281=0.1284590.00000.00000.0303-4.314630-4.264637GARCH (2,1)=0.000434=0.459434=0.208128=-0.0739370.00000.00000.02730.1361-4.314609-4.252118EGARCH=-3.428093=0.215611=0.483839=0.5534910.00000.00050.00000.0000-4.403681-4.341190The results in Table 1 show that the EGARCH model has the minimum AIC and minimumSC. However, the parameteris negative, then the assumption of positivity is not met.Therefore, the best model that met the criterion s is the GARCH (1, 1).
E. Avilés Ochoa y M.M. Flores Sosa /Contaduría y Administración 66(2), 2021, 1-149To 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 standarddeviation 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 2Analysis of results in SV modelsModelModel parametersMontecarlo standarderror parametersMax Efficiency MCMCSV (1)=0.0009798=0.22098910.000970.001690.1342SV (2)=0.0007921=0.183780=0.1720500.000010.002150.002090.1032Table 2 presents the resulting parameters of stochastic models. The Monte Carlo standarderror shows that the parameteris better in the second model, but the rest of the parametersare more significant in the first model. The efficiency MCMC demonstrates that SV1 is thebest model with 13.42%.Comparison of modelsIn this section, the GARCH (1, 1) and the SV (1) models are compared in the forecast for thenext seven periods. It is observable that the following period which corresponds toNovember2018 is a period of high volatility, while the fourth period which corresponds to February2019 shows low volatility. We useandthat were calculated previously on dependentvariables. 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 PercentageError (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 periodsof instability (high or low volatility). It is observable that it minimizes the absolute error inall periods except for the last two. The squared error is small in the stochastic model for mostperiods, except in periods five and six.
E. Avilés Ochoa y M.M. Flores Sosa /Contaduría y Administración 66(2), 2021, 1-1410The global results in MAD, RMSE, and MAPE are smaller in the SV1 model than in theGARCH (1.1) model. Therefore, the SV1 model is considered as the best model to predictthe variability in the exchange rate of the outside sample.

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Term
Winter
Professor
NoProfessor
Tags
Maximum likelihood, Mathematical finance, Autoregressive conditional heteroskedasticity, Markov chain Monte Carlo, Stochastic volatility, M M Flores Sosa
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