Cópulas para combinação de modelos de séries temporais

Abstract

Time series combined forecasts have shown better results than individual models in terms of both accuracy as efficiency. Alternatives of aggregation well adopted are linear combination, which include methods such as the simple average and the weighted average resultant method of minimum variance here named Classic Model (CM) due to coincide with the maximum likelihood estimator under the assumption that the errors of the individual models follow a multivariate normal distribution. Thus, it has been usual to assume the normality of the errors of the individual models. However, improper assumption of normality may result in biased estimators and thus misleading estimates of the aggregated model. This thesis proposes a method for maximum likelihood predictors focused on aggregating time series forecasting models through copulas, where the errors of these individual models can not be normally distributed. The models via copulas are multivariate functions that operate on the marginal probability distribution, allowing the modeling of the prediction errors, and after, the dependency structure between these predictors. The usefulness of the proposed combined model via copula Frank and Gumbel is illustrated by study eight phenomena of the real world: three fish growth series (yellow tuna, striped seabream and bigeye tuna species), four financial series (Nasdaq (ND), Google (GG), S&P500 (SP) and Dow jones (DJ) and one time series of precipitation. For fish growth series, the following individual models were considered: VBGM (Von Bertalanffy Growth Model), Gompertz, logistic, generalized VBGM and Schnute-Richards. Regarding financial ND series, GG, SP and DJ, the individual models for each case are: ANN (Artificial Neural Network) TAEF (Timedelay Added Evolutionary Forecasting) and ARIMA (AutoRegressive Integrated Moving Average). And for the series of precipitation, nine GARCH (Generalized Autoregressive Conditional heteroscedasticity) are involved. The performance of the proposed combined model is highlighted by means of a comparison with the individual and combined models SA and MC through the Mean Squared Error (MSE). In this sense, it can clearly be seen the usefulness of the combined estimator proposed via Frank and Gumbel copulas. These combined estimators achieve better results when at least one marginal distribution of errors of individuais models not follow a normal distribution. Discussions about the best performance of these copulas in combining determined models, to the detriment of all those available, are also presented.