1. Introduction

Prediction of economic or financial variable using related independent variables could be done by either using a super model which contains all the available independent variables or using the forecast combination methodology. Generally, it is admitted in the literature of econometrics that the forecast obtained by all the information integrated in one step is much better than the combination of forecast from individual models. For example, [17] argued that "The best forecast is obtained by combining information sets, not forecasts from information sets. If both

© 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

models are known, one should combine the information that goes into the models, not the forecasts that come out of the models." Authors of Refs. [13, 23, 25] expressed similar opinions. As it seems the investigators in this field lean more to prefer the combination of information in one model.

The main questions that arise in researchers' minds are "To combine or not to combine" and "how to combine." In this chapter, we are concerned with the question of "combining forecasts from different models or combining information in one model." This is an area that has been discussed by many researchers but not in detail (see [9, 11, 12, 29, 35, 40]).

Huang [29] state that "the common belief that combination of information is better than combination of forecasts might be based on the in-sample analysis." On the contrary, from out-of-sample analysis, they found out that combination of forecasts performs better than combination of information. Many articles typically account for the out-of-sample success of combination of forecasts over combination of information by pointing out various disadvantages that combination of information may possibly possess. For example, (a) in many forecasting situations, particularly in real time, combination of information by pooling all information sets is either impossible or too expensive (see [12, 13, 42]); (b) in a data substantial medium where there are much closed input variables in hand, the super combination of information model may bear from exclusion problem [42]; and (c) in the absence of linearity and, simple dynamics, building an excellent model using combination of information is more likely to be misspecified [26]. We believe that the above-mentioned points can be maintained through the precise selection of the model that is used to estimate the combined information. In our case we used the artificial neural networks to overcome the nonlinearity problem that can be inherent in the series. On the other hand, the factor model is used to tame the problem of the dimensionality, where a large dataset can be summarized in few numbers of factors.

The seminal work of [7] opened the door to examine the prediction combination in different fields of studies in economics and finance. Consequently, a new scope in forecasting study has been to combine the forecasts generated by individual models, using different combinations of techniques. This lets the ultimate forecast result to extract strength from the individual forecasting techniques that cannot be carried out by a single method. Empirically, forecast combinations have been used successfully in diverse areas such as forecasting gross national product, currency market volatility, inflation, money supply, stock prices, interest rates, meteorological data, city populations, and outcomes of football games.

Factor models were introduced in macroeconomics and finance by [22, 36]. The literature on the large factor models starts with [19, 37]. Further theoretical advances were made among others [4, 5, 20]. Upon the successive performance of the DFMs in forecasting, factors augmented to other models are introduced. For example, Bernanke et al. [8] proposed a forecasting model which they called the factor-augmented vector autoregressive (FAVAR) model, a model which merges a factor model with a vector autoregressive component. A factoraugmented vector autoregressive moving average (VARMA) model is suggested by Dufour and Pelletier [16]. Factor-augmented error correction model (FECM) was introduced by Banerjee and Marcellino [6]; Ng and Stevanovic [38] proposed a factor-augmented autoregressive distributed lag (FADL) framework for analyzing the dynamic effects of common and idiosyncratic shocks. Babikir and Mwambi [2] introduced a factor-augmented artificial neural network (FAANN) that showed improved forecasts compared to DFM and AR models.

models are known, one should combine the information that goes into the models, not the forecasts that come out of the models." Authors of Refs. [13, 23, 25] expressed similar opinions. As it seems the investigators in this field lean more to prefer the combination of information in

The main questions that arise in researchers' minds are "To combine or not to combine" and "how to combine." In this chapter, we are concerned with the question of "combining forecasts from different models or combining information in one model." This is an area that has been

Huang [29] state that "the common belief that combination of information is better than combination of forecasts might be based on the in-sample analysis." On the contrary, from out-of-sample analysis, they found out that combination of forecasts performs better than combination of information. Many articles typically account for the out-of-sample success of combination of forecasts over combination of information by pointing out various disadvantages that combination of information may possibly possess. For example, (a) in many forecasting situations, particularly in real time, combination of information by pooling all information sets is either impossible or too expensive (see [12, 13, 42]); (b) in a data substantial medium where there are much closed input variables in hand, the super combination of information model may bear from exclusion problem [42]; and (c) in the absence of linearity and, simple dynamics, building an excellent model using combination of information is more likely to be misspecified [26]. We believe that the above-mentioned points can be maintained through the precise selection of the model that is used to estimate the combined information. In our case we used the artificial neural networks to overcome the nonlinearity problem that can be inherent in the series. On the other hand, the factor model is used to tame the problem of the dimensionality, where a large dataset

The seminal work of [7] opened the door to examine the prediction combination in different fields of studies in economics and finance. Consequently, a new scope in forecasting study has been to combine the forecasts generated by individual models, using different combinations of techniques. This lets the ultimate forecast result to extract strength from the individual forecasting techniques that cannot be carried out by a single method. Empirically, forecast combinations have been used successfully in diverse areas such as forecasting gross national product, currency market volatility, inflation, money supply, stock prices, interest rates, mete-

Factor models were introduced in macroeconomics and finance by [22, 36]. The literature on the large factor models starts with [19, 37]. Further theoretical advances were made among others [4, 5, 20]. Upon the successive performance of the DFMs in forecasting, factors augmented to other models are introduced. For example, Bernanke et al. [8] proposed a forecasting model which they called the factor-augmented vector autoregressive (FAVAR) model, a model which merges a factor model with a vector autoregressive component. A factoraugmented vector autoregressive moving average (VARMA) model is suggested by Dufour and Pelletier [16]. Factor-augmented error correction model (FECM) was introduced by Banerjee and Marcellino [6]; Ng and Stevanovic [38] proposed a factor-augmented autoregressive distributed lag (FADL) framework for analyzing the dynamic effects of common and idiosyncratic

discussed by many researchers but not in detail (see [9, 11, 12, 29, 35, 40]).

can be summarized in few numbers of factors.

orological data, city populations, and outcomes of football games.

one model.

78 Advanced Applications for Artificial Neural Networks

On the contrary, artificial neural networks (ANNs) have become one of the most scientific projection methods and have been extensively used in different fields of projection goal. Artificial neural networks have several aspects that make them interesting and authentic for projection work. First, ANNs are common functional approximators. Second, ANNs are datainduced self-flexible approach in that there are less a priori presumptions to be stated about the models for the problem under examination; thus, ANN modeling is not similar to classical model-based approaches. Third, an ANN model is a nonlinear model which is in contrast to the conventional time series forecasting models, which postulate linearity of the series under consideration. [45] demonstrated that systems of the real world are often nonlinear. These advantages of ANNs have attracted attention in time series forecasting and have become a competitive method to traditional time series forecasting methods, and the literature is very vast in this area. The hybrid approach or combining models represent the most important developments in ANNs over the last decade. More hybrid models of ANNs with different forecasting models have been introduced in the recent time, which successfully improve the forecasting performance. [44] proposed the integration of the generalized linear autoregression (GLAR) model with artificial neural networks in order to obtain accurate forecasts for foreign exchange market. [43] proposed a hybrid model called SARIMABP that combines the seasonal autoregressive integrated moving average (SARIMA) model and the back-propagation neural network model to predict seasonal time series data. [34] introduced a hybrid model of ANNs and ARIMA models for forecasting purpose. [1] introduced a hybrid model where the factors were used as input to the ANN model. The model produced more accurate forecasts compared to ANN and DFM.

In this chapter, through the artificial neural networks framework and factor model, for insample and out-of-sample forecasting, we show analytically that combination of forecasts—of dynamic factor model and artificial neural networks—can be outclassed by combination of models (information)—of the factors to be used as additional input variables to the artificial neural networks.

To the best of our knowledge, the evaluation of the forecasting performance of the combination of information or models of factors and ANN—the FAANN—and combination of forecasts of ANN and DFM using different linear and nonlinear combinations is new, and this is the first attempt in general and in South Africa in particular. The empirical results show sizable gains in terms of the forecasting ability of the FAANN compared to both the standard ANN and the DFM and their forecasts combination; in other words it seems that combination of models outperforms combination of forecasts meaning that combination of information could be better than the combination of forecasts.

The remaining of the chapter is formulated as follow: Section 2 in brief expresses the DFM, the ANN, and the FAANN projection models and the combination techniques; Section 3 introduces the data; the results obtained from forecasting models and their combinations are presented in Section 4; finally, Section 5 gives a concise conclusion of the study and some suggestions for future researches.
