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Factor Augmented Artificial Neural Network Model

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Abstract

This paper brings together two important developments in forecasting literature; the artificial neural networks and factor models. The paper introduces the factor augmented artificial neural network (FAANN) hybrid model in order to produce a more accurate forecasting. Theoretical and empirical findings have indicated that integration of various models can be an effective way of improving on their predictive performance, especially when the models in the ensemble are quite different. The proposed model is used to forecast three time series variables using large South African monthly panel, namely, deposit rate, gold mining share prices and Long term interest rate, using monthly data over the in-sample period (training set) 1992:1–2006:12. The variables are used to compute out-of-sample (testing set) results for 3, 6 and 12 month-ahead forecasts for the period of 2007:1–2011:12. The out-of-sample root mean square error findings show that the FAANN model yields substantial improvements over the autoregressive AR benchmark model and standard dynamic factor model (DFM). The Diebold–Mariano test results also further confirm the superiority of the FAANN model forecast performance over the AR benchmark model and the DFM model forecasts. The superiority of the FAANN model is due to the ANN flexibility to account for potentially complex nonlinear relationships that are not easily captured by linear models.

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Notes

  1. The approach works as follows; Suppose a factor model is represented as \(X_{it} =\lambda ^{\prime }_i F_t +e_{it}\) where \(X_{it}\) is the observed datum for the \(i\mathrm{th}\) series at time \(t\,(i=1,\ldots , N; t=1,\ldots ,T); F_t \) is a vector \((r\times 1)\) of common factors; \(\lambda _i\) is a vector \(\left( {r\times 1} \right) \) of factor loadings; and \(e_{it}\) is the idiosyncratic component of \(X_{it}\). The right hand side variables are not observed. The method of principal components minimizes \(V\left( r \right) =\textit{min}_{{\Lambda }, F} \left( {NT} \right) ^{-1}\mathop {\sum }_{i=1}^N \mathop {\sum }_{t=1}^T \left( {X_{it} -\lambda ^{\prime }_i F_t} \right) ^{2}\) where \(\varLambda =\left( {\lambda _1, \ldots ,\lambda _N} \right) \). Concentrating out \(\Lambda \) and using the normalization that \(F^{\prime }F/T=I_r\), where \(I_r\) is \(r\times r\) identity matrix, the problem is identical to maximizing \(\textit{tr}\left( {{F}^{\prime }}(XX^{\prime })F\right) \). The estimated factor matrix, denoted by \(\tilde{F}\), is \(\sqrt{T}\) times the eigenvectors corresponding to the r largest eigenvalues of the \(T\times T\) matrix \(X^{\prime }X\), and \(\tilde{\varLambda }^{\prime }=(\tilde{F}^{\prime }\tilde{F})^{-1}\tilde{F} X=\tilde{F} X/T\) is the corresponding loading matrix.

  2. In this paper we choose iterated forecast instead of direct forecast. Marcellino et al. [27] found that iterated forecast using AIC lag length selection performed better than direct forecasts, especially when forecast horizon increases. They argued that iterated forecast models with lag length selected based on information criterion are good estimates for the best linear predictor.

  3. The data sources are the South Africa Reserve Bank, ABSA Bank, Stats South Africa, National Association of Automobile Manufacturers of South Africa (NAAMSA), South African Revenue Service (SARS), Quantec and World Bank.

  4. The RMSE statistic can be defined as \(\sqrt{\frac{1}{N}{\sum }\left( {Y_{t+n} -{}_{t} \hat{Y}_{t+n}}\right) ^{2}}\), where \(Y_{t+n}\) denotes the actual value of a specific variable in period \(t+n\) and \({}_t\hat{Y}_{t+n}\) is the forecast made in period t for \(t+n.\)

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Authors and Affiliations

  1. School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville, Pietermaritzburg, 3209, South Africa

    Ali Babikir & Henry Mwambi

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  1. Ali Babikir
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  2. Henry Mwambi
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Correspondence to Ali Babikir.

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Babikir, A., Mwambi, H. Factor Augmented Artificial Neural Network Model. Neural Process Lett 45, 507–521 (2017). https://doi.org/10.1007/s11063-016-9538-6

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