The aim of this research work was to empirically study hidden patterns of Nigeria’s foreign reserves and developed a valid and reliable hybrid model that can forecast monthly external reserves position of Nigeria using the proposed model which will empirically clarify contradictions in different literatures as to which of the existing linear and nonlinear models are more suitable for forecasting time series data of Nigeria’s foreign reserves. The main intent is to obtain a new hybrid model that is multiplicative in nature while most of the existing ones are additive, it comprises three main components namely: the linear component, the nonlinear component and the residuals component. In the first step, an ARIMA was used to analyze the linear part. In the second step, an artificial neural network system (ANNs) was used to model the nonlinear part. And the third step, the residuals of the artificial neural network system (ANNs) was examined for possible nonlinear correlation. The combined forecast was obtained by multiplying forecasted linear component, forecasted nonlinear component and the residuals. Coming to the end of this research work it was find out that the original data is not stationary but attained stationary after first non-seasonal log differencing of the original data. However, At the end of the rigorous ARIMA model search using R three (3) models were obtained as the most suitable models namely ARIMA (4,1,4)(4,0,4)x12, ARIMA (3,2,3)(2,0,3)X12 and ARIMA (2,1,1)X12. The best model among them is ARIMA (4,1,4)(4,0,4)x12 having met all the requirements with the least information criteria. It was therefore chosen to be used for residuals analysis and subsequently the residuals of the fitted ARIMA model were found not to be white noise (random) as against what is usually assumes to be obtainable in ARIMA modeling. As such the artificial neural network system (ANNs) was applied to the residuals of the best ARIMA (4,1,4)(4,0,4)x 12 model. The original data was divided by the fitted values to obtained residuals (R t ) of the proposed hybrid model on which artificial neural network was used to train and develop model using input layer 12, hidden layers 17 and 1 output layer (12-17-1). However, the finding shows that residuals of ARIMA model are more nonlinear in nature and may contain vital information that can be modeled by chaotic models such as artificial neural networks (ANNs) model. The autocorrelation function (ACF) and the partial autocorrelation function (PACF) of
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