Comparison of direct and iterative artificial neural network forecast approaches in multi-periodic time series forecasting

Abstract

Artificial neural network is a valuable tool for time series forecasting. In the case of performing multi-periodic forecasting with artificial neural networks, two methods, namely iterative and direct, can be used. In iterative method, first subsequent period information is predicted through past observations. Afterwards, the estimated value is used as an input; thereby the next period is predicted. The process is carried on until the end of the forecast horizon. In the direct forecast method, successive periods can be predicted all at once. Hence, this method is thought to yield better results as only observed data is utilized in order to predict future periods. In this study, forecasting was performed using direct and iterative methods, and results of the methods are compared using grey relational analysis to find the method which gives a better result.

Introduction

There are a few methods commonly used for time series forecasting. The Box–Jenkins method, which gives quite good results with linear time series, is one of them. The Box–Jenkins technique is considerably effective especially with linear and stationary data sets and with series that are non-stationary but turned into stationary via transformations. However, series extracted from the real world are not generally linear. Therefore, modeling nonlinear time series requires different techniques. For the last 25 years, a number of nonlinear time series models have been developed; such as the Bilinear Model, threshold autoregressive (TAR) model, and autoregressive conditional heteroscedastic (ARCH) model. These models are applicable, when information concerning the correlation between data is available and clear (Zhang, Patuwo, & Hu, 1998). Moreover, none of these models is effective in elucidating a whole nonlinear structure hidden in the data set (Zhang, Patuwo, & Hu, 2001). Although these models are better than the linear models, their applications are difficult, problem specific and not prone to generalization (Ghiassi, Saidane, & Zimbra, 2004).

One of the techniques that has been used for time series forecasting since the late 1980s is artificial neural networks (ANN). ANN, an approach to linear and nonlinear time series, is widely used to forecast the future. ANN provides linear and nonlinear modeling without the necessity of preliminary information and assumptions as to the relation between input and output variables. Therefore, ANN is more flexible and applicable than other methods (Zhang et al., 1998).

There have been many studies aimed at the utilization of ANN for time series forecasting. Tang, Almeida, & Fishwick, 1991 studied ANN and Box–Jenkins forecasting comparatively in time series. They remarked that ANN structure and training parameters such as learning rate and momentum coefficient affect ANN performance. Hill, O’Connor, and Remus (1996) discussed the data period (annual, quarterly, monthly), functional form of the series (linear, nonlinear), forecasting horizon, and number of observation as factors that affect the ANN performance. Faraway and Chatfield (1998) studied with a seasonal time series which is called airline data. Faraway and Chatfield’s (1998) study showed the dependence of different ANN structure on time series forecasting performance. Detailed literature studies were presented by Zhang et al. (1998), and Adya and Collopy (1998). Nelson, Hill, Remus, and O’Connor (1999) focused on seasonality in time series structure and discussed the necessity of deseasonalizing the data. Chu and Zhang (2003) compared the accuracy of various linear and nonlinear models for forecasting aggregate retail sales.

Time series forecasting can be performed for both single and multiple periods. Two different approaches can be used for forecasting multiple periods. One of them is a single period iterative forecast, as in the Box–Jenkins models. The other one is a direct method in which multiple periods are estimated simultaneously.

Using the autoregressive methods, Findley (1985) showed that the direct forecasting approach is better than the iterative forecasting approach for a covariance stationary autoregressive process that is not degenerate to a finite order. The results founded by Bhansali, 1996, Bhansali, 1997 support Findley’s (1985) conclusion. Kang (2003) studied monthly data on various US economic time series. The results found by Kang (2003) show that the direct method may or may not improve forecast accuracy upon the iterative method. Kang stated that the forecast performance of the direct method relative to the iterative method appears to depend on, optimal order selection criteria, forecast periods, forecast horizons and the time series to be forecasted.

On the other hand, there are contrary findings when forecasting the time series with ANN. Weigend, Huberman, and Rumelhart (1992) showed that the iterative forecast yields better results than the direct forecast method in their sunspot data analysis. This conclusion is supported by Hill, Marquez, O’Connor, and Remus (1994), in their 111 M-competition time series study. According to Zhang (1994), the direct method gives better results. Lachtermacher and Fuller (1995) emphasize that the direct method requires a larger time series than the iterative method in order to avoid generalization. Kline (2004) used three methods (iterative, independent and joint method) for multi-step forecasting. In Kline’s study (2004), the independent method is based on the separated networks forecasting for each period, and the joint method is the same as the direct method used in this study. According to Kline (2004), the independent method is better than joint method but training sample size and forecast horizon might affect this superiority.

The above studies show that it is not clear which method gives better results. It is thought that the direct method gives better results when compared with the iterative method because it is based on past data. In this paper, a comparison of the iterative and direct forecasting methods is presented. They are considered to be influential on multi-periodic forecast performance of ANN. The organization of rest of the paper is as follows: the second section presents time series. Important parameters of the ANN models are given in the third section. The fourth section discusses an example application. To assess and compare the performance of the methods in the application part, grey relational analysis (GRA) is utilized. The last section gives the main conclusions.