A moving-average filter based hybrid ARIMA-ANN model for forecasting time series data

A suitable combination of linear and nonlinear models provides a more accurate prediction model than an individual linear or nonlinear model for forecasting time series data originating from various applications. The linear autoregressive integrated moving average (ARIMA) and nonlinear artificial neural network (ANN) models are explored in this paper to devise a new hybrid ARIMA–ANN model for the prediction of time series data. Many of the hybrid ARIMA–ANN models which exist in the literature apply an ARIMA model to given time series data, consider the error between the original and the ARIMA-predicted data as a nonlinear component, and model it using an ANN in different ways. Though these models give predictions with higher accuracy than the individual models, there is scope for further improvement in the accuracy if the nature of the given time series is taken into account before applying the models. In the work described in this paper, the nature of volatility was explored using a moving-average filter, and then an ARIMA and ox–Jenkins methodology an ANN model were suitably applied. Using a simulated data set and experimental data sets such as sunspot data, electricity price data, and stock market data, the proposed hybrid ARIMA–ANN model was applied along with individual ARIMA and ANN models and some existing hybrid ARIMA–ANN models. The results obtained from all of these data sets show that for both one-step-ahead and multistep-ahead forecasts, the proposed hybrid model has higher prediction accuracy. © 2014 Elsevier B.V. All rights reserved. 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 ntroduction and related work Time series forecasting is now a very important research area, wing to the importance of prediction in various applications. Foreasting Internet traffic helps service providers to enhance their ervices. Forecasting climate change helps the agricultural sector. orecasting disasters aids in taking necessary precautions and helps ankind to be prepared. Forecasting financial data helps investors o invest safely in the market. However, time series data do not lways have the same characteristics. Some time series are seaonal: for example, road traffic is high at some particular times n the day, climate variations repeat according to the seasons, etc. ome other time series are nonseasonal, such as financial and stock arket data. Some time series are highly volatile, such as wind peed data, and some are less volatile, such as global temperature nd annual rainfall. Some data are almost linear in nature, such as Please cite this article in press as: C.N. Babu, B.E. Reddy, A moving-ave series data, Appl. Soft Comput. J. (2014), http://dx.doi.org/10.1016/j.as he growth of an animal, plant, or human being, but many other sets f data are nonlinear in nature. Some data are Gaussian in nature, hereas some other data are non-Gaussian. For forecasting such ∗ Corresponding author. Tel.: +91 9035644182. E-mail address: narendrababu.c@gmail.com (C.N. Babu). ttp://dx.doi.org/10.1016/j.asoc.2014.05.028 568-4946/© 2014 Elsevier B.V. All rights reserved. 55 56 57 time series data, various prediction techniques have been proposed in the literature, which may use either linear or nonlinear models. A type of linear model, namely the autoregressive integrated moving average (ARIMA), and a type of nonlinear model, the artificial neural network (ANN), were chosen for study in this paper. ARIMA models assume that the present data are a linear function of past data points and past errors. They also assume that the errors are white in nature, and require that the data be made stationary before fitting a linear equation to the data. In the literature, ARIMA models have been applied to various time series data, such as electricity prices [1,2], sugar prices [3], stock market data [4], and wind speeds [5], for the prediction of future values. ARIMA models can help in understanding the dynamics of the data in a given application. Before forecasting time series data, various preprocessing steps can be applied to the raw data if necessary. In [6], a wavelet transformation was applied before forecasting of global temperature data. In [7], new classification and feature extraction techniques were proposed for electrocardiography data. These preprocessing steps can be applied to the raw data to obtain more rage-filter-based hybrid ARIMA–ANN model for forecasting time oc.2014.05.028 accurate predictions. In this paper, the basic ARIMA model was chosen as the linear prediction model. One efficient nonlinear technique for time series forecasting is ANNs [8]. ANNs are advantageous compared with ARIMA in many 58 59 60 61