Disaggregation & aggregation of time series components: A hybrid forecasting approach using generalized regression neural networks and the theta method
Introduction
Since the pioneering work of [1] on the decomposition of time series, a large number of decomposition procedures have been developed to perform additive or multiplicative disaggregation of the data into salient components such as trend, seasonality and error [2], [3], [4], [5]. These were primarily employed to facilitate time series analysis and understanding of the business cycle [6]. However, after the seminal work of [7] on modeling seasonally adjusted data, decomposition techniques were also seen as a useful tool in forecasting.
Nevertheless, an important weakness of the use of classical decomposition techniques in forecasting lies in the manipulation of the irregular component, the residual variability left in the data after the removal of the salient components (usually trend-cyclical and seasonal components). Although academics agree that important information can still be found in the irregular component and, therefore its exclusion from the prediction process can result in negative ramifications for forecast accuracy, nonetheless, existing statistical techniques are unable to model and predict the erratic behavior of its sub-series. Consequently, in all applications the irregular component is excluded or is assumed to be a white noise process with zero mean [8].
To our knowledge, the only published work to attempt the extrapolation of a time series through the individual extrapolation of the additive components obtained from the application of a classical decomposition procedure, and including the residual component, is that of [9]. The authors implemented the Census X-11 [10] procedure for additive decomposition of the time series into trend-cycle, seasonality and error, and used a time-delay neural network to obtain forecasts of the three components, which were then synthesized into a single forecast through a backpropagation algorithm. In the current paper,1 an attempt is made to also extrapolate a time series through the individual extrapolation of its constituent components, including the residual error component. The Generalized Regression Neural Networks (hereafter GRNN) [12] are employed for the extrapolation of the seasonal and residual components, whilst the Theta method [13] is used for the estimation of the trend component.
The strength of the proposed forecasting method is tested on 60 time series from the NN3 competition and 227 monthly time series from the M1 competition dataset. The results confirm the capability of GRNN to forecast a wide range of time series with strong seasonal characteristics and high levels of residual variability. Nevertheless, it is also concluded from the analysis that GRNN are not able to predict trending series. Therefore, the Theta method [13] was preferred for the extrapolation of the trend component.
The paper unfolds as follows. In Section 2 a brief overview of Artificial Neural Networks (ANNs) and GRNNs is given, followed by a description of the proposed forecasting method in Section 3. The results from the preliminary analysis and performance evaluation of the new method are presented in Section 4. Concluding remarks are given in Section 5.
Section snippets
An overview of artificial neural networks
Neural Networks (hereafter NN) were developed through the realization that the human brain, being a complex, non-linear and parallel computer, functions in a radically diverse manner to a computer processor. Since the early 1950s, scientists have studied extensively the structure and capabilities of the human brain in processing information, and have tried to encompass as many of those characteristics into a NN. This novel approach to information processing has gained a lot of popularity
Research methodology
A forecasting method is proposed which is based on the estimated inherent structural properties of the observed time series. The structural evolution of a time series is studied through its decomposed seasonal, trend and residual components. Each of these components is modeled individually and appropriate linear and non-linear forecasting methods are employed to perform multi-step ahead prediction on each of the obtained sub-series.
Data description
For the evaluation of the new forecasting method, the complete set of 60 times series was used from the NN3 competition on computational techniques.5 These time series were chosen from the sample of the 111 time series of the NN3 competition as the longer time series, each having more than 84 observations (7 years of monthly data). Selecting the longer time series from the dataset
Conclusions & future research
A new hybrid forecasting method is proposed which is based on the application of the STL structural decomposition technique to disaggregate the data into its structural components. The proposed method performs multi-step ahead forecasting of each component individually through the use of a class of radial basis neural network models, the GRNN, and a statistical method, the Theta method. Each component is predicted with a relatively high accuracy and therefore, the linear combination of the
Marina Theodosiou is a Ph.D. candidate at Imperial College Business School working under the supervision of Prof. Nigel Meade. She received her undergraduate degree in Warwick University in M.M.O.R.S.E (Master in Mathematics, Operational Research, Statistics and Economics) from where she graduated in 2006.
In 2007 she worked as a portfolio analyst for a fund of funds where she carried out a research project on the application of artificial intelligence techniques for portfolio analysis and risk
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Marina Theodosiou is a Ph.D. candidate at Imperial College Business School working under the supervision of Prof. Nigel Meade. She received her undergraduate degree in Warwick University in M.M.O.R.S.E (Master in Mathematics, Operational Research, Statistics and Economics) from where she graduated in 2006.
In 2007 she worked as a portfolio analyst for a fund of funds where she carried out a research project on the application of artificial intelligence techniques for portfolio analysis and risk management. She now works for the Economic Research Department of the Central Bank of Cyprus.
Her main research interests are the application of statistical and computational intelligence techniques in forecasting.