Forecasting correlated time series with exponential smoothing models

This paper presents the Bayesian analysis of a general multivariate exponential smoothing model that allows us to forecast time series jointly, subject to correlated random disturbances. The general multivariate model, which can be formulated as a seemingly unrelated regression model, includes the previously studied homogeneous multivariate Holt-Winters’ model as a special case when all of the univariate series share a common structure. MCMC simulation techniques are required in order to approach the non-analytically tractable posterior distribution of the model parameters. The predictive distribution is then estimated using Monte Carlo integration. A Bayesian model selection criterion is introduced into the forecasting scheme for selecting the most adequate multivariate model for describing the behaviour of the time series under study. The forecasting performance of this procedure is tested using some real examples.     

Forecast combinations of computational intelligence and linear models for the NN5 time series forecasting competition

In this work we introduce the forecasting model with which we participated in the NN5 forecasting competition (the forecasting of 111 time series representing daily cash withdrawal amounts at ATM machines). The main idea of this model is to utilize the concept of forecast combination, which has proven to be an effective methodology in the forecasting literature. In the proposed system we attempted to follow a principled approach, and make use of some of the guidelines and concepts that are known in the forecasting literature to lead to superior performance. For example, we considered various previous comparison studies and time series competitions as guidance in determining which individual forecasting models to test (for possible inclusion in the forecast combination system). The final model ended up consisting of neural networks, Gaussian process regression, and linear models, combined by simple average. We also paid extra attention to the seasonality aspect, decomposing the seasonality into weekly (which is the strongest one), day of the month, and month of the year seasonality.     

Automatic neural network modeling for univariate time series

Artificial neural networks (ANNs) are an information processing paradigm inspired by the way the brain processes information. Using neural networks requires the investigator to make decisions concerning the architecture or structure used. ANNs are known to be universal function approximators and are capable of exploiting nonlinear relationships between variables. This method, called Automated ANNs, is an attempt to develop an automatic procedure for selecting the architecture of an artificial neural network for forecasting purposes. It was entered into the M-3 Time Series Competition. Results show that ANNs compete well with the other methods investigated, but may produce poor results if used under certain conditions.     

Validation and forecasting accuracy in models of climate change

Forecasting researchers, with few exceptions, have ignored the current major forecasting controversy: global warming and the role of climate modelling in resolving this challenging topic. In this paper, we take a forecaster’s perspective in reviewing established principles for validating the atmospheric-ocean general circulation models (AOGCMs) used in most climate forecasting, and in particular by the Intergovernmental Panel on Climate Change (IPCC). Such models should reproduce the behaviours characterising key model outputs, such as global and regional temperature changes. We develop various time series models and compare them with forecasts based on one well-established AOGCM from the UK Hadley Centre. Time series models perform strongly, and structural deficiencies in the AOGCM forecasts are identified using encompassing tests. Regional forecasts from various GCMs had even more deficiencies. We conclude that combining standard time series methods with the structure of AOGCMs may result in a higher forecasting accuracy. The methodology described here has implications for improving AOGCMs and for the effectiveness of environmental control policies which are focussed on carbon dioxide emissions alone. Critically, the forecast accuracy in decadal prediction has important consequences for environmental planning, so its improvement through this multiple modelling approach should be a priority.     

Graphical interaction models for multivariate time series1

In this paper we extend the concept of graphical models for multivariate data to multivariate time series. We define a partial correlation graph for time series and use the partial spectral coherence between two components given the remaining components to identify the edges of the graph. As an example we consider multivariate autoregressive processes. The method is applied to air pollution data. Received: June 1999     

Optimal transformations for categorical autoregressive time series

This paper describes a method for finding optimal transformations for analyzing time series by autoregressive models. 'Optimal' implies that the agreement between the autoregressive model and the transformed data is maximal. Such transformations help 1) to increase the model fit, and 2) to analyze categorical time series. The method uses an alternating least squares algorithm that consists of two main steps: estimation and transformation. Nominal, ordinal and numerical data can be analyzed. Some alternative applications of the general idea are highlighted: intervention analysis, smoothing categorical time series, predictable components, spatial modeling and cross-sectional multivariate analysis. Limitations, modeling issues and possible extensions are briefly indicated.     

Mixture of MLP-experts for trend forecasting of time series: A case study of the Tehran stock exchange

A new method for forecasting the trend of time series, based on mixture of MLP experts, is presented. In this paper, three neural network combining methods and an Adaptive Network-Based Fuzzy Inference System (ANFIS) are applied to trend forecasting in the Tehran stock exchange. There are two experiments in this study. In experiment I, the time series data are the Kharg petrochemical company’s daily closing prices on the Tehran stock exchange. In this case study, which considers different schemes for forecasting the trend of the time series, the recognition rates are 75.97%, 77.13% and 81.64% for stacked generalization, modified stacked generalization and ANFIS, respectively. Using the mixture of MLP experts (ME) scheme, the recognition rate is strongly increased to 86.35%. A gain and loss analysis is also used, showing the relative forecasting success of the ME method with and without rejection criteria, compared to a simple buy and hold approach. In experiment II, the time series data are the daily closing prices of 37 companies on the Tehran stock exchange. This experiment is conducted to verify the results of experiment I and to show the efficiency of the ME method compared to stacked generalization, modified stacked generalization and ANFIS.