Optimising time series forecasts through linear programming

Panagiotopoulos, Apostolos (2012) Optimising time series forecasts through linear programming. PhD thesis, University of Nottingham.

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Abstract

This study explores the usage of linear programming (LP) as a tool to optimise the parameters of time series forecasting models. LP is the most well-known tool in the field of operational research and it has been used for a wide range of optimisation problems. Nonetheless, there are very few applications in forecasting and all of them are limited to causal modelling. The rationale behind this study is that time series forecasting problems can be treated as optimisation problems, where the objective is to minimise the forecasting error.

The research topic is very interesting from a theoretical and mathematical prospective. LP is a very strong tool but simple to use; hence, an LP-based approach will give to forecasters the opportunity to do accurate forecasts quickly and easily. In addition, the flexibility of LP can help analysts to deal with situations that other methods cannot deal with.

The study consists of five parts where the parameters of forecasting models are estimated by using LP to minimise one or more accuracy (error) indices (sum of absolute deviations – SAD, sum of absolute percentage errors – SAPE, maximum absolute deviation – MaxAD, absolute differences between deviations – ADBD and absolute differences between percentage deviations – ADBPD). In order to test the accuracy of the approaches two samples of series from the M3 competition are used and the results are compared with traditional techniques that are found in the literature.

In the first part simple LP is used to estimate the parameters of autoregressive based forecasting models by minimising one error index and they are compared with the method of the ordinary least squares (OLS minimises the sum of squared errors, SSE). The experiments show that the decision maker has to choose the best optimisation objective according to the characteristic of the series. In the second part, goal programming (GP) formulations are applied to similar models by minimising a combination of two accuracy indices. The experiments show that goal programming improves the performance of the single objective approaches.

In the third part, several constraints to the initial simple LP and GP formulations are added to improve their performance on series with high randomness and their accuracy is compared with techniques that perform well on these series. The additional constraints improve the results and outperform all the other techniques. In the fourth part, simple LP and GP are used to combine forecasts. Eight simple individual techniques are combined and LP is compared with five traditional combination methods. The LP combinations outperform the other methods according to several performance indices. Finally, LP is used to estimate the parameters of autoregressive based models with optimisation objectives to minimise forecasting cost and it is compared them with the OLS. The experiments show that LP approaches perform better in terms of cost.

The research shows that LP is a very useful tool that can be used to make accurate time series forecasts, which can outperform the traditional approaches that are found in forecasting literature and in practise.

Item Type:Thesis (PhD)
Supervisors:Muyldermans, L.
Tan, K.H.
Faculties/Schools:UK Campuses > Faculty of Social Sciences, Law and Education > Nottingham University Business School
ID Code:2515
Deposited By:Mr Apostolos Panagiotopoulos
Deposited On:07 Sep 2012 15:44
Last Modified:07 Sep 2012 15:44

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