Mitigating parameter uncertainty in business forecasting

Pritularga, Kandrika and Svetunkov, Ivan and Kourentzes, Nikos (2023) Mitigating parameter uncertainty in business forecasting. PhD thesis, Lancaster University.

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Abstract

Organisations make multiple decisions, and each layer requires different types of information. The main task of forecasting in these different situations is to support each decision with relevant future information in point and interval forecasts. The consequence is that we have multiple and correlated time series. To produce point and interval forecasts for multiple decisions, we have three modeling options, namely: • modeling each time series with a set of univariate Exponential Smoothing methods, • modeling all time series with a Vector Exponential Smoothing model, and • utilising state-of-the-art forecast reconciliation. Each option has the same idea: to approximate the ‘true’ data-generating process. Consequently, we have uncertainties around each modeling option, namely (a) model structure, (b) parameter, and (c) sampling uncertainty. The literature mainly focuses on mitigating the model structure uncertainty, which is believed to harm forecast accuracy significantly. On the other hand, this thesis mitigates the parameter uncertainty in each modeling case (Exponential Smoothing, Vector Exponential Smoothing, and Forecast Reconciliation). We propose parameter shrinkage in each modeling option. Specifically, we propose a shrinkage estimator for the univariate and the multivariate exponential smoothing. We also suggest forcing some covariances to zero to mitigate the covariance matrix estimation uncertainty in the forecast reconciliation. Our study relies on theoretical investigations, simulation, and empirical studies. The theoretical analysis provides solid and rational arguments to mitigate the parameter uncertainty. We complement it with empirical findings, where the difference between the simulation and the empirical study is how much we can control the experimental designs. We also ensure that each design follows sound principles of forecasting evaluation. Our findings show that the shrinkage estimator improves forecast accuracy. However, the results are mixed for the Vector Exponential Smoothing. We also find that forcing some covariances in the covariance matrix approximation improves both the forecast accuracy and the variability of the forecasting performance. By understanding the parameter uncertainty, we find important correlations between parameters that may affect forecast accuracy. We also propose the concept of stochastic coherency to encapsulate the overlooked uncertainties in forecast reconciliation. Our thesis emphasises the importance of revisiting uncertainty in business forecasting. We decipher it via the bias-variance decomposition and understand how the interdependence between parameters affects our understanding of the uncertainty. It is not only essential to address each uncertainty individually but also to address all uncertainties comprehensively. In particular, we propose different types of parameter shrinkage. The implementation depends on whether we have sufficient information to estimate parameters in the model. In the univariate case, the parameters’ estimates tend to be inefficient when the sample size is limited. In the multivariate case, either the shrinkage estimator or forcing some parameters to zero by design is also a potential solution to the problem. These forms of shrinkage avoid overfitting and potentially improve foecast accuracy. Concerning decision makers, our understanding of uncertainty highlights the importance of reliability in forecasting, i.e., unmitigated parameter uncertainty results in unreliable forecasting performance. This reliability is essential to gain the decision-maker’s trust in our forecasts. It is a new business forecasting concept and is open to investigation.