TY - JOUR

T1 - Staying Positive

T2 - Challenges and Solutions in Using Pure Multiplicative ETS Models

AU - Svetunkov, Ivan

AU - Boylan, John E

PY - 2023/12/15

Y1 - 2023/12/15

N2 - Exponential smoothing in state space form (ETS) is a popular forecasting technique, widely used in research and practice. While the additive error ETS models have been well studied, the multiplicative error ones have received much less attention in forecasting literature. Still, these models can be useful in cases, when one deals with positive data, because they are supposed to work in such situations. Unfortunately, the classical assumption of normality for the error term might break this property and lead to non-positive forecasts on positive data. In order to address this issue we propose using Log-Normal, Gamma and Inverse Gaussian distributions, which are defined for positive values only. We demonstrate what happens with ETS(M,*,*) models in this case, discuss conditional moments of ETS with these distribution and show that they are more natural for the models than the Normal one. We conduct the simulation experiments in order to study the bias introduced by point forecasts in these models and then compare the models with different distributions. We finish the paper with an example of application, showing how pure multiplicative ETS with a positive distribution works.

AB - Exponential smoothing in state space form (ETS) is a popular forecasting technique, widely used in research and practice. While the additive error ETS models have been well studied, the multiplicative error ones have received much less attention in forecasting literature. Still, these models can be useful in cases, when one deals with positive data, because they are supposed to work in such situations. Unfortunately, the classical assumption of normality for the error term might break this property and lead to non-positive forecasts on positive data. In order to address this issue we propose using Log-Normal, Gamma and Inverse Gaussian distributions, which are defined for positive values only. We demonstrate what happens with ETS(M,*,*) models in this case, discuss conditional moments of ETS with these distribution and show that they are more natural for the models than the Normal one. We conduct the simulation experiments in order to study the bias introduced by point forecasts in these models and then compare the models with different distributions. We finish the paper with an example of application, showing how pure multiplicative ETS with a positive distribution works.

KW - Applied Mathematics

KW - Management Science and Operations Research

KW - Strategy and Management

KW - General Economics, Econometrics and Finance

KW - Modeling and Simulation

KW - Management Information Systems

U2 - 10.1093/imaman/dpad028

DO - 10.1093/imaman/dpad028

M3 - Journal article

JO - IMA Journal of Management Mathematics

JF - IMA Journal of Management Mathematics

SN - 1471-678X

ER -