Geometric series representation for robust bounds of exponential smoothing difference between protected and confidential data

Exponential smoothing is one of the most widely used forecasting methods for univariate time series data. Based on the difference between protected and confidential time series data, we derive theoretical bounds for the absolute change to forecasts generated from additive exponential smoothing models. Given time series data up to time t, we discover a functional form of robust bounds for the absolute change to forecasts for any T & GE;t+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T \ge t+1$$\end{document}, which can be represented as a compact form of geometric series. We also find robust bounds for the Change in Mean Absolute Error (& UDelta;MAE\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta \text {MAE}$$\end{document}) and Measured Mean Absolute Error (MMAE).

Automated summary

Exponential smoothing is a widely used forecasting method for time series data. This study derives theoretical bounds for the absolute change to forecasts generated from additive exponential smoothing models, based on the difference between protected and confidential time series data. It is found that the absolute change to forecasts can be represented as a compact form of geometric series and robust bounds are also identified for the Change in Mean Absolute Error (ΔMAE) and Measured Mean Absolute Error (MMAE).