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

Abstract

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 \(T \ge t+1\), which can be represented as a compact form of geometric series. We also find robust bounds for the Change in Mean Absolute Error (\(\varDelta \text {MAE}\)) and Measured Mean Absolute Error (MMAE).