Time-Rescaling Regression Method for Exponential Decay Time Series Predictions

Abstract

The exponential law has been discovered in various systems around the world. In this study, we introduce two existing and one proposed analytical method for exponential decay time-series predictions. The proposed method is given by a linear regression that is based on rescaling the time axis in terms of exponential decay laws. We confirm that the proposed method has a higher prediction accuracy than existing methods by performance evaluation using random numbers and verification using actual data. The proposed method can be used for analyzing real data modeled with exponential functions, which are ubiquitous in the world.

Cross-Industry Statistical Law: Average Booking Curves Draw Exponential Functions

“…One of the advantages of the application is that it is industrially unlimited. Some applications for forecasting or dynamic pricing that can be applied in various perishable asset industries have already been proposed [21,45].…”

“…Therefore, the use of booking curves for forecasting in RM has been widely studied by many researchers and professionals in the perishable assets industries. This has led to the development of several advanced and highly accurate forecasting models [16,17,18,4,9,11,10,19,20,14,21], including exponential smoothing [22,23,24,25], stochastic process models [3,26], generalized linear mixed models [27], and methods utilizing neural nets that incorporate seasonal and day-of-week trends into their parameters [28,29].…”

General dynamic pricing algorithms based on universal exponential booking curves

“…In addition, according to previous research, a time series prediction method for improving the accuracy of demand forecast using the exponential function law of booking curves has been proposed [13]. This approach t * t days before the usage day…”

“…Given a finite inventory Q max , we consider a situation in which we have a booking curve with the sales price Price before at t * days before the usage day. Based on Model (1) with the time series over t ≥ t * and the time-rescaling regression method [13], we obtain the predicted quantity demanded A i pred . Here, given the quantity targeted Q i target ≤ Q max on the usage date i, we have an opportunity to adjust the price by comparing A i pred and Q i target for each usage day.…”