Joint Prediction Regions for time-series models

TL;DR

This paper develops and compares methods for constructing joint prediction regions for time-series models, addressing the challenge of dependence in data and introducing a novel approach to estimate prediction standard errors.

Contribution

It implements Wolf and Wunderli's bootstrap-based method for joint prediction regions in time series and introduces a new technique for estimating prediction standard errors.

Findings

Stronger predictors like neural networks produce narrower prediction regions.

Prediction region width increases with forecast horizon and decreases significance level.

The proposed method effectively narrows prediction regions compared to existing approaches.

Abstract

Machine Learning algorithms are notorious for providing point predictions but not prediction intervals. There are many applications where one requires confidence in predictions and prediction intervals. Stringing together, these intervals give rise to joint prediction regions with the desired significance level. It is an easy task to compute Joint Prediction regions (JPR) when the data is IID. However, the task becomes overly difficult when JPR is needed for time series because of the dependence between the observations. This project aims to implement Wolf and Wunderli's method for constructing JPRs and compare it with other methods (e.g. NP heuristic, Joint Marginals). The method under study is based on bootstrapping and is applied to different datasets (Min Temp, Sunspots), using different predictors (e.g. ARIMA and LSTM). One challenge of applying the method under study is to derive prediction standard errors for models, it cannot be obtained analytically. A novel method to estimate prediction standard error for different predictors is also devised. Finally, the method is applied to a synthetic dataset to find empirical averages and empirical widths and the results from the Wolf and Wunderli paper are consolidated. The experimental results show a narrowing of width with strong predictors like neural nets, widening of width with increasing forecast horizon H and decreasing significance level alpha, controlling the width with parameter k in K-FWE, and loss of information using Joint Marginals.