Autoregressive-Model-Based Methods for Online Time Series Prediction with Missing Values: an Experimental Evaluation

TL;DR

This paper evaluates five autoregressive-based online methods for time series prediction with missing data, demonstrating that imputation is a simple and effective strategy across synthetic and real datasets.

Contribution

It provides a comprehensive experimental comparison of five AR-model-based methods for online prediction with missing values, highlighting the effectiveness of imputation strategies.

Findings

Imputation is a reliable strategy for handling missing data in online prediction.

Different methods vary in performance depending on data type and missing level.

Experimental results guide best practices for online time series prediction with missing data.

Abstract

Time series prediction with missing values is an important problem of time series analysis since complete data is usually hard to obtain in many real-world applications. To model the generation of time series, autoregressive (AR) model is a basic and widely used one, which assumes that each observation in the time series is a noisy linear combination of some previous observations along with a constant shift. To tackle the problem of prediction with missing values, a number of methods were proposed based on various data models. For real application scenarios, how do these methods perform over different types of time series with different levels of data missing remains to be investigated. In this paper, we focus on online methods for AR-model-based time series prediction with missing values. We adapted five mainstream methods to fit in such a scenario. We make detailed discussion on each of them by introducing their core ideas about how to estimate the AR coefficients and their different strategies to deal with missing values. We also present algorithmic implementations for better understanding. In order to comprehensively evaluate these methods and do the comparison, we conduct experiments with various configurations of relative parameters over both synthetic and real data. From the experimental results, we derived several noteworthy conclusions and shows that imputation is a simple but reliable strategy to handle missing values in online prediction tasks.