Toeplitz Least Squares Problems, Fast Algorithms and Big Data

TL;DR

This paper compares two randomized algorithms for solving Toeplitz least squares problems in large-scale time series analysis, demonstrating their effectiveness and robustness on synthetic and real-world data.

Contribution

It provides a comparative analysis of LSAR and Repeated Halving algorithms, highlighting LSAR's robustness for real-world big data time series.

Findings

Both algorithms perform similarly on synthetic data.

LSAR is more robust on real-world data.

RandNLA techniques are effective for big-data time series.

Abstract

In time series analysis, when fitting an autoregressive model, one must solve a Toeplitz ordinary least squares problem numerous times to find an appropriate model, which can severely affect computational times with large data sets. Two recent algorithms (LSAR and Repeated Halving) have applied randomized numerical linear algebra (RandNLA) techniques to fitting an autoregressive model to big time-series data. We investigate and compare the quality of these two approximation algorithms on large-scale synthetic and real-world data. While both algorithms display comparable results for synthetic datasets, the LSAR algorithm appears to be more robust when applied to real-world time series data. We conclude that RandNLA is effective in the context of big-data time series.