  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.
