  In this paper we examine the relation between market returns and volatility
measures through machine learning methods in a high-frequency environment. We
implement a minute-by-minute rolling window intraday estimation method using
two nonlinear models: Long-Short-Term Memory (LSTM) neural networks and Random
Forests (RF). Our estimations show that the CBOE Volatility Index (VIX) is the
strongest candidate predictor for intraday market returns in our analysis,
specially when implemented through the LSTM model. This model also improves
significantly the performance of the lagged market return as predictive
variable. Finally, intraday RF estimation outputs indicate that there is no
performance improvement with this method, and it may even worsen the results in
some cases.
