  In this work, we apply machine learning techniques to historical stock prices
to forecast future prices. To achieve this, we use recursive approaches that
are appropriate for handling time series data. In particular, we apply a linear
Kalman filter and different varieties of long short-term memory (LSTM)
architectures to historical stock prices over a 10-year range (1/1/2011 -
1/1/2021). We quantify the results of these models by computing the error of
the predicted values versus the historical values of each stock. We find that
of the algorithms we investigated, a simple linear Kalman filter can predict
the next-day value of stocks with low-volatility (e.g., Microsoft) surprisingly
well. However, in the case of high-volatility stocks (e.g., Tesla) the more
complex LSTM algorithms significantly outperform the Kalman filter. Our results
show that we can classify different types of stocks and then train an LSTM for
each stock type. This method could be used to automate portfolio generation for
a target return rate.
