  Time series forecasting is widely used in a multitude of domains. In this
paper, we present four models to predict the stock price using the SPX index as
input time series data. The martingale and ordinary linear models require the
strongest assumption in stationarity which we use as baseline models. The
generalized linear model requires lesser assumptions but is unable to
outperform the martingale. In empirical testing, the RNN model performs the
best comparing to other two models, because it will update the input through
LSTM instantaneously, but also does not beat the martingale. In addition, we
introduce an online to batch algorithm and discrepancy measure to inform
readers the newest research in time series predicting method, which doesn't
require any stationarity or non mixing assumptions in time series data.
Finally, to apply these forecasting to practice, we introduce basic trading
strategies that can create Win win and Zero sum situations.
