ABSTRACT
We provide a review of some basic and some advanced statistical methodologies that are useful for developing trading algorithms. We begin with time series models for univariate data and provide a broad discussion of autoregressive integrated moving average (ARIMA) models-from model identification, estimation, inference to model diagnostics. The stock price and return data exhibit some unique features and so we identify certain stylized facts regarding their behavior that have been empirically confirmed; this work will greatly help to discern any anomalies as and when they arise, as these anomalies generally indicate deviation from efficient market hypothesis. Although for modeling price and return data, only lower order (ARIMA) models are needed, increasingly other trading features such as volume, volatility-that are being used in developing trading strategies-require higher order models. In particular, predicting future volume flow is useful to determine when to enter the market. Wherever possible we illustrate the methodology with examples and make the data accessible to the reader. We also introduce some novel methodologies that have potential for developing competing trading models.
