Posted on Feb 04, 2016 by Kris Longmore

[latexpage] Recently, I wrote about fitting mean-reversion time series models to financial data and using the models' predictions as the basis of a trading strategy. Continuing my exploration of time series modelling, I decided to research the autoregressive and conditionally heteroskedastic family of time series models. In particular, I wanted to understand the autogressive integrated moving average (ARIMA) and generalized autoregressive conditional heteroskedasticity (GARCH) models, since they are referenced frequently in the quantitative finance literature, and its about time I got up to speed. What follows is a summary of what I learned about these models, a general fitting procedure and a simple trading strategy based on the forecasts of a fitted model. Several definitions are necessary to set the scene. I don't want to reproduce the theory I've been wading through; rather here is my very high level summary of what I've learned about time series modelling, in particular the ARIMA and GARCH models and how they are related to their component models: At its most basic level, fitting ARIMA and GARCH models is an exercise in uncovering the way in...