How and Why: Decorrelate Time Series

When dealing with time series, the first step consists in isolating trends and periodicites. Once this is done, we are left with a normalized time series, and studying the auto-correlation structure is the next step, called model fitting. The purpose is to check whether the underlying data follows some well known stochastic process with a similar auto-correlation structure, such as ARMA processes, using tools such as Box and Jenkins. Once a fit with a specific model is found, model parameters can be estimated and used to make predictions. A deeper investigation consists in isolating the auto-correlations to see whether the remaining values, once decorrelated, behave like white noise, or not.