How and Why: Decorrelate Time Series

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O problemas das autocorrelações nas séries cronológicas.

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. If departure from white noise is found (using a few tests of randomness), then it means that the time series in question exhibits unusual patterns not explained by trends, seasonality or auto correlations. This can be useful knowledge in some contexts  such as high frequency trading, random number generation, cryptography or cyber-security. The analysis of decorrelated residuals can also help identify change points and instances of slope changes in time series, or reveal otherwise undetected outliers.


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