NumPy, Pandas and Matplotlib basics

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Autoregressive and Moving Average Operators


Differencing


AIC, AICc, and BIC metrics

Maximum Likelihood Model Selection

In the previous section, we saw how Gaussian assumptions allow us to obtain and maximize the likelihood of some ARMA(p,q) process to obtain parameter estimates for the thetas and alphas. That is, for any model, we are looking to find parameters such that


The likelihood for a Gaussian Time Series


The ARMA(p,q) model implies that X_{t} can be expressed in the form above.

Estimation of MA(q) (Innovations)

As you may guess by the title, the way to estimate the MA(q) coefficients is… the Innovations Algorithm we saw before. Recall that the MA(q) process can be written as


Burg’s Algorithm Estimation Formulas

Estimation of AR(p) :: Yale-Walker

In real world problems, the ACVF is the easiest thing to estimate using the sample data…


The recursive forecasting form of the Innovations algorithm3.

Hair Parra

Data Scientist & Data Engineer at Cisco, Canada. McGill University CS, Stats & Linguistics graduate. Polyglot.

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