Example 1 - Problem Description
In this example we simulate a stationary, zero mean Gaussian autoregressive model of order 2
and perform various operations on the resulting realization.
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- Plot the realization.
- Estimate and plot the autocorrelation and autocovariance functions.
- Estimate and plot the Fourier spectrum by smoothing the periodogram and
using and autoregressive approximation.
- Estimate and plot the empirical distribution function of the realization and
perform two tests for Gaussianity: the Kolmogorov-Smirnov test and the test
based on the QQ (quantile-quantile) correlation coefficient.
- Estimate the parameters of the 'true' order (=2) and the order of an autoregressive model
selected by order selection criteria.
- Perform a likelihood ratio test for the statistical significance of the extra estimated
- Compute the roots of the associated autoregressive polynomial of the model selected
using the order selection criteria.
- Compute and plot the impulse responses of the model, i.e. the associated MA coefficients
in the infinite MA representation of the AR model.
Example 1 - Graphics Output
Example 1 - Text Output