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  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.
  1. Plot the realization.
  2. Estimate and plot the autocorrelation and autocovariance functions.
  3. Estimate and plot the Fourier spectrum by smoothing the periodogram and using and autoregressive approximation.
  4. 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.
  5. Estimate the parameters of the 'true' order (=2) and the order of an autoregressive model selected by order selection criteria.
  6. Perform a likelihood ratio test for the statistical significance of the extra estimated coefficients.
  7. Compute the roots of the associated autoregressive polynomial of the model selected using the order selection criteria.
  8. Compute and plot the impulse responses of the model, i.e. the associated MA coefficients in the infinite MA representation of the AR model.
View Complete Source for STSA Example 1

  Example 1 - Graphics Output

  Example 1 - Text Output

STSA Example 1 Command Output
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