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Example 2 - Problem Description
In this example we simulate a nonlinear (exponential) trend with Gaussian MA innovations
and illustrate how one can use the functions gauss_newton and bhhh_ml with a user-specified
function for optimization and estimation of a model's parameters.
1. Plot the realization along with the 'true' exponential trend and a fitted linear quadratic trend for comparison.
2. Draw a scatterplot of the series vs. its first lagged value to indicate the strong linearity in adjacent values generated by the exponential trend.
3. Use the function gauss_newton to estimate the parameters of the trend function only.
4. Analyze the resulting residuals for evidence of remaining serial correlation; as expected,
5. the residuals have serial correlation indicating a MA model.
6. Estimate MA parameters of the residuals.
7. Then, jointly estimate all the parameters of the model (including the trend parameters,
8. the MA parameters and the innovation variance) using Maximum Likelihood.

View Complete Source for STSA Example 2

Example 2 - Graphics Output

Example 2 - Text Output