Introduction to Time Series and Forecasting【solution manual 】

5.5 3000 observations of a Gaussian MA(1) with coefficient 0.6 and WNV=1.0were generated using ITSM. The option Transform>Subsequence allowsyou to pick out the independent subsamples 1-200, 301-500, …, 2701-2900,and get independent estimates for each of these ten samples of length 200.Using the seed 1111111111 gives the results below. Notice that the momentestimator is conveniently calculated in Excel by pasting in the sample ACFat lag 1 and computing the moment estimator from the explicit formula onp. 146.

Simulation rho(1)hat thetahat Moments Innov. Alg. MLE1 0.3901 0.479966 0.48 0.592 0.66862 0.4001 0.500208 0.5002 0.5909 0.61353 0.4611 0.665026 0.665 0.5649 0.5574 0.4569 0.649853 0.6499 0.6567 0.615 0.5489 #NUM! 1 0.755 0.67716 0.464 0.676099 0.6761 0.548 0.48597 0.4274 0.562754 0.5628 0.5284 0.55218 0.4238 0.553757 0.5538 0.6318 0.63789 0.3825 0.46532 0.4653 0.5324 0.5741

10 0.3611 0.426912 0.4269 0.5103 0.5581Sample variance = 0.027606 0.005475 0.003502Sample mean = 0.598 0.59104 0.59342

Asymptotic theory: 0.023704 0.005 0.00320.6 0.6 0.6

The MLE is clearly best in terms of sample variance and the moment estimator is worst.The empirical means and variances of the estimators are in good agreement with theasymptotic theory.

Introduction to Time Series and Forecasting【solution manual 】

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Transcript of Introduction to Time Series and Forecasting【solution manual 】

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