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Autocovariance and Autocorrelation of Moving Average Process

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Please help me answer the attached exercise on independent random variables.

Let {X1} be the moving average process of order 2 given by

X1 = Z_t + theta(Z_t-2),

Where {Z_t} is WN (0, 1).

a) Find the auto covariance and the autocorrelation functions for this process when theta = .8

b) Compute the variance of the sample mean (X_1 + X_2 + X_3 + X_4)/4 when theta = .8

c) Repeat (b) when theta = -.8 and compare your answer with the result obtained in (b).

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Solution Summary

This solution guides you to calculate the autocovariance and autocorrelation of the order 2 moving average process. Also, the mean and the standard error of the special combination of Xt is calculated step by step.

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Univariate time series modelling and forecasting

1 -Consider the following 3 models that a researcher suggests might be a reasonable model of stock market prices
Yt = Yt -1 +Ut
Yt = 0.5 Yt -1 + Ut
Yt = 0.8 Yt -1 + Ut

a) What classes of models are these examples of ?
b) What would the autocorrelation function for each of these processes look like ? (only consider the shape no calculation necessary)
c) Which model is more likely to represent stock market prices from a theoretical perspective , and why ? if any of the three models truly represented the way stock market prices move, which could potentially be used to make money by forecasting future values of the series?
d) By making a series of successive substitutions or from your knowledge of the behavior of these types of processes ,consider the extent of persistence of shocks in the series in each case

2 - What are the differences between autoregressive and moving average models


see attached for multiple choice questions

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