Univariate time series models are especially useful when it comes to forecasting. Consider the following MA(1) process: yt = 0.5ut-1 + ut What is your forecast for yt+1 if you observe ut-1 = 0.2 and ut = -0.8? What is your forecast for yt+2? What is the forecast for 10-step ahead? How does the forecast for the distant future compare to the unconditional expectation of this MA(1) process? How is the forecasting exercise related to the expectation of the stochastic process (vt}?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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Univariate time series models are especially useful
when it comes to forecasting. Consider the
following MA(1) process: yt = 0.5ut-1 + ut What is
your forecast for yt+1 if you observe ut-1 = 0.2 and
ut = -0.8? What is your forecast for yt+2? What is
the forecast for 10-step ahead? How does the
forecast for the distant future compare to the
unconditional expectation of this MA(1) process?
How is the forecasting exercise related to the
expectation of the stochastic process {vt}?
%3D
%3|
Transcribed Image Text:Univariate time series models are especially useful when it comes to forecasting. Consider the following MA(1) process: yt = 0.5ut-1 + ut What is your forecast for yt+1 if you observe ut-1 = 0.2 and ut = -0.8? What is your forecast for yt+2? What is the forecast for 10-step ahead? How does the forecast for the distant future compare to the unconditional expectation of this MA(1) process? How is the forecasting exercise related to the expectation of the stochastic process {vt}? %3D %3|
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