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P1.T2.508. Wold's theorem

Nicole Seaman

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Learning outcomes: Describe Wold’s theorem. Define a general linear process. Relate rational distributed lags to Wold’s theorem

Questions:

508.1. Wold's representation theorem points to an appropriate model for a covariance stationary residual such that:

a. Any autoregressive process of (p) order can be expressed as a rational polynomial of lagged errors
b. Any purely nondeterministic covariance-stationary process is a linear regression of y(t) on a lagged conditional mean
c. Any purely nondeterministic covariance-stationary process is some linear combination of lagged values of a white noise process
d. Any autoregressive moving average model, ARMA(p,q), can be shown as the sum of autoregressive (AR) and moving average (MA) processes


508.2. Wold’s theorem tells us that when formulating forecasting models for covariance stationary time series we need only consider models according to the the general linear process. “General” refers to the fact that any covariance stationary series can be captured by the process. “Linear” reflects the fact that the Wold representation expresses the series as a linear function of its innovations. Under the general linear process, each of the following is true EXCEPT which is false?

a. Unconditional mean is constant
b. Unconditional variance is constant
c. Conditional mean moves over time in response to the information set
d. Conditional variance moves over time in response to the information set


508.3. In regard to rational distributed lag models, each of the following is true EXCEPT which is false?

a. It is possible to approximate the Wold representation using a rational distributed lag
b. ARMA and ARIMA forecasting models are simply rational approximations to the Wold representation
c. Rational distributed lags produce models that are parsimonious yet provide accurate approximations to the Wold representation
d. ARMA(1,1) is not practical for two reasons: it cannot be covariance stationary; and its unconditional mean is time-varying while its conditional mean is fixed

Answers here:
 

Nicole Seaman

Chief Admin Officer
Staff member
Subscriber
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I cannot understand wat it tries to explain. Pls explain in simple language
@Lubna29

We only provide the practice questions here in this section. The in-depth answers and explanations are available to paid members only. If you would like to gain access to the full answers and explanations, you can view the study packages that we offer here: https://www.bionicturtle.com/features-pricing-2/.

Thank you,

Nicole
 
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