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P1.T2.510. First-order and general finite-order moving average process, MA(1) and MA(q)

Nicole Seaman

Director of FRM Operations
Staff member
Subscriber
Learning outcomes: Describe the properties of the first-order moving average (MA(1)) process, and distinguish between autoregressive representation and moving average representation. Describe the properties of a general finite-order process of order q (MA(q)) process

Questions:

510.1. Assume the shock (aka, innovation), ε(t), in a time series is approximated by Gaussian white noise. The lagged (yesterday's) realization was 0.0160 and the lagged shock was -0.280; i.e., y(t-1) = 0.0160 and ε(t-1) = -0.280. Today's shock, ε(t), is 0.190. If the weight parameter theta, θ, is equal to 0.60, which is nearest to the today's realization, y(t), under a first-order moving average, MA(1), process?

a. -0.0027
b. 0.0018
c. 0.0220
d. 0.1140


510.2. About the first-order moving average, MA(1), process where σ^2 is the variance of the shock theta (θ) is the weight, each of the following is true EXCEPT which is false?

a. The unconditional mean is zero
b. The unconditional variance is σ^2*(1+θ^2)
c. At displacements of two or higher, the autocorrelation is zero
d. By definition, MA(1) cannot meet the requirements of covariance stationarity


510.3. In comparing the first-order moving average process, MA(1), to the general finite-order process of order q, MA(q), which of the following is TRUE?

a. The MA(1) has the potential for longer memory than the MA(q)
b. Neither can be covariance stationary under any conditions due to the autocorrelation function
c. The MA(1) has the potential to deliver better approximations to the Wold representation than the MA(q)
d. If a root condition is satisfied, both are invertible; i.e., the current value can be expressed in terms of a current shock and lagged values of the series

Answers here:
 

Nicole Seaman

Director of FRM Operations
Staff member
Subscriber
Hello @JocelynN

In addition to this set of practice questions, we have posted the following daily practice questions for the Diebold reading so far:
Once we have a complete set of practice questions covering all of the learning objectives, we will publish a practice question set in the study planner consisting of all of the practice questions posted in the forum threads above.

Thank you,

Nicole
 

Nicole Seaman

Director of FRM Operations
Staff member
Subscriber
@CarlosB

Please see above where I stated "Once we have a complete set of practice questions covering all of the learning objectives, we will publish a practice question set in the study planner consisting of all of the practice questions posted in the forum threads above." This means that once all of the Diebold learning objectives are covered, the question set will be published. We do not give specific dates of when materials will be published, but the Dibold learning objectives should be covered completely by next week.

Thank you,

Nicole
 
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