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:
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:
