Learning outcomes: Define and describe the properties of the autoregressive moving average (ARMA) process. Describe the application of AR and ARMA processes.
Questions:
512.1. Each of the following is a motivating for an autoregressive moving average (ARMA) process EXCEPT which is not?
a. AR processes observed subject to measurement error also turn out to be ARMA processes
b. When we need to violate or cannot achieve the stationarity condition, an ARMA(1,1) process becomes necessary over MA(1) or AR(1) processes
c. If the random shock that drives an autoregressive process is itself a moving average process, then it can be shown that we obtain an ARMA process
d. ARMA processes can arise from aggregation; for example, sums of AR processes, or sums of AR and MA processes, can be shown to be ARMA processes
512.2. If both an AR(5) and ARMA(2,1) achieve the same approximation accuracy, why would we prefer one over the other?
a. We would not have a preference
b. We would prefer the AR(5) because it uses more data
c. We would prefer the AR(5) due to its relative simplicity
d. We would prefer the ARMA(2,1) due to its fewer parameters
512.3. Each of the following is true about ARMA processes EXCEPT which is false?
a. As with autoregressions and moving averages, ARMA processes have a fixed unconditional mean but a time-varying conditional mean
b. The demonstrated presence of common factors in an ARMA(3,1) validate its superiority over an AR(2) model; a.k.a, ARMA(2,0)
c. ARMA models, by allowing for both moving average and autoregressive components, often provide accurate approximations to the Wold representation that nevertheless have just a few parameters; i.e., ARMA models are often both highly accurate and highly parsimonious
d. In contrast to pure moving average or pure autoregressive processes, however, neither the autocorrelation nor partial autocorrelation functions of ARMA processes cut off at any particular displacement. Instead, each damps gradually, with the precise pattern depending on the process
Answers here:
Questions:
512.1. Each of the following is a motivating for an autoregressive moving average (ARMA) process EXCEPT which is not?
a. AR processes observed subject to measurement error also turn out to be ARMA processes
b. When we need to violate or cannot achieve the stationarity condition, an ARMA(1,1) process becomes necessary over MA(1) or AR(1) processes
c. If the random shock that drives an autoregressive process is itself a moving average process, then it can be shown that we obtain an ARMA process
d. ARMA processes can arise from aggregation; for example, sums of AR processes, or sums of AR and MA processes, can be shown to be ARMA processes
512.2. If both an AR(5) and ARMA(2,1) achieve the same approximation accuracy, why would we prefer one over the other?
a. We would not have a preference
b. We would prefer the AR(5) because it uses more data
c. We would prefer the AR(5) due to its relative simplicity
d. We would prefer the ARMA(2,1) due to its fewer parameters
512.3. Each of the following is true about ARMA processes EXCEPT which is false?
a. As with autoregressions and moving averages, ARMA processes have a fixed unconditional mean but a time-varying conditional mean
b. The demonstrated presence of common factors in an ARMA(3,1) validate its superiority over an AR(2) model; a.k.a, ARMA(2,0)
c. ARMA models, by allowing for both moving average and autoregressive components, often provide accurate approximations to the Wold representation that nevertheless have just a few parameters; i.e., ARMA models are often both highly accurate and highly parsimonious
d. In contrast to pure moving average or pure autoregressive processes, however, neither the autocorrelation nor partial autocorrelation functions of ARMA processes cut off at any particular displacement. Instead, each damps gradually, with the precise pattern depending on the process
Answers here:
