Learning outcomes: Describe the properties of the first-order autoregressive (AR(1)) process, and define and explain the Yule-Walker equation. Describe the properties of a general pth order autoregressive (AR(p)) process
Questions:
511.1. Each of the following is true about a first-order autoregressive, AR(1), process with parameter phi (φ) EXCEPT which is false?
a. The processes are always invertible
b. The unconditional mean is zero and the conditional mean of y(t) is φ*y(t-1)
c. If phi (φ) = 0.95, the AR(1) is far LESS persistent than an MA(1) with the same parameter value
d. If phi(φ) is greater than -1.0 and less than +1.0, the process is covariance stationary
511.2. What does the Yule-Walker equation do?
a. It is the equation that allows for a test designed to detect first-order serial correlation
b. It is the equation that transforms an autogressive, AR(p), process into white noise
c. It gives us the autocovariance and autocorrelation function of an autogressive, AR(p), process
d. It applies the AR(p) process to macroeconomic variables; e.g., it estimates employment as a function of gross domestic product (GDP)
511.3. Assume the following AR(1) process: y(t) = 0.95*y(t-1) + ε(t). Which of the following is TRUE about this AR(1) process?
a. The unconditional mean is 0.95
b. The unconditional variance is one (1)
c. The conditional variance is 0.90250 = 0.95^2
d. At displacement (tau) of three, τ = 3,the autocorrelation of this AR(1) process is about 0.857 ~= 0.95^3
Answers:
Questions:
511.1. Each of the following is true about a first-order autoregressive, AR(1), process with parameter phi (φ) EXCEPT which is false?
a. The processes are always invertible
b. The unconditional mean is zero and the conditional mean of y(t) is φ*y(t-1)
c. If phi (φ) = 0.95, the AR(1) is far LESS persistent than an MA(1) with the same parameter value
d. If phi(φ) is greater than -1.0 and less than +1.0, the process is covariance stationary
511.2. What does the Yule-Walker equation do?
a. It is the equation that allows for a test designed to detect first-order serial correlation
b. It is the equation that transforms an autogressive, AR(p), process into white noise
c. It gives us the autocovariance and autocorrelation function of an autogressive, AR(p), process
d. It applies the AR(p) process to macroeconomic variables; e.g., it estimates employment as a function of gross domestic product (GDP)
511.3. Assume the following AR(1) process: y(t) = 0.95*y(t-1) + ε(t). Which of the following is TRUE about this AR(1) process?
a. The unconditional mean is 0.95
b. The unconditional variance is one (1)
c. The conditional variance is 0.90250 = 0.95^2
d. At displacement (tau) of three, τ = 3,the autocorrelation of this AR(1) process is about 0.857 ~= 0.95^3
Answers:
