H.W. (unitroot) 1. Consider a Difference Stationary Model Xt - Xt-1 = + t, where t is a stationary ARMA term and X0 = . a. Rewrite Xt as a function of , and i. b. Verify that the variance of Xt is t-dependent and t has a permanent effect on Xt. c. Show th
Homework (cointegration) 1. Ans. What does Yt ~ I(d) mean? Yt ~ I(d) means (1-L)dYt is stationary; that is after differencing d times, the series cfw_Yt is stationary. Let Yt (Y1t, Y2t). What does Yt ~ CI(d,b) mean? Yt ~ CI(d,b) means the elements of the
Homework (cointegration) 1. 2. 3. 4. What does Yt ~ I(d) mean? Let Yt (Y1t, Y2t). What does Yt ~ CI(d,b) mean? Explain how the cointegration concept could be used to study economic equilibrium relationships. Use an economic example to illustrate your argu
1.
An ARCH(1) process is given by t t 1 ~ N (0, ht ), where ht Vt 1 t 0 1 t21;
o , 1 0 and 1 1 .
a. Find the unconditional mean and variance of t . E t 0 and E t2 0 / 1 1 . (Show the derivation) Show that t 's are correlated but not independent.
b.
t 's
ECON217_HW_ARMA 1. 2. 3. 4. If a time series cfw_Xt is covariance stationary, what do we know about E(Xt) and COV(Xt, Xt-k) for t = 1, ., T and k = 0, 1, 2, .? If cfw_Xt is a white noise process, what do we know about E(Xt), and COV(Xt, Xt-k) for for t =
ECON217_HW_ARMA Suggested Solutions 1. As. If a time series cfw_Xt is covariance stationary, what do we know about E(Xt) and COV(Xt, Xt-k) for t = 1, ., T and k = 0, 1, 2, .? E(Xt) denotes the mean of Xt. If cfw_Xt is covariance stationary, E(Xt)is time i
1.
An ARCH(1) process is given by
t t 1 ~ N (0, ht ),
where ht Vt 1 ( t ) 0 1 t21; o , 1 0 and 1 1 .
2.
3.
a. Find the unconditional mean and variance of t . b. Show that t 's are uncorrelated but not independent. c. Discuss the properties of this proces
H.W. (unitroot) 1. Consider a Difference Stationary Model Xt - Xt-1 = + t, where t is a stationary ARMA term and X0 = . a. Rewrite Xt as a function of , and i. b. Verify that the variance of Xt is t-dependent and t has a permanent effect on Xt. c. Show th
1. What is a VAR model? What are the stationarity conditions for a VAR model? What are the advantages/disadvantages of using a VAR model to analyze economic data? AS. A vector autoregressive model can be interpreted as an unconstrained reduced form of a d
ECON217_HW_VAR 1. What is a VAR model? What are the stationarity conditions for a VAR model? What are the advantages/disadvantages of using a VAR model to analyze economic data? 2. a. Use a bivariate VAR(1) model to discuss and explain i) impulse response