MFIN 6609 A & B  Assignment 3

r1 r2 r3 r4 r5

b。检验H0：ρs= 0相对于H1：ρs≠0，在s = 1,2 …，5的显着性水平为5％时。你的结论是什么？ （4分）

lneuro= β1 + β2lnster + ei

where lneuro is the log of the Euro/US\$ exchange rate, and lnster is the log of the Sterling/US\$ exchange rate.

A.1. Estimate the model and present the following information  (3 points)

 b1  = b2  = 95% confidence interval for β2 se(b1) = se(b2) = N= R2= d statistic = BG statistic (1 lag)=

1. At the 5% level determine whether β2 =1 using a two-tail test, (2 points)

H0:                                                  H1:

1. Test for first-order autocorrelation using the Durbin-Watson and BG tests. Use the 5% significance level. (3 points)

Durbin-Watson:   H0:                                  H1:

BG: H0:                                               H1:

B.1.  Re-estimate the model by GLS using the Prais-Winsten procedure and present your results below (3 points)

 b1* = b2* = 95% confidence interval for β2 se(b1*) = se(b2*) =

b1* and b2* are GLS estimators.

1. How do your results here compare to those in A.1 above? Explain. (3 points)
2. Estimate an ARDL (1, 1) model by OLS. Present the following information and check whether a BG test for zero first

order autocorrelation is supported by the evidence at the 5% significance level. (4 points)

ARDL estimator of β2:  b2 =                                                   BG statistic =

se(b2) =

Question 3  (14 points)

Consider the model as yt= βyt-1 +et, which describes the dynamics of price of a company’s stock (y).

1. Assuming that et has zero mean, constant variance σe2 and is not serially correlated, obtain expressions for E(yt),

var(yt) and cov(yt, yt-1 ) and the first-order autocorrelation coefficient. Does y represent a stationary process?

Explain briefly. (4 points)

1. If now et follows an AR(1) process, that is et =ρet-1 +vt, where vt is white noise and 0 < ρ < 1, is this process stationary?

1. Given b, show how you would get GLS estimates, assuming the sample is small, and you do not want to lose any

observations? (4 points)

1. Show that the GLS model can be written as an AR(2) model for T> 1. (2 points)

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