这个作业是完成3个统计学的问题: 英镑欧元汇率、股票收益等

MFIN 6609 A & B  Assignment 3

问题1(8分)
大多数时间序列都显示出很大的持久性(即自相关)。考虑文件sterling.dta,其中包含1999年1月至2006年12月之间的欧元/美元和英镑/美元汇率的月度数据。

一个。对于每一个,获取自相关系数的相关图(最高5阶)。在下表中列出这些内容。
不要出示计算机打印输出。 (4分)

r1 r2 r3 r4 r5
欧元
英镑

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)
问题2(18分)
在有关汇率变动的讨论中,人们经常听到有关一国货币升值或贬值的消息。对于美元,欧元和英镑等主要货币,一个有趣的问题是,美元兑主要货币(例如英镑)的价值变动是否与美元兑主要货币的价值变动相匹配。美元兑其他主要货币(例如欧元)的价值,如果央行试图保持欧元兑英镑汇率不变,可能会发生这种情况。换句话说,美元的欧元价格相对于美元的英镑价格的弹性等于一吗?考虑以下模型来评估此问题。

 

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?

Show your work. (4 points)

  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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