1. The weekly rates of return for five stocks listed on the New York Stock Exchange are given
(a) Construct the sample covariance matrix S, and find the sample principal components.
(b) Determine the proportion of the total sample variance explained by the first three prin-
cipal components. Interpret these components.
(c) Given the results in Parts (a)-(b), do you feel that the stock rates-of-return data can be
summarized in fewer than five dimensions? Explain.
2. Consider a time series model:
where wt are i.i.d. with zero mean and variance 2. 0 and 1 are fixed constants.
(a) Is Xt weakly stationary?
(b) Define Xt = Xt Xt 1. Is Xt weakly stationary?
(c) Assume wt in is replaced by yt where yt is a weakly stationary process with mean y
and autocovariance y(h). Is Xt still weakly stationary?
EasyDue™ 支持PayPal, AliPay, WechatPay, Taobao等各种付款方式!
E-mail: firstname.lastname@example.org 微信:easydue