project | 统计代写 | time series | R代写 – Consider a stationary three-dimensional time series Xt. Let r1

2023-07-05

Consider a stationary three-dimensional time series Xt. Let r1

project | 统计代写 | time series | R代写 – 这是时间序列代写方面的统计题目, 这个项目是project代写的代写题目

project代写 代写project

Problem A For questions 1 to 2[10 MARK]
Consider a stationary three-dimensional time series Xt. Let r1 =
Cov(Xt, Xt_ 1 ) be the lag- 1 auto-covariance matrix of Xt. More
specifically, we have

####### 1. Write down the meanings of r 11 (1) and f 33 (1)

####### 2. Write down the meaning of r 12 (1) and r2 3 (1)

Problem B For questions 3 to 4 [15 MARK]

Below are two regression models with Time Series Errors. Model ml is
the model which residuals follow an MA(2) model. Model m2 is the
model which residuals follow an AR(l) model. According to the output
below,
  1. Please write down the fitted models ofml including the residual variance. What are the 1 step ahead and 2 step ahead forecast and the associated standard errors?
  2. Please write down the fitted models ofm2 including the residual vanance.
  3. Which model is better?
rm1 ii resrduals follow ari N!Am inodel:J

c———-::——–o:1Jso———=o:ous9—–o-:oso s:.-.—–::–oo-29s—–o:0Js-s——o:0102—-o:onll

sigma"2estimiilecl-a,rn:10:-1og;-1ikeliliood=::2972:10;-.ic=245Q

i!teoicl\llb)
nrel!

Slart__:=JllJ
End#2"92J

$laff'cf2"87]
Eifd292J
!'wliiency=TJ
(1]'5;43756784-5:76f8C5:76J8-5:76J

8ii2Jfresioiiliis-foIIowan-AK(ffmJi'llell
Calll
ai'n:na(@ otoer =.c(l, O, Q), xreg = cD

L....:._..   -__ arr--....---. -iiltercepy ___ .. --c

######## c-,–. -=03,r23=-:oowo,:-::::o;o:61s

'e::---.-. o:ons---.. -o]rr2::i--: -o'.QTKi\

Problem C For questions 6 to 8 [15 MARK] A one-year project has a 98% chance of leading to a gain of $2 million, a 1.5% chance of a loss of $4 million, and a 0.5% chance of a loss of $ million. Please answer the questions below:

  1. What is the VaR with a 99% confidence level?
  2. What is the VaR with a 99.9% confidence level?
  3. What is the VaR with a 99.5% confidence level?

Problem D For questions 9 to 11[30MARK]

Consider the quarterly earnings per share of FedEX starting from the
second quarter of2012 to the fourth quarter of 2018. We analyze the log
earnings per share, denoted by Yt Answer the following questions.
  1. Write down the fitted time series model ml for the Yt series, including the residual variance. 10.Is the model adequate base on 5% significance level? Why? 11.Let 91 be the coefficient oflag-1 of the MA polynomial. Test Ho : 91 = 0 versus H1 : 91 ;t,O. Calculate the test statistic and draw the conclusion base on 5% significance level.

&ay/:hion;.Yg 1!14′ ‘7{.’ .. 20)20:’l- [16 .. ,., ,/’;’,’ ‘2012, >; ll: F"itl’eclli[;1Jni!ot;TJ .yt,;,1og(xi);,l!lo!MJ5iiiJi!YJ E> acf(Y!); frcf(di!!(yj))}a’cf(difilill.i’!@),4)] 2(ml#ariiria(l’!,ordet#2_(Q,l,1),seasonal=list(ordei=c(Q,1,!),period=4)j [!!1] ITTITT.rihiaordef-=c(Q,i,J};sasartiif=list{Qiilerdc(Q,i,!),periocI;;;-5J

c—:o:10-s-:c

s.e=-‘2-:-:::02):@

]p"2 stiinalea.as0:01ff6:-lo/f]ikelinooff=:n3:aic = l 4A:

l?JfuxJesf(ml$iesiaua1,;1a1e12:tyfe=’Liung’J

c= .. -:-Box:!::JungkJ

Problem E For questions 12 to 14[30MARK] GARCH models and their variants are often employed in economics and finance. Please comment on the following two methods for volatility modeling:

  1. ARCH and GARCH, and their parameter restrictions;
  2. Discuss the symmetry in these two models;
  3. Discuss the selections of the lag length of an ARCH(p) and an GARCH(p,q) model.
---END OF PAPER ---