security – TITLE

PAPER CODE: ECO3 10 / 20 – 21 /S 2 /Final Exam

security – 这道题目是利用security进行的编程代写任务, 是有一定代表意义的security等代写方向

``````University
``````

PAPER CODE: ECO3 10 / 20 – 21 /S 2 /Final Exam

Problem A For questions 1 to 2 [ 20 MARKS]

Based on the information below:

``````# R output:
``````
``````Call:
``````
``````arima(x = y, order = c(0, 1, 1), seasonal = list(order = c(0, 1, 1), period = 4))
``````
``````Coefficients:
``````
``````ma1 sma
``````
1. 3872 – 0.3 765
``````s.e. 0.0 645 0. 1804
``````
``````sigma^2 estimated as 0. 0564 : log likelihood = 81.93, aic = - 189. 23
``````
1. Please tell what the seasonal coefficient is and what the standard
``````deviation of!
``````
``````"
``````
``````is? [1 0 MARKS]
``````
1. Please write down the fitted model. [1 0 MARKS]
Problem B For questions 3 to 4 [ 20 MARKS]
``````Consider a stationary four-dimensional time series &
``````
``````"
``````

. Let

``````)
``````

####### =

####### +,-(&

``````"
``````

####### ,&

``````" 0 )
``````
``````) be the lag- 1 auto-covariance matrix of &
``````
``````"
``````

. More specifically,

``````we have
``````

####### &

``````"
``````

####### =

#######

#######

#######

#######

####### &

``````),"
``````

####### &

``````5 ,"
``````

####### &

``````6 ,"
``````

####### &

``````7 ,"
``````

#######

#######

#######

#######

#######

``````)
``````

####### =

#######

#######

#######

#######

#######

``````))
``````

####### ( 1 )

``````)
``````

####### ( 1 )

``````)
``````

####### ( 1 )

``````)
``````

####### ( 1 )

#######

``````5)
``````

####### ( 1 )

``````55
``````

####### ( 1 )

``````56
``````

####### ( 1 )

``````57
``````

####### ( 1 )

#######

``````6)
``````

####### (

####### 1

####### )

#######

``````65
``````

####### (

####### 1

####### )

#######

``````66
``````

####### (

####### 1

####### )

#######

``````67
``````

####### (

####### 1

####### )

#######

``````7)
``````

####### (

####### 1

####### )

#######

``````75
``````

####### (

####### 1

####### )

#######

``````76
``````

####### (

####### 1

####### )

#######

``````77
``````

####### (

####### 1

####### )

#######

#######

#######

#######

1. Write down the meanings of
``````))
``````

####### (

####### 1

####### )

####### ,

``````77
``````

####### (

####### 1

####### )

####### . [10 MARKS]

1. Write down the meanings of
``````)
``````
``````( 1 ) and
``````
``````75
``````

####### ( 1 ). [10 MARKS]

``````Problem C For questions 5 to 6 [ 20 MARKS]
``````
``````Based on the R output of the tests and the figure listed below:
``````
``````# R output:
``````
``````University
``````

PAPER CODE: ECO3 10 / 20 – 21 /S 2 /Final Exam

``````> t.test(x)
``````
``````One Sample t-test
``````
``````data: x
``````
``````t = 3.5818, df = 431, p-value = 0.
``````
``````alternative hypothesis: true mean is not equal to 0
``````
``````95 percent confidence interval:
``````
``````0.009990214 0.
``````
``````sample estimates:
``````
``````mean of x
``````
``````0.
``````
``````>Plot(x)
``````
``````> adfTest(x,lags=1 5 ,type=c("##"))
``````
``````Title:
``````
``````Augmented Dickey-Fuller Test
``````
``````Test Results:
``````
``````PARAMETER:
``````
``````Lag Order: 1 5
``````
``````STATISTIC:
``````
``````Dickey-Fuller: -1. 9456
``````
``````P VALUE:
``````
1. 7421
``````Please answer the questions:
``````
1. Should we keep the drift for the random walk? Should we keep the time
``````trend for the random walk? [10 MARKS]
``````
1. Is this time series stationary? Why? And what should you do to get a
``````stationary time series? [10 MARKS]
``````
``````University
``````

PAPER CODE: ECO3 10 / 20 – 21 /S 2 /Final Exam

``````Problem D For questions 7 to 8 [ 20 MARKS]
``````
``````Suppose that the daily log return of a  security follows the model:
``````

####### <

``````"
``````

####### = 0. 02 + 0. 3 <

``````" 05
``````

####### +!

``````"
``````
``````where
``````

####### {

####### !

``````"
``````

####### }

``````is a Gaussian white noise series with mean 0 and variance 0.0 5.
``````
``````Assume that <
``````
``````)CC
``````
``````= 0. 022 , and <
``````
``````DD
``````
``````= 0. 015. Please answer the questions:
``````
1. Compute the 1-step ahead forecast of the return series at the forecast
``````origin G= 100. What are the associated standard deviation of the
``````
``````forecast error?
``````
1. Compute the 2-step ahead forecast of the return series at the forecast
``````origin G= 100. What are the associated standard deviation of the
``````
``````forecast error?
``````
Problem E For questions 9 to 10 [ 20 MARKS]
``````Based on the R output below:
``````
``````# R output:
``````
``````Title:
``````
``````GARCH Modelling
``````
``````Call:
``````
``````garchFit(formula = ~garch(3, 0), data = abcd, trace = F)
``````
``````Mean and Variance Equation:
``````
``````data ~ garch(3, 0)
``````
``````[data = abcd]
``````
``````Conditional Distribution:
``````
``````norm
``````
``````Coefficient(s):
``````
``````mu omega alpha1 alpha2 alpha
``````
``````0.011852 0.010588 0.237149 0.072747 0.
``````
``````Std. Errors:
``````
``````based on Hessian
``````
``````Error Analysis:
``````
``````Estimate Std. Error t value Pr(>|t|)
``````
``````University
``````

PAPER CODE: ECO3 10 / 20 – 21 /S 2 /Final Exam

``````mu 0.011852 0.005640 2.102 0.0356 *
``````
``````omega 0.010588 0.001284 8.249 2.22e-16 ***
``````
``````alpha1 0.237149 0.114734 2.067 0.0387 *
``````
``````alpha2 0.072747 0.046990 1.548 0.
``````
``````alpha3 0.053080 0.046526 1.141 0.
``````
``````---
``````
``````Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1   1
``````
``````Log Likelihood:
``````
``````291.8891 normalized: 0.
``````
``````Standardised Residuals Tests:
``````
``````Statistic p-Value
``````
``````Jarque-Bera Test R Chi^2 192.312 0
``````
``````Shapiro-Wilk Test R W 0.9638102 7.82629e- 09
``````
``````Ljung-Box Test R Q(10) 9.731163 0.
``````
``````Ljung-Box Test R Q(15) 18.39307 0.
``````
``````Ljung-Box Test R Q(20) 19.28568 0.
``````
``````Ljung-Box Test R^2 Q(10) 27 .2857 0. 0182258
``````
``````Ljung-Box Test R^2 Q(15) 26.92023 0.
``````
``````Ljung-Box Test R^2 Q(20) 27.70902 0.
``````
``````LM Arch Test R TR^2 24.88263 0.
``````
``````Information Criterion Statistics:
``````
``````AIC BIC SIC HQIC
``````
• 1.328190 – 1.281102 – 1.328454 – 1.
``````Please answer the questions:
``````
1. Does the standardized residuals follows a normal distribution? Why? Is
``````this GARCH model adequate? Why? [ 10 MARKS]
``````
1. How to improve these model? [ 10 MARKS]

####### — END OF PAPER —