# CS代考 End-of-year Examinations, 2017 – cscodehelp代写

End-of-year Examinations, 2017
STAT317 / STAT456 / ECON323 -17S2 (C)
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Seat Number
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No electronic/communication devices are permitted. No exam materials may be removed from the exam room.
Mathematics and Statistics EXAMINATION
End-of-year Examinations, 2017
STAT317-17S2 (C) Time Series Methods
STAT456-17S2 (C) Time Series and Stochastic Processes ECON323-17S2 (C) Time Series Methods
Examination Duration: 120 minutes Exam Conditions:
Restricted Book exam: Approved materials only. Calculators with a ‘UC’ sticker approved. Materials Permitted in the Exam Venue: Restricted Book exam materials.
One A4 double-sided, hand-written, sheet of notes.
Materials to be Supplied to Students:
1 x Standard 16-page UC answer book
Instructions to Students:
Use black or blue ink only.
Show all working.
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End-of-year Examinations, 2017 ECON323/614,STAT317/456-17S2 (C)
Questions Start on Page 3
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End-of-year Examinations, 2017 ECON323/614,STAT317/456-17S2 (C)
1. [9 marks] Give the definitions of the following concepts.
(a) Weak white noise
(b) Random walk with drift
(c) Weakly stationary time series
2. [9 marks] Are the following processes stationary or not? Give reasons for your answer.
(a) Random walk without drift.
(b) The AR(1) process Xt = 53 Xt-1 + Wt (c) Log-exchange rate of NZD and USD
3. [9 marks] Assume you observe a time series Xt and there seems to be a trend in the series that looks like a quadratic function.
(a) Write down a regression model for the quadratic trend.
(b) Extend the regression model in a way that it can account for seasonality that repeats after four observations. Point out how all four seasonal components can be estimated with your model. Explain in one or two sentences what might go wrong if such a model is written down in a naive way.
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End-of-year Examinations, 2017 ECON323/614,STAT317/456-17S2 (C)
4. [8 marks] Please explain the relationship between the Wold’s decomposition and the the ARMA models.
5. [8 marks] Consider the AR(2) model
Xt= 0.5Xt−1+0.4Xt−2+εt
where εt is a white noise process with mean 0 and variance 4.
(a) Give the numeric value of the autocovariance functions, γ(0), γ(1) and γ(2)
given the actual value of the parameters.
(b) Give the numeric value of the autocorrelation functions, ρ(0), ρ(1) and ρ(2).
6. [8 marks] Show how an AR(1) can be seen as an infinite MA and and how an MA(1) can be seen as an infinite AR.
End of Examination
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