EQC7006: Time Series Analysis 2020/2021
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ACADEMIC SESSION 2020/2021: SEMESTER II
EQC7006: Time Series Analysis
1. Answer the following questions.
a) Explain the role played by autocorrelation and partial autocorrelation in the formulation of ARIMA modelling.
(1 mark)
b) Re-write ∆
using backshift operator, 
.
(0.5 mark)
c) Write in full the equation associated with each of the following notations:
i) 
(
12
)
ii) (1 − 
)2 (1 − 
4)
(1.5 marks)
d) The following table give the estimation results of a regression model. Y denotes the monthly series of new passenger vehicle sales in Australia (in thousands of units). @TREND+1 represents time trend (@TREND+1 = 1, 2, 3, …, 96). @MONTH’s are seasonal dummies where @MONTH=1 is equal to 1 for January and 0 otherwise, and @MONTH=2, @MONTH=3, @MONTH=4, @MONTH=5, @MONTH=6, @MONTH=7, @MONTH=8, @MONTH=9, @MONTH=10, @MONTH=11 and @MONTH=12 are similarly defined for February, March until December, respectively.
Dependent Variable: Y
Method: ARMA Conditional Least Squares (Marquardt - EViews legacy)
Sample (adjusted): 2010M03 2017M12
Included observations: 94 after adjustments
|
|
|
Std. Error
|
|
Prob. |
|
@TREND+1 |
-0.136061 |
0.015509 |
-8.773169 |
0.0000 |
|
@MONTH=1 |
46.38593 |
1.125425 |
41.21635 |
0.0000 |
|
@MONTH=2 |
48.59619 |
1.126565 |
43.13660 |
0.0000 |
|
@MONTH=3 |
53.81213 |
1.077650 |
49.93469 |
0.0000 |
|
@MONTH=4 |
45.61058 |
1.063967 |
42.86841 |
0.0000 |
|
@MONTH=5 |
50.10263 |
1.061100 |
47.21762 |
0.0000 |
|
@MONTH=6 |
62.14184 |
1.064322 |
58.38632 |
0.0000 |
|
@MONTH=7 |
49.37327 |
1.070907 |
46.10416 |
0.0000 |
|
@MONTH=8 |
50.25234 |
1.079429 |
46.55454 |
0.0000 |
|
@MONTH=9 |
52.47846 |
1.089117 |
48.18443 |
0.0000 |
|
@MONTH=10 |
50.47818 |
1.099530 |
45.90889 |
0.0000 |
|
@MONTH=11 |
52.01437 |
1.110413 |
46.84236 |
0.0000 |
|
@MONTH=12 |
52.77996 |
1.121616 |
47.05707 |
0.0000 |
|
AR(1) |
0.472265 |
0.112947 |
4.181310 |
0.0001 |
|
AR(2) |
0.080468 |
0.113200 |
0.710843 |
0.4793 |
i) Write the model in terms of the backshift operator and without the backshift operator.
(3 marks)
ii) Given that Y95 = 36.929 (November 2017) and Y96 = 36.748 (December 2017), compute the forecast values for January and February of 2018 ( 
97 and 
98 ).
(4 marks)
(Total: 10 marks)
2. Answer the following questions.
a) Explain whether a random walk process, 
= 
−1 + 
is stationary or non- stationary.
(1 mark)
b) Given below are the estimation results of an ARIMA model with its correlogram of residuals. Y denotes the monthly series of new passenger vehicle sales in Australia (in thousands of units).
Dependent Variable: D(Y)
Method: ARMA Conditional Least Squares (Marquardt - EViews legacy)
Sample (adjusted): 2010M06 2017M12
Included observations: 91 after adjustments
|
Variable |
|
Std. Error
|
|
Prob. |
|
AR(1) |
-0.621050 |
0.104652 |
-5.934446 |
0.0000 |
|
AR(2) |
-0.751300 |
0.125180 |
-6.001773 |
0.0000 |
|
AR(3) |
-0.151753 |
0.123449 |
- 1.229275 |
0.2223 |
|
AR(4) |
-0.247945 |
0.104784 |
-2.366253 |
0.0202 |
|
SMA(12) |
|
0.026852
|
32.66702
|
0.0000 |
i) Is the estimated process an adequate model? Explain.
(2 marks)
ii) Write the model in terms of the backshift operator and without the backshift operator.
(3 marks)
iii) Table A below gives the last 13 observations of the series (December 2016 to December 2017). Table B on the other hand gives the last 13 residuals generated by the model. Compute the forecasts for January and February of 2018.
Table A: Observed values of 
|
2016 |
2017 |
|||||
|
December |
January |
February |
March |
April |
May |
June |
|
42.385 |
34.920 |
34.740 |
38.972 |
32.147 |
38.842 |
50.646 |
|
|
July |
August |
September |
October |
November |
December |
|
|
35.792 |
35.733 |
38.147 |
36.396 |
36.929 |
36.748 |
2022-05-19