[1] Historical data (1965 – 2012) for the price of crude oil in US$ per barrel o
ID: 3152742 • Letter: #
Question
[1] Historical data (1965 – 2012) for the price of crude oil in US$ per barrel on the Saudi market is shown in table 1. Use the data to answer the following questions:
Table 1: Selected Data Series 1965 – 2012
Year
Crude Oil US$/barrel
Year
Crude Oil US$/barrel
1965
26.96
1989
38.10
1966
29.14
1990
39.61
1967
26.88
1991
42.1
1968
23.01
1992
46.81
1969
23.90
1993
44.97
1970
24.96
1994
50.42
1971
26.23
1995
52.86
1972
27.18
1996
58.55
1973
24.88
1997
57.74
1974
26.68
1998
54.39
1975
26.98
1999
51.74
1976
27.46
2000
53.84
1977
28.57
2001
58.96
1978
28.28
2002
57.62
1979
30.27
2003
58.93
1980
30.70
2004
64.75
1981
34.02
2005
65.48
1982
25.83
2006
65.81
1983
34.36
2007
69.67
1984
37.42
2008
68.94
1985
36.43
2009
62.43
1986
38.85
2010
57.22
1987
35.94
2011
57.49
1988
34.62
2012
58.70
a. Plot the data on a time plot and comment on the pattern in terms of seasonality, cyclicality and trend. [2 marks]
b. A suitable dynamic model for crude oil prices is Auto Regression (AR) of the form
Yt = a + bYt-1 + cYt-2 + dYt-3 + et
Estimate the model using the data provided.[5 marks]
c. Forecast the price of crude oil on the Saudi market in 2016 [3 marks]
d. Determine whether your model in b) is stable/stationary. Show your working [10 marks]
Year
Crude Oil US$/barrel
Year
Crude Oil US$/barrel
1965
26.96
1989
38.10
1966
29.14
1990
39.61
1967
26.88
1991
42.1
1968
23.01
1992
46.81
1969
23.90
1993
44.97
1970
24.96
1994
50.42
1971
26.23
1995
52.86
1972
27.18
1996
58.55
1973
24.88
1997
57.74
1974
26.68
1998
54.39
1975
26.98
1999
51.74
1976
27.46
2000
53.84
1977
28.57
2001
58.96
1978
28.28
2002
57.62
1979
30.27
2003
58.93
1980
30.70
2004
64.75
1981
34.02
2005
65.48
1982
25.83
2006
65.81
1983
34.36
2007
69.67
1984
37.42
2008
68.94
1985
36.43
2009
62.43
1986
38.85
2010
57.22
1987
35.94
2011
57.49
1988
34.62
2012
58.70
Explanation / Answer
a. We can plot the problem in Excel
the pattern is trend
b.
Yt = a + bYt-1 + cYt-2 + dYt-3 + et
By using R, the estimate model is
The code is
T=seq(1965,2012,1)
y=c(26.96,29.14,26.88,23.01,23.9,24.96,26.23,27.18,24.88,26.68,26.98,27.46,28.57,
28.28,30.27,30.7,34.02,25.38,34.36,37.42,36.43,38.85,35.94,34.62,38.1,39.61,42.1,
46.81,44.97,50.42,52.86,58.55,57.74,54.39,51.74,53.84, 58.96,57.62,58.93,64.57,
65.48,65.81,69.67,68.94,62.43,57.22,57.94,58.7)
arima(y,c(3,0,0))
Call:
arima(x = y, order = c(3, 0, 0))
Coefficients:
ar1 ar2 ar3 intercept
0.9636 -0.0174 0.0311 42.7746
s.e. 0.1436 0.2018 0.1444 12.4164
sigma^2 estimated as 10.98: log likelihood = -127.14, aic = 264.28
Yt = 42.77 + 0.9636Yt-1 -0.0174Yt-2 + 0.0311Yt-3 + et
c.
predict(x, n.ahead=4)
$pred
Time Series:
Start = 49
End = 52
Frequency = 1
[1] 58.30548 57.93444 57.60737 57.28640
$se
Time Series:
Start = 49
End = 52
Frequency = 1
[1] 3.313108 4.601014 5.502961 6.246807
d.
PP.test(y)
Phillips-Perron Unit Root Test
data: y
Dickey-Fuller = -2.5909, Truncation lag parameter = 3, p-value = 0.3382
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