MATH38032 Time Series Analysis 2024-25
Coursework (Deadline 6pm Friday 4th April)
The data in jnj.txt are quarterly earnings per share of Johnson and Johnson from the first quarter of 1960 to the last of 1980. You can download the file from MATH38032 on Bb under Assessment and Feedback (menu on the left).
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0 .710000
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0 .630000
|
0 .850000
|
0 .440000
|
0 .610000
|
0 .690000
|
0 .920000
|
|
0 .550000
|
0 .720000
|
0 .770000
|
0 .920000
|
0 .600000
|
0 .830000
|
0 .800000
|
|
1 .000000
|
0 .770000
|
0 .920000
|
1 .000000
|
1 .240000
|
1 .000000
|
1 .160000
|
|
1 .300000
|
1 .450000
|
1 .250000
|
1 .260000
|
1 .380000
|
1 .860000
|
1 .560000
|
|
1 .530000
|
1 .590000
|
1 .830000
|
1 .860000
|
1 .530000
|
2 .070000
|
2 .340000
|
|
2 .250000
|
2 .160000
|
2 .430000
|
2 .700000
|
2 .250000
|
2 .790000
|
3.420000
|
|
3 .690000
|
3 .600000
|
3 .600000
|
4.320000
|
4.320000
|
4 .050000
|
4.860000
|
|
5 .040000
|
5 .040000
|
4.410000
|
5 .580000
|
5 .850000
|
6 .570000
|
5 .310000
|
|
6 .030000
|
6 .390000
|
6 .930000
|
5 .850000
|
6 .930000
|
7.740000
|
7.830000
|
|
6 .120000
|
7.740000
|
8 .910000
|
8 .280000
|
6 .840000
|
9 .540000
|
10 .260000
|
|
9 .540000
|
8.729999
|
11 .880000
|
12 .060000
|
12 .150000
|
8 .910000
|
14 .040000
|
12 .960000 14.850000 9 .990000 16 .200000 14 .670000 16 .020000 11 .610000
Fit an appropriate ARIMA model to the data. Do the following in R without using any additional package.
1. Read the data into R. No log transform here. [1]
2. Plot the data for 1960-80 and apply diferencing if necessary to remove trend and seasonal pattern. [3]
3. Produce sample acf and pacf plots of the diferenced data. [2]
4. Specify a tentative ARIMA model by examining the sample acf and pacf together. [3]
5. Estimate the parameters of the specified model. [2]
6. Examine the residuals of the fitted model, check correlation and Gaussianity of the residuals. [3]
7. Fit the same model to log quarterly earnings and report any improvement. [1]
8. Choose a model that is adequate for your (earnings or log earnings) data and see if the number of parameters can be reduced. [2]
9. Do 2.—4. above for the log quarterly earnings. [3]
Submit a brief report (about 6 pages) on Bb by the deadline. This should be in .pdf format and include an introduction, description of data, results, analysis, and a summary or conclusion. While it is not necessary to list all the R code you used, there should be sufficient information for your results to be reproduced.
The weighting of this coursework is 20%. The suggestion is to spend 4-6 hours including computer work and writing up, but excluding revision/catching up.