Quarterly earnings per share of Caterpillar from the second quarter of 1983 to the second quarter of 2014.

da=read.table("q-earn-cat83.txt",header=T)

(a) Build a time series model for the earnings series.

Based on the ACF of the first differenced data, specify a model and then perform model checking (tsdiag) and write down the fitted model.

Do you specify an ARIMA(0, 1, 1)(1, 0, 1)4 model for the earnings?

(b) Fit the following model to the earnings series: m2=arima(xt,order=c(0,1,0),seasonal=list(order=c(0,1,1),period=4)) where xt denotes the earnings series.

Write down the fitted model.

(c) Compare the two time series models.

Which model is preferred in terms of in-sample fitting? Why?

(d) Use the backtest procedure to compare the two models via 1-step ahead forecasts.

You may use t = 101 as the starting forecast origin. Which model is preferred? Why?

Save following data in a text file and named as per given in the command at the start

OFTIC TICKER ANNDATS MEASURE PDICITY VALUE CAT CAT 19830414 EPS QTR -0.2438 CAT CAT 19830711 EPS QTR -0.1363 CAT CAT 19831019 EPS QTR -0.0925 CAT CAT 19840120 EPS QTR 0.0050 CAT CAT 19840413 EPS QTR -0.1450 CAT CAT 19840710 EPS QTR 0.0450 CAT CAT 19841019 EPS QTR -0.0963 CAT CAT 19850121 EPS QTR 0.7687 CAT CAT 19850411 EPS QTR -0.0913 CAT CAT 19850711 EPS QTR 0.0638 CAT CAT 19851017 EPS QTR 0.1663 CAT CAT 19860121 EPS QTR 0.1688 CAT CAT 19860416 EPS QTR 0.1412 CAT CAT 19860711 EPS QTR 0.1750 CAT CAT 19861020 EPS QTR -0.0325 CAT CAT 19870123 EPS QTR -0.0638 CAT CAT 19870416 EPS QTR -0.0450 CAT CAT 19870713 EPS QTR 0.1500 CAT CAT 19871020 EPS QTR 0.1837 CAT CAT 19880123 EPS QTR 0.1713 CAT CAT 19880414 EPS QTR 0.1450 CAT CAT 19880714 EPS QTR 0.1800 CAT CAT 19881022 EPS QTR 0.2338 CAT CAT 19890120 EPS QTR 0.2013 CAT CAT 19890424 EPS QTR 0.1737 CAT CAT 19890725 EPS QTR 0.1737 CAT CAT 19891023 EPS QTR 0.1337 CAT CAT 19900121 EPS QTR 0.1312 CAT CAT 19900424 EPS QTR 0.1213 CAT CAT 19900721 EPS QTR 0.0575 CAT CAT 19901020 EPS QTR 0.0675 CAT CAT 19910122 EPS QTR 0.0137 CAT CAT 19910420 EPS QTR -0.0400 CAT CAT 19910720 EPS QTR -0.0200 CAT CAT 19911021 EPS QTR -0.0463 CAT CAT 19920122 EPS QTR -0.3950 CAT CAT 19920422 EPS QTR -0.1637 CAT CAT 19920718 EPS QTR -0.0650 CAT CAT 19921023 EPS QTR 0.0287 CAT CAT 19930201 EPS QTR -0.0788 CAT CAT 19930422 EPS QTR 0.0425 CAT CAT 19930723 EPS QTR 0.0825 CAT CAT 19931022 EPS QTR 0.1188 CAT CAT 19940121 EPS QTR 0.1825 CAT CAT 19940420 EPS QTR 0.2363 CAT CAT 19940721 EPS QTR 0.2950 CAT CAT 19941024 EPS QTR 0.3000 CAT CAT 19950119 EPS QTR 0.3450 CAT CAT 19950419 EPS QTR 0.3750 CAT CAT 19950719 EPS QTR 0.4050 CAT CAT 19951017 EPS QTR 0.2675 CAT CAT 19960118 EPS QTR 0.3825 CAT CAT 19960416 EPS QTR 0.3825 CAT CAT 19960716 EPS QTR 0.4850 CAT CAT 19961015 EPS QTR 0.4025 CAT CAT 19970121 EPS QTR 0.4975 CAT CAT 19970415 EPS QTR 0.5200 CAT CAT 19970722 EPS QTR 0.5750 CAT CAT 19971015 EPS QTR 0.5150 CAT CAT 19980121 EPS QTR 0.6000 CAT CAT 19980417 EPS QTR 0.5750 CAT CAT 19980715 EPS QTR 0.6000 CAT CAT 19981016 EPS QTR 0.4600 CAT CAT 19990120 EPS QTR 0.4150 CAT CAT 19990416 EPS QTR 0.2850 CAT CAT 19990716 EPS QTR 0.3900 CAT CAT 19991015 EPS QTR 0.3050 CAT CAT 20000121 EPS QTR 0.3350 CAT CAT 20000418 EPS QTR 0.3650 CAT CAT 20000720 EPS QTR 0.4500 CAT CAT 20001017 EPS QTR 0.3100 CAT CAT 20010118 EPS QTR 0.3800 CAT CAT 20010417 EPS QTR 0.2350 CAT CAT 20010717 EPS QTR 0.3900 CAT CAT 20011016 EPS QTR 0.2950 CAT CAT 20020123 EPS QTR 0.3800 CAT CAT 20020416 EPS QTR 0.1150 CAT CAT 20020716 EPS QTR 0.2900 CAT CAT 20021016 EPS QTR 0.3050 CAT CAT 20030123 EPS QTR 0.4400 CAT CAT 20030416 EPS QTR 0.1850 CAT CAT 20030717 EPS QTR 0.5750 CAT CAT 20031016 EPS QTR 0.3100 CAT CAT 20040127 EPS QTR 0.4850 CAT CAT 20040422 EPS QTR 0.5800 CAT CAT 20040722 EPS QTR 0.7750 CAT CAT 20041021 EPS QTR 0.7050 CAT CAT 20050127 EPS QTR 0.7750 CAT CAT 20050420 EPS QTR 0.8150 CAT CAT 20050721 EPS QTR 1.0800 CAT CAT 20051021 EPS QTR 0.9400 CAT CAT 20060126 EPS QTR 1.2000 CAT CAT 20060424 EPS QTR 1.2000 CAT CAT 20060721 EPS QTR 1.5200 CAT CAT 20061020 EPS QTR 1.1400 CAT CAT 20070126 EPS QTR 1.3200 CAT CAT 20070420 EPS QTR 1.2300 CAT CAT 20070720 EPS QTR 1.2400 CAT CAT 20071019 EPS QTR 1.4000 CAT CAT 20080125 EPS QTR 1.5000 CAT CAT 20080418 EPS QTR 1.4500 CAT CAT 20080722 EPS QTR 1.7400 CAT CAT 20081021 EPS QTR 1.3900 CAT CAT 20090126 EPS QTR 1.0800 CAT CAT 20090421 EPS QTR 0.3900 CAT CAT 20090721 EPS QTR 0.7200 CAT CAT 20091020 EPS QTR 0.6400 CAT CAT 20100127 EPS QTR 0.4100 CAT CAT 20100426 EPS QTR 0.3600 CAT CAT 20100722 EPS QTR 1.0900 CAT CAT 20101021 EPS QTR 1.2200 CAT CAT 20110127 EPS QTR 1.4700 CAT CAT 20110429 EPS QTR 1.8400 CAT CAT 20110722 EPS QTR 1.7200 CAT CAT 20111024 EPS QTR 1.7100 CAT CAT 20120126 EPS QTR 2.3200 CAT CAT 20120425 EPS QTR 2.3700 CAT CAT 20120725 EPS QTR 2.5400 CAT CAT 20121022 EPS QTR 2.2600 CAT CAT 20130128 EPS QTR 1.4600 CAT CAT 20130422 EPS QTR 1.3100 CAT CAT 20130724 EPS QTR 1.4500 CAT CAT 20131023 EPS QTR 1.4500 CAT CAT 20140127 EPS QTR 1.5800 CAT CAT 20140424 EPS QTR 1.6100