I present here two examples one with transformed data and the other without any transformation. In the transformed data case, the upper interval gets enormous large, whereas not in the untransformed case. (Function in forecast package in R)
dmnd=c(8.6,9.8,11.2,12.4,13.5,15.7,18.6,21.1,22.3,23.6,24.6,26.3,28.3,29.6,33.3,36.4,40.5,44.9,48.4,52.6,56.8,60.5,67.2,73.4,77.8,85.6,94.8,105.5,114.0,118.5,128.3,126.9,132.6,141.2,150.0,160.8,174.6,190.0,198.1,194.1,210.4,230.3,242.4,246.4,255.5)
#with transformation
fit <- Arima(dmnd[11:45], order=c(1,2,0), lambda=-0.25)
prg=forecast(fit,h=16,level=c(95),fan=FALSE,lambda=-0.25)
prg
Point Forecast Lo 95 Hi 95
36 262.8665 241.34010 286.8475
37 271.4097 231.18466 320.7765
38 279.9162 216.75679 367.8499
39 288.9224 201.26616 429.9376
40 298.2242 184.91488 513.2452
41 307.9328 168.56079 626.1724
42 318.0273 152.59291 782.3793
43 328.5442 137.35984 1003.7047
44 339.4971 123.06285 1326.8115
45 350.9112 109.82630 1815.8213
46 362.8087 97.70297 2589.1252
47 375.2149 86.69722 3879.8347
48 388.1558 76.77777 6185.0627
49 401.6596 67.89002 10677.4213
50 415.7557 59.96484 20513.6022
51 430.4756 52.92545 45881.0816
#without transformation
fit <- Arima(dmnd[11:45], order=c(1,2,0))
prg=forecast(fit,h=16,level=c(95),fan=FALSE)
prg
36 263.5024 252.64559 274.3592
37 271.7410 249.52972 293.9523
38 279.9288 243.87448 315.9832
39 288.1275 236.23983 340.0153
40 296.3239 226.81344 365.8344
41 304.5208 215.76687 393.2747
42 312.7176 203.22448 422.2107
43 320.9144 189.28707 452.5417
44 329.1112 174.03721 484.1851
45 337.3079 157.54444 517.0715
46 345.5047 139.86827 551.1412
47 353.7015 121.06045 586.3426
48 361.8983 101.16647 622.6302
49 370.0951 80.22673 659.9635
50 378.2919 58.27746 698.3063
51 386.4887 35.35135 737.6260
