IN R PLEASE

DATA SET GIVEN IN QUESTION AND BELOW:

Using the oil.price data set, assess stationarity and transform the data to stationarity WITHOUT fitting a deterministic trend. Once you have done that, do the following:

1. Specify and fit an ARMA model to the transformed data using the methods discussed in class. Specify the type of model for the original data that results from your selection. For fitting the chosen model, use the method of maximum likelihood. Be sure to carry out all model diagnostics, and if they don't support your model, try again. Include only the plots from this portion for the final model you chose.

2. Forecast the oil price for the next six months, along with 95% prediction limits. Describe what happens to the prediction limits and the predictions themselves.

install.packages("TSA") library(TSA) data(oil.price) summary(oil.price) print(oil.price)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov 1986 22.93 15.45 12.61 12.84 15.38 13.43 11.58 15.10 14.87 14.90 15.22 1987 18.65 17.75 18.30 18.68 19.44 20.07 21.34 20.31 19.53 19.86 18.85 1988 17.13 16.80 16.20 17.86 17.42 16.53 15.50 15.52 14.54 13.77 14.14 1989 18.02 17.94 19.48 21.07 20.12 20.05 19.78 18.58 19.59 20.10 19.86 1990 22.86 22.11 20.39 18.43 18.20 16.70 18.45 27.31 33.51 36.04 32.33 1991 25.23 20.48 19.90 20.83 21.23 20.19 21.40 21.69 21.89 23.23 22.46 1992 18.79 19.01 18.92 20.23 20.98 22.38 21.77 21.34 21.88 21.68 20.34 1993 19.03 20.09 20.32 20.25 19.95 19.09 17.89 18.01 17.50 18.15 16.61 1994 15.03 14.78 14.68 16.42 17.89 19.06 19.65 18.38 17.45 17.72 18.07 1995 18.04 18.57 18.54 19.90 19.74 18.45 17.32 18.02 18.23 17.43 17.99 1996 18.85 19.09 21.33 23.50 21.16 20.42 21.30 21.90 23.97 24.88 23.70 1997 25.13 22.18 20.97 19.70 20.82 19.26 19.66 19.95 19.80 21.32 20.19 1998 16.72 16.06 15.12 15.35 14.91 13.72 14.17 13.47 15.03 14.46 13.00 1999 12.51 12.01 14.68 17.31 17.72 17.92 20.10 21.28 23.80 22.69 25.00 2000 27.26 29.37 29.84 25.72 28.79 31.82 29.70 31.26 33.88 33.11 34.42 2001 29.59 29.61 27.24 27.49 28.63 27.60 26.42 27.37 26.20 22.17 19.64 2002 19.71 20.72 24.53 26.18 27.04 25.52 26.97 28.39 29.66 28.84 26.35 2003 32.95 35.83 33.51 28.17 28.11 30.66 30.75 31.57 28.31 30.34 31.11 2004 34.31 34.68 36.74 36.75 40.27 38.02 40.78 44.90 45.94 53.28 48.47 2005 46.84 48.15 54.19 52.98 49.83 56.35 58.99 64.98 65.59 62.26 58.32

Dec 1986 16.11 1987 17.27 1988 16.38 1989 21.10 1990 27.28 1991 19.50 1992 19.41 1993 14.51 1994 17.16 1995 19.03 1996 25.23 1997 18.33 1998 11.35 1999 26.10 2000 28.44 2001 19.39 2002 29.46 2003 32.13 2004 43.15 2005 59.41 2006