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The time series object UKgas in the datasets package contains quarterly gas usage from 1960 through 1986. Type library(datasets); data(UKgas); print(UKgas); to see the data.

The time series object UKgas in the datasets package contains quarterly gas usage from 1960 through 1986. Type library(datasets); data(UKgas); print(UKgas); to see the data. You should analyze this data the best you can and help me create a report to address the following questions. Augment your report with relevant graphics and outputs, and be sure to comment clearly about what the graphs and outputs tell us.

a. Are any transformations of the data necessary and why? If you need to make transformation, try log transformation and BoxCox transformation. Use a=BoxCox(UKgas, lambda="auto") to perform BoxCox transformation. In the following, we will use the BoxCox transformed data.

b. Are there significant trend patterns? Use the decomposition model we have learned to extract the trend information, and make a plot of the trend.

c. Make a plot of the de-trended data , what can you say about the behavior of the detrended data?

d. Fit the best decomposition model and HoltWinters smoothing models you can on the transformed data. Obtain the residuals series. For stl, it's the remainder series. For HoltWinters, you can compute the residuals by res1=a-res$fitted[,1], assuming "a" is the Box-Cox transformed time series and res is the result of your HoltWinters model on "a".

e. Use ACF, PACF, and Box test to check if there are significant autocorrelations remaining in the residuals of the two models respectively. If there is, fit an AR model using the function "ar", and check the adequacy of the fitted model.

f. Make conclusions that relate to how the gas usage changes, both long-term over the observed period of years, and in terms of patterns of quarter- to-quarter variation.

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