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Usint R studio to do this project. All R code you use must be included. All code and plots should be clearly identified and referenced in the problem.
For this project, you will be analyzing the Los Angeles cardiovascular mortality dataset in the astsa package. This data set ranges from 1970 to part way through the year 1979. Therefore, we will remove the data for the partial year 1979 and analyze the data from 1970 through 1978. You can obtain the data with the following code:

“require(astsa)
data(cmort)
cmort.part = window(cmort, start=c(1970,1), end=c(1978,52))”

Use “?cmort” for a description of the data.

(5 points) Plot the observed data. Remove any trend by fitting an appropriate polynomial. Plot the residuals after the trend is removed. Comment on any apparent seasonality in these residuals. What do you think is the period d?

(10 points) Remove the seasonal component by using a sum of harmonics. Plot the residuals (after the trend is removed) and then plot the fitted season component on

the same plot. Plot the residuals after the seasonal component is removed. Comment on whether these residuals look stationary.

(5 points) Plot the ACF and PACF of the residuals resulting form part 2. Comment on what type of time series model you believe is appropriate for these residuals based on these plots.

(10 points) Use “auto.arima()” with “stepwise=F” to fit a model to the residuals. What model results from this? Now use “auto.arima()” with “stepwise=T”. What model results from this?

(5 points) Plot the ACF and PACF of the residuals after the time series model is fit in part 4. Comment on if there is any dependence structure remaining in these residuals.

(5 points) Conduct a Ljung-Box test to see if there is any dependence structure remaining. Report the p-value of this test and interpret it.

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