Steps

1. Use graphical techniques to inspect the data. Describe the behavior of the data. Mention any features you think may be important for analysis and forecasting.

2. In what way(s) is the data not stationary? Use transformations and/or differencing to make the series stationary. Include a time plot of the transformed and/or differenced data. If you chose a transformation, use this transformation for the remainder of the steps.

3. Using the transformed and/or differenced data from the previous part, obtain the sample ACF and PACF plots, as well as plots of the raw periodogram, and its smoothed version. Comment on the plots. Use the plots to make a preliminary guess for an appropriate ARIMA model. Keep in mind that differencing plays a part in determining whether the model should be ARMA or ARIMA.

4. Fit the model from the previous step. Include the model, and the parameter estimates. Plot the fitted values and the observed values on the same plot.

5. Examine the residuals. Provide necessary plots and/or hypothesis test results. Do the residu-als resemble Gaussian white noise?

6. Use AICc to select an ARIMA model for the (possibly transformed) data. Keep in mind that differencing should be incorporated into the model. It is fine to use the funciton auto . a r ima ( ) here. It is enough to consider p = 0, ...., 8, q = 0, ...., 8, and d = 0, 1, 2. Include the chosen model, and provide parameter estimates and their standard errors.

7. Inspect the residuals of this model. Provide necessary plots and/or hypothesis test results. Do the residuals resemble Gaussian white noise?

8. Plot the (theoretical) spectral density of the final model together with the smoothed peri-odogram. Comment on the plots. Describe the method you chose for smoothing the peri-odogram.

9. Now remove the data for 1975 (the last 10 observations). Using only data from 1966-1975 (the first 108 observations), fit an ARIMA model using AICc. Again, it is fine to use auto.arima(). Then do the following.
- Write down the chosen model. Include parameter estimates.
- Inspect the residuals of this model. Do they resemble Gaussian white noise?
- Compute point forecasts of the values for January through October 1975. If you used a transformation, then be sure to compute forecasts of the original data, not the trans¬formed data.
- Make a time plot of the entire data set, the point forecasts, and 95% prediction intervals. Make another plot of just the observed values from 1975 along with the point forecasts and the prediction intervals. Comment on the forecast performance.

Attachment:- bostonArmedRobberies.txt