Using the random number seed 1893, simulate an ARIMA(2,1,1) series of length 25 with 1= 0.4, 2= 0.3, and = 0.6, along with a mean term = 100 (to do this, simulate an ARIMA(2,1,1) series without a mean term and then add 100 to the series). Provide estimates of all model parameters, along with standard errors, and compare them to the true values of the parameters. Repeat the whole process for a series of length 100 and all the same model parameters, and then again for a series of length 1000 with all the same model parameters. Describe what happens to the parameter estimates with regard to the true values as

the series length increases, and describe what happens to the standard errors as well. Provide actual numbers to support your description/assessment. For each simulation, compare your estimates to the true values in a quantitative way that can help you evaluate the significance of the difference between the estimates and the true parameter values. Use maximum likelihood for all estimations.