CIS 418 – Spring 2020
Assignment 1
Due Wednesday, April 1 @ 5:30 PM
Please cut and paste your work into Word (or similar) and upload to BB as one single pdf or document file. You may use Excel and/or R to complete the assignment (R will be easier for some of the questions, but nothing is impossible in any of the languages/software). You may include your output (charts, model results) as well as the code that you used to create it, but please edit down your code to just the important lines.
1.) Consider the data file HW1_question1.txt on BB. The data series is the monthly growth rate of the Consumer Price Index for 5 years ranging from 2013 – 2017.
a. Consider whether the data series exhibits evidence of serial correlation. Test the null hypothesis that the first 12 lags of autocorrelations are 0 at the 5% significance level. Describe the conclusion that you draw from the hypothesis test.
b. Plot the ACF and PACF function for the CPI growth rate data series.
c. Use the ar() function to obtain ARIMA model fitting statistics for the data series. List the
Akaike information criteria for orders p=1,….,12. What model and order is identified by
the ar() function? Do the ACF and PACF support this specification? Why or why not?
d. Build an ARMA model based on your above findings for the data series. Write down the
equation for the fitted model.
e. Plot the ACF for the model residuals. Use the Box-Ljung test to determine whether the
model residuals have any remaining autocorrelation. Describe your conclusions.
2.) Use Excel to create a simulation of an AR(9) time series, similar to the AR(4) simulation we looked at in class. Choose your own values for the simulation’s lagged variables coefficients (use different values than other students).
a. Make a graph showing the first 250 observations from your simulation when there is no error term. Then, add an error term to each time period drawn from a standard normal distribution (mean=0, variance=1). Graph the stochastic version of your simulation.
b. Plot the ACF and PACF for your stochastic simulation.
c. Use the ar() function to identify the order of your data series. Did the ar() function
identify order = 9?
d. Build an AR(9) model for your simulated data series. Write down the equation for the
fitted model and compare the estimated coefficients to those you used to generate the
series.
e. Plot your data series and add a dotted line for the fitted values of your estimated model.
f. Plot the next 25 out-of-sample forecasts for your data series.
g. Build an AR(6) model and an AR(12) model for your simulated data series. Write down
the equations for the fitted models. Perform model checking on the residuals of your AR(6) and AR(12) specifications and discuss the impact of varying the order on the adequacy of the models. Describe in words the relative goodness of fit of the 3 models that you built for your simulated data series.