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PS 2: Late submissions receive a grade of 0. While you are allowed to discuss the problem set with
other students, you will need to hand in your own answers using your own words and list all the
students you worked with. Make sure to report all results and submit your r files or excel files as well.
1. For the following data series on FRED, create an AR(p) model to predict it (TOTLQ). You want
to first check for trend and seasonality and remove them if necessary and then find the
optimal p. Make sure to explain whether you found a trend and/or seasonality and how you
decided on the p.
2. Assume you have a variable yt that follows an AR(3). What will be the mean of the series?
3. In the retail sales example, we have seen that there can be outliers. This question will include
dummy variables to avoid the issues with outliers. In the AR2.r file, we saw that a three lag
ARIMA model was optimal. Using IIS, we found, that there are 13 months of outliers in our
sample. Generate 12 dummies, one for each outlier month and include them in the
regression with four lags. How do your estimates and your fit compare? Hint 1: AR2.r shows
how to create dummies. Hint 2: you will need to use the dynlm command for the regression,
as arima does not work (see Season2.r).
4. Use the arima.sim function to simulate a time series with an AR term of 0.8 and an MA term
of 0.5 and 1000 observations. Modify the loops used in class to check whether the AIC
correctly identifies the model. Then test the same thins using the BIC. Now, create the ACF
and partial ACF graph of this series. Do the graphs look closer to an AR(1) or an MA(1)
process?

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PS 2: Late submissions receive a grade of 0. While you are allowed to discuss the problem set with other students, you will need to hand in your own answers using your own words and list all the students you worked with. Make sure to report all results and submit your r files or excel files as well. 1. For the following data series on FRED, create an AR(p) model to predict it (TOTLQ). You want to first check for trend and seasonality and remove them if necessary and then find the optimal p. Make sure to explain whether you found a trend and/or seasonality and how you decided on the p. 2. Assume you have a variable yt that follows an AR(3). What will be the mean of the series? 3. In the retail sales example, we have seen that there can be outliers. This question will include dummy variables to avoid the issues with outliers. In the AR2.r file, we saw that a three lag ARIMA model was optimal. Using IIS, we found, that there are 13 months of outliers in our sample. Generate 12 dummies, one for each outlier month and include them in the regression with four lags. How do your estimates and your fit compare? Hint 1: AR2.r shows how to create dummies. Hint 2: you will need to use the dynlm command for the regression, as arima does not work (see Season2.r). 4. Use the arima.sim function to simulate a time series with an AR term of 0.8 and an MA term of 0.5 and 1000 observations. Modify the loops used in class to check whether the AIC correctly identifies the model. Then test the same thins using the BIC. Now, create the ACF and partial ACF graph of this series. Do the graphs look closer to an AR(1) or an MA(1) process? Name: Description: ...
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