Exercises
Here is a series of exercises. The answers to all the exercises are given in the Answers_to_Exercises_Chap6.ipynb Jupyter notebook in the GitHub repository.
- For the AR(1) process defined by the following equation,
Eq. 35
show that 
and 
as 
, for any starting value 
. For this exercise you can assume that 
.
2. For the AR(1) process defined by the following equation,
Eq. 36
show that 
and as , for any starting value . For this exercise, you can assume that . See if you can derive the values of 
and 
for any value of 
, not just the asymptotically limiting values.
3. Use the ARIMA model form in Eq. 28 to generate a sample time series of length 
timepoints, that is of order 
, with coefficients 
. The noise values should be i.i.d. 
. You can set the first value, 
, of the generated series to zero. Use the statsmodels.tsa.arima.model.ARIMA function from the statsmodels package to fit an ARIMA(1,1,1) model to the simulated data you have just generated...
