Based on the in-class discussion of how the AR and MA regressions work and what the differentiation does (when active), explore the combinations of generation parameters and ARIMA parameters to experimentally discover some rules of thumb on what seems to work well and what seems to be a horrible idea in terms of forecasting precision.
Organize your writings in a report that briefly explains what each parameter appears to control and how it seems to interact with the other parameters, if at all.
There is no need to read any reference materials, but if you run out of ideas and need to consult external sources, please cite the sources clearly in your report.
Pen and paper time: either pick a real-world open dataset (for example from open.canada.ca) with a time series or just come up with some numbers whichever way you please. Pick a small interval of the time series (10 to 20 data points is perfectly sufficient) and plot it (completely by hand, no matter how roughly, or with some computer software of your choice).
Then, mimic step by step the simplied ARIMA process we studied in class, with some simple values of the parameters p, d, and q. Avoid making the calculations for the regression lines and instead just draw approximate regression lines (freehand) on your plot and on an auxiliary plot of the forecast errors you will end up making. Note that if you chose a non-zero value of d, you should also prepare a difference plot separately. Try to carry out at least five forecasts, no matter how rough approximates they end up being.
Include in your report photos or screenshots of different stages of your handicrafted ARIMA. Once you feel that you have understood what happens in each step, express that in writing as clearly as you can. if you notice that you made a mistake early on, no need to start over: just document what happened and continue with your new and improved understanding in the steps to come.
Consider any three of the the following four hypothetical scenarios and their impact on how mathematical forecasting methods might be able to cope with such situations. Instead of typing in a search engine, try to just think about how the method we studied together worked and what and how could be tweaked to adjust for the proposed scenarios.
Express your thoughts in writing. If you consulted any sources, please cite them clearly, but since this is a thought experiment, you are encouraged to just think instead of looking things up.
What kind of forecast methods do climate scientists use to study global warming? Find and browse peer-reviewed scientific publications. Discuss your findings in writing, with particular attention to what kind of seasonalities, sources of noise, and trends are present.
Remember to clearly cite your sources and share interesting findings with other participants.