Problem Set 1
ECON 6376 Time Series Analysis September 8, 2019
Provide a screenshot of your R or RStudio environment.
Download the series ‘MSACSR’ from https://fred.stlouisfed.org/series/MSACS and using the ‘getSymbols’ function from the package ‘quantmod ’, transform the series into a ts object. Plot the time series and provide a brief description of any notable features. Finally, decompose the series and also provide a description of its elements. If you want full credit, you will need to provide an analysis of your findings as well as the model choice used.
[Enders (3.Ed) Ex.1]
Consider the difference equation: yt = a0 + a1yt−1 with the initial condition y0. Jill solved the difference equation by iterating backwards:
yt = a0 + a1yt−1
= a0 + a1(a0 + a1yt−1)
= a0 + a0a1 + a0a2 + · · · + a0at−1 + a1y0
Bill added the homogeneous and particular solutions to obtain:
y = a0 + at Σ y0 − a0 Σ
1 − a1 1 − a1
- Show that the two solutions are identical for |a1|< 1.
- Show that for a1= 1, Jill’s solution is equivalent to: yt = a0t + y0. How would you use Bill’s method to arrive at this same conclusion in the case a1 = 1 ?
[Enders (3.Ed) Ex.5]
The Unit Root Problem in time-series econometrics is concerned with characteristic roots that are equal to unity. In order to preview the issue:
a Find the homogeneous solution to each of the following:
- yt= 1.5yt−1− 0.5yt−2 + εt
- yt= yt−2 + εt
- yt= 2yt−1 − yt−2 + εt
- yt= yt−1+ 0.25yt−2 − 0.25yt−3 + εt
[Cowpertwait and Metcalfe (2009) – Ex.1 pg. 24 ]
Complete Exercise #1 (Chapter 1, pg. 24) from Cowpertwait and Metcalfe (2009). Use the data from Section 1.4 and concepts explained in Section 1.5 from Cowpertwait and Metcalfe (2009) to complete this exercise. Also, you need explain and justify the choice of models used in your analysis. In other words, it’s not enough to just apply the code and provide a pretty graph. If you want full credit, you will need to provide an analysis of your findings as well as the model choice used.