Problem Set 1
ECON 6376 Time Series Analysis September
Problem 1
Provide a screenshot of your R or RStudio environment.
Problem 2
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.
Problem 3
[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 ?
Problem 4
[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