Click here to flip Canadian pennies. Recommendation: Flip 10 coins, reload page 16 times so it's easier to keep track. We emphasize here that every student should have a different series !
Series 1: For observations t = 1,2, … , 160, enter 1 if that flip comes up head and -1 if that flip comes up tails. Call this data series {e_{t}}.
Series 2: Generate this series with
X_{t} = e_{t }+ 100 , t=1,2, … , 160
Series 3: Generate this series by
X_{t+1} = r X_{t} + (1-r ) 100 + e_{t} , t=1, 2, … , 160
for r = 0.5 and for X_{1 }= 100.
Series 4: The trend component for series 3, that is a smooth curve passing through plot of series 3 versus time.
Series 5: The deviation from trend of series 3. For each observation t, the value of series 5 is the value of series 3 minus the value of series 4.
Series 6: Generate this series by
X_{t+1} = r X_{t} + (1-r ) 100 + e_{t} , t=1, 2, … , 160
for r = 0.95 and for X_{1 }= 100.
Series 7: The trend component for series 6.
Series 8: The deviation component
for series 6.
Part 3: Producing the plots.
Produce the plots A-E listed below using the time series
that you generated in Part 1 and Part 2. Open your Excel file, select the columns
that you wish to plot, click the chart wizard button, then click the selected
area, and follow the instructions of the chart wizard.
Read the section "Where are the Shocks?" in "Some
Skeptical Observations on Real Business Cycle Theory" by L. Summers,
MPLS FRB Quarterly Review of Fall 1986. The following paragraph
is from "Response
to a skeptic", by E. Prescott (same issue, p. 29):
Instructions for carrying out the exercise.
1. Create a Slutsky folder
2. Click HERE to download sum.exe. Save this file in the Slutsky folder you just created.
3. Open NotePad or WordPad. Type in the first number (1 or -1), then press the enter key. Repeat until you have entered all 160 numbers. Save the file as sumin.txt in Slutsky folder.
4. Run program sum. This entails clicking on sum.exe in Slutsky folder. The output file is sumout.txt.
5. Open sumout.txt in Excel. It is a space delimited .txt file. Save it as sumout.xls
6. Click HERE for instructions to plot the time series.
What to turn in:
1. Five plots from Part 3.
2. The essay in Part 4.