Provide four separate line plots of the four data series for the first 50 observations only.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Assignment 1

General Comments

• Please write a self-explanatory report. Explain your answers using economic and/or econometric reasoning and any equations (or figures) needed to make your point. Calculations:

Provide final results and also show how you achieved your results using intermediate steps.

. The report nîay not exceed 5 pages.

. Frontpage, bibliography, and appendices are excluded from the page count. There is no character count. Instead, incorporate the format specifications provided in the Fornial Requirements for Standard Page.”

. The tables and graphs you refer to should be in the iiiain text of your report. Every number in any of your tables needs to be explained in your text. Do NOT paste the raw output from Stata or other software directly into the main text of your report (except for figures). You can use Stata or other software to obtain results and figures.

. Upload your report in pdf-format before the deadline.

. It is not necessary to hand in programming code. If you want to provide your code. include it in an appendix and refer to it only if needed. Make sure everything, including the code itself, is contained in a single pdf file.

. If you find help in hooks, papers, or on the web, remember to cite these sources in your report. Please only cite publicly available sources (do not cite the lecture slides).

. Collaboration among different groups is strictly forbidden and assignments will he checked for excessive similarity.

• Throughout the assignment use a 5% significance level (if not indicated otherwise). The normal distribution is denoted as N(p, q2)

Part 1: Simulations

Trends in Time Series

Simulate the following model for different values of the parameters (o, ß, ) specified below.

uf =n+/9t+4Yth...l+et, e-.IIDN(0,1)

. Set the seed to 1232020 at the beginning of your simulations. Assume a starting value

Yo = O where necessary and obtain 500 observations for four different sets of parameters:

 

1. (c,ß,4) = (1.0,0.8)

2. (o,ß,) = (1.0.1,0.8)

3. (a,ß,) = (0,0, 1)

4. (a,ß,41’) = (0.1,0,1)

. Provide four separate line plots of the four data series for the first 50 observations only.

. Provide four separate line plots of the four data series for all 500 observations.

. How can you characterize the four-time series? Are they stationary? Do they have a drift?

Do they have a trend?

. How can the characteristics be assessed from the 50 periods plots? Ftom the 500 periods plots?

. Explain how you could make the four data series stationary (in case they are not stationary)

The Dangers of Non-Stationarity

. Obtain 150 observatIons from two independent variables r and y = O and = 0): = l.00dx_1 + u, Yr = ‘.°4Yt—i + vi

where you simulate Ug and y1 as independent Gaussian (=normally distributed) white noise proces with p = O and o’ = 0.01. (You can look up the steps you have to take for generating variables from a random distribution in Problem Set 1, Exercise 2. Remeinlwr that you can call the previous value of a variable as variahle[..n-11).

. Are z and y stationary? Vhy / why not? Which time series processes do z and y come from?

. regress on r to estimate the OLS regression model: = (k + $1g) generate a variable R2 and store the regression’s R2 into the variable R2 using the replace command. You can either calculate I?2 b hand as R2 = 2d2/62 or obtain the value from the results Stat a stores for the most recent regression.

(— help regress —* scroll down to Stored results). Program a f orvalues loop to repeat these tasks 150 times in total and every time store the results for R2 in the variable R2.

. Repeat the whole exercise for the variables rs and ys: 15g = O.96t- ÷ u1, yst = O.58yr-1 + y1

Remember to store the results for R2 into another variable Rs2.

. Obtain two histograms for R2 and Rs2. Vhat is your interpretation?

What is the danger of non-stat ionarity?

. What is the probability that you observe R2 > 0.8 and Rs2 > 0.8?

. What happens if 4» 1? What happens if t = 1000?

Attachments:

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