Boğaziçi University, Department of Economics
Course Code: EC 58D
Course Name: Selected Topics in Financial Econometrics
Problem Session 4 volatility modeling
Lecturer: Prof Burak Saltoglu
Deadline (1st of May 2017)
Data set: EC683.xls, MATLAB,Excel
Instructions:
· This is a group project, each group can have up to 2 students
· We will be using this data set for future assignment.
· You can bring your data with you so that we can discuss at the beginning of each class.
· You can use R which is similar to Matlab in GARCH. I will add both Matlab and R codes.
QUESTIONS
1. Descriptive ANALYSIS OF FINANCIAL TIME SERIES (STYLIZED FACTS)
a. In the following data set you are give a large daily data set:
b. ISE100 series (both the index many different individual stocks),source: IMKB or reuters
c. Dow Jones Industrial Average and SandP500, and an individual stock (google) (source yahoo finance)
d. (USD/TL)
e. You don’t have to work on them all.Choose a clear classification
i. Compare in the following way: Commodities, Developed vs emerging market stock indices, single stocks vs stock indices and FX return vs stock returns.
i. By using MATLAB (ACF code ) show that the ACF’s of return levels are unpredictable but Absolute values and squared returns are predictable. Compare whether absolute value or squared returns are more predictable. How does it change across different time series.
a. i.e. are commodity volatilities are more predictable than stock returns or FX returns. Do you observe a general rule on these return series?
j. Estimate the Box Ljung test statistics. You can use Matlab to do that please work on the matlab codes I have sent you.
k. Do the same for various frequency levels (i.e. daily, weekly or monthly). What do you observe? Can we conclude that “as we decrease the sampling frequency (i.e. from daily to weekly or monthly etc) volatility becomes less predictable”?
l. Calculate autocovariance and autocorrelations (r(t),r(t-i), daily returns i=1,...50, for weekly and monthly it can be lesser) (use EVIEWS or MATLAB). Comment on your findings very carefully.
2. Theoretical: Loglikelihood and ARCH and GARCH (BONUS)
a. By using a simple AR(0) and AR(1) regression model derive the likelihood and loglikelihood functions for
i. ARCH(1)
ii. GARCH(1,1) model
iii. Find the first derivatives of (Jacobian) of loglikelihood function for (i.) and (ii.)
iv. Derive the hessian (i.e.thesecond derivative matrix).
v. Sketch the Newton algorithm where you can estimate the ARCH or GARCH coefficients.
vi. You can also use Matlab numerical derivatives to obtain Jacobian and Hessian GARCH.
3. TIME SERIES ANALYSIS
a) By using the MATLAB codes you are given
i. Estimate each return series you have chosen in 1 by using GARCH(1,1),
ii. Find the long term volaility for your USD/TL is it changing across time?.
iii. Choose the lag length of GARCH and others (up to lag of 3 both ARCH and GARCH order).
iv. GJR and EGARCH with Normal and t-distributed innovations, Also estimate an EWMA model with lambda=0.94
v. First, test whether the squared residuals are predictable by using ACF, and Barlett tests.
vi. Then carry out Box Ljung test to see whether squared residulas are statisticaly significant.
vii. Conduct an ARCH LM test for each of the series and specifications (6 specifications) . Use MATLAB but you can even check with EVIEWS. In VIEW Option it does it.
viii. Then do the same tests of (iii. And iv.) for standardized residulas. You standardize residuals by dividing them into fitted ARCH model. See my MATLAB code.
ix. Conclude which model fits well for each series.
x. Only for one GARCH model try different sampling frequencies (i.e. weekly and monthly series). Do we see ARCH effect for the monthly data.
b.) In your previous PS you have estimated the Sharp Ratio is and betas. Do the same analysis with GARCH model. (i.e. in an AR(0) model your variance is the fitted GARCH model’s observations). Do you really see a time varying beta’s and sharp ratios? Just do it for one beta.
4. FORECASTING
Choose at least 3 time series and estimate GARCH model. Then do a forecasting experiment. Matlab has an option even though you can code by yourself. Look at MATLAB’s help on GARCH and check the volatility prediction. Then by reserving the last 10% of your data set obtain one-step-ahead forecasts of volatilities. For daily,weekly and monthly data conduct one-step ahead, forecasting.
Similar to what ı did in my book and in my slides use RMSE to discuss which model fares best. eserve the last 10% of your data for forecasting experiment.
a. Plot your actual your point forecasts.
b. Do your forecasting experiment in both dynamic and static fashion (note in dynamic forecasting, the previous estimate is treated as a realized value whereas in static one we need the actual value).
c. Calculate Root Mean Square Error statistics both the dynamic and static forecasts.
d. Discuss the differences in RMSE in between the dynamic and static cases.
e. What do you observe if you consider weekly and monthly frequencies.
f. You can use EVIEWS forecast menu but your excel spreadsheet would be also useful.
g. What can you say about return predictability of various frequencies (i.e. daily vs weekly monthly).
5. GRANGER CASUALITY
The granger causality test examines the causality between series, the direction of the relation. We can test whether GNP causes money supply to increase or a monetary expansion lead GNP to rise, under conditions defined by Granger.
Granger Causality Test
a. Steps for testing x (granger) causes y;
n Regress y on all lagged y to obtain RSS1
n Regress y on all lagged y and all lagged x obtain RSS2
n The null is ’s are alll zero.
n Test statistics;
b. Steps for testing y (granger) causes x;
n Regress x on all lagge x to obtain RSS1
n Regress x on all lagged x and all lagged y obtain RSS2
n The null is ’s are alll zero.
n
If we obtain Granger casuality both from a and b then we will have bivariate casuation.
Now we will apply this test for Stock Market volatility and Volume relationship. By using the daily data between 1929-2009 we can test whether volume causes stock return volatility. Also test whether stock return volatilities cause volume. Comment on you results