*
* Week 10
*
*
*
*Load data, file -> import -> ASCII data created by spreadsheet
*
*insheet FTSE_BARC.csv.csv
*
rename v1 time
rename v2 ftse100
rename v3 barc
tsset time

*Generate returns
generate lrftse100 = log(ftse100 /L.ftse100)
generate rftse100 = ftse100 /L.ftse100 -1

generate lrbarc = log(barc /L.barc)
generate rbarc = barc /L.barc -1

*Checking graphs
twoway (line ftse100 time) (line barc time, yaxis(2))
twoway (line lrbarc time) (line lrftse100 time, yaxis(2))

*Spurious regression example
drawnorm error1 error2, n(1568) seed(1000)
gen tempY = 0.05 + error1
gen tempX = 0.02 + error2

replace tempY = 0.05 + error1 + L.tempY in 2/1568
replace tempX = 0.02 + error2 + L.tempX in 2/1568

drop error1 error2

*False results, serial correlation invalidates results
reg tempY tempX

*Difference is stationary, results are good
gen tempDiffY = (tempY - L.tempY)
gen tempDiffX = (tempX - L.tempX)
reg tempDiffY tempDiffX

*Look for significantly negative values to reject Ho of unit root, nonstationarity. 
*Dickey–Fuller test for unit root. Determining the length of lag
dfgls rbarc, ers
dfgls rftse100, ers

reg rbarc rftse100

*Breusch–Godfrey test for serial correlation. Look for high prob to state no serial correlation.
* Formal definition: insufficient evidence to reject h0 of no serial correlation

*If lag values included, lags is not 0
estat bgodfrey, lags(0)

*Breusch–Pagan test for heteroskedasticity. Ho: homoskedasticity (High prob -> constant variance)

estat hettest

*Non-linear model, help arch - for more details
*ARCH effects, testing if there is arch 1 effect 

estat archlm, lags(1)
*check t values of added lags, if significant add more
arch rbarc rftse100,arch(1/1)

*Information criteria - to evaluate if the fit is better, smaller values indicate a better fit
estat ic

arch rbarc rftse100,arch(1/2)
estat ic

*Using robust against heteroskedasticity variance-covariance matrix

reg rbarc rftse100,robust

*Jarque - Berra test for normality. In this case testing the distribution of the error term.
predict res, residuals
histogram res, normal bin(50)
su res, detail
*Manual implementation, formula as below.
*JarBer = (n/6)*((skew^2)+1/4(Kurt-3)^3)
*Chi^2 distribution with 2 df to compare against critical value.
*Ho residuals are normally distributed

*Ramsey RESET test for misspecification. Testing against higher polynomial transformations. High F values -> reject Ho of correctly specified model
ovtest

**CAPM testint
* Risk free rate assume: 2.5% annual return -> (1+0.025)^1/365 = 1.0001
*model: returnI - returnRiskFree = b(returnMarket - returnRiskFree)

*Implies no constant
gen erbarc = rbarc - 0.0001
gen erftse100 = rbarc - 0.0001

reg rbarc rftse100,robust

*Can not reject Ho of CAPM being true
test _cons == 0