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financial data series econometric test result interpretation

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azim on 10 Nov 2018
Closed: MATLAB Answer Bot on 20 Aug 2021
Hi I was testing the daily log returns of s&p500 closing price for all unit root, stationarity and arch effect tests. I first downloaded the dates and closing prices in to variables [dated1 close1] around 6800 days data. Then found daily returns using :
tdret=totaldailyreturn(:,2); %daily return
tdlret=log(tdret+1); %log return
found the mean of the log return and found the residuals by subtracting the mean. Do these calculations of the data seem correct
Then on the data did the following test: adftest(tdlret,'model',’ARD’,'Lags',1:40); lags were chosen as per the Schwert recommendation as per matlab website. Model ARD was chosen as log returns showed no trend but a non zero mean. Similarly pptest, kpsstest, vratiotest were done on the data. On the residuals I did the lbqtest(lags as per schwert criteria) and the archtest (lags 1:5). I got all the results my question is on the interpretation of the results as I cannot understand the meaning from the mathwork documentation.
For lbqtest I got h=1 for all lags so does it mean the residuals of the return are autocorrelated or not autocorrelated?
For kpsstest I got h=0 for all lags (model ARD) so does it mean to show that the series is stationary or not stationary?
For vratiotest(tdlret,'period',[2 4 8 2 4 8],'IID',[1 1 1 0 0 0]); I got all h=1 so does this reject that the series is random walk? Is this due to hetroscedasticity? Am I doing something wrong as the example on mathwork website shows that test on s&p 500 has most values as h=0? My rho value is -0.49181 (negative) does this mean something as rho of the mathwork sample is 0.011?
For pptest I got h=1 for all lags so does it mean rejection of unit root or unit root present?
For archtest I got h=1 for all lags so does it mean there are arch effects in the series?
Please inform if I’am doing something wrong. Have I processed the data wrong if I am getting wrong results? Can this data if correct be used for arma-garch or arma-gjr model?
Your answer in this matter would be highly obliged.

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