Dear Matlab Community, ----------- SHORT VERSION: I have time series data x(t) that has garch effects present. I want to "detrend" this series using GARCH(1,1), that is have matlab compute y(t) = x(t)/sigma(t) where sigma(t) is the GARCH variance estimated by matlab.
I watched the econometrics toolbox introduction where they estimate GARCH models, but they are only used for forecasting. In particular I am confused on how to get sigma(t) that is different for each t
----------- DETAILED VERSION: I have monthly financial time series data (returns and CDS quotes) of serveral companies and I would like to do pairwise granger causality tests on them in order to replicate a paper. To this end I first have to get stationary time series data.
- Therefore I computed differences and the dickeyfuller tests suggests no unit root (after differencing) which is nice. However the archtest() function still detects present arch effects.
- Like the authors, I would like to 'detrend' the data (clean it of conditional heteroscedasticity) using a GARCH(1,1) model.
In the end I want to run my granger tests on R(t)/sigma(t) where sigma(t) is the GARCH(1,1) variance that I need to estimate first.