Detrend timeseries of conditional heteroscedasticiy using GARCH(1,1)

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.

1. 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.
2. 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.

Answer 1

[Hang Qian]

Hi Jannic,

To remove the conditional variance from the observations, we may first estimate the model, and then we infer the conditional variance from the fitted model.

Suppose that we have a vector of data x.

1. Estimate the model:

Mdl = garch(1,1);

EstMdl = estimate(Mdl,x);

2. Infer the conditional variance from the fitted model:

variance = infer(EstMdl,x);

3. Remove the conditional variance

y = x ./ sqrt(variance);

Thank you.

Hang Qian

[roblocks]

thanks so much!