# How to calculate the conditional variance of a time series?

I am reading a paper where the term conditional variance is mentioned, but I am not really sure what is meant by this and how this can be calculated:

Fig. 2 shows the conditional variances of the centered returns of the series of prices under study.

As far is know the term conditional variances is used only in GARCH models. So, I assume that in order to calculate these variances one has to use a GARCH Model for the returns. First, one has to calculate the returns $r_t = \ln(p_t) - \ln(p_{t-1})$. Then, the returns should be centered via $\hat{r}_t = r_t-\bar{r}$ (quite unsure if this meant by centered). The last step would be to apply a GARCH model. Is this going into the right direction or am I completely lost here?

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Most Garch packages will output the conditional variances for you. For the centered returns, you could estimate an autoregressive model and subtract out the conditional mean. They are assuming a constant mean, which is also fine. –  John Jun 18 '13 at 14:41
@John I used a GARCH(1,1) model and calculated the conditional variances via Excel, but my results differed from the results from the paper. Could you elaborate a bit more one your comment? I understand from it that I am doing okay, I just have to apply an GARCH model. Is that right? –  Mark80 Jun 19 '13 at 8:18
Assuming the Garch model is the same as the one from the paper and the data is the same (and same frequency), I would expect them to look very similar. One difference is that most packages initialize the conditional variance with the long-run variance, so that's one area I would check but if you used the sample variance to initialize though the difference should be small. –  John Jun 19 '13 at 13:54