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1h
accepted reference question about portfolio optimization
23h
comment reference question about portfolio optimization
Thank you so much for your answer. I will have a look at the books. It seems you have a quite good overview over the topic. Are there any paper which you would recommend as well?
1d
comment reference question about portfolio optimization
@Taran thanks for your comment. I did not say I want use it. I'm just interested in. If there are more sophisticated models, I would also be interested in a reference. I will update the dynamic part this evening.
2d
asked reference question about portfolio optimization
May
17
revised How to derive equivalent martingale measure using Ito's Lemma
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May
17
answered How to derive equivalent martingale measure using Ito's Lemma
May
17
awarded  Enthusiast
May
7
comment Calculating the VaR from a GARCH(1,1) with Student-t innovations
Maybe this could help: quant.stackexchange.com/questions/11019/… I think predict returns the estimated $\sigma$. Note: GARCH models the conditional variance but has zero conditional mean! Try to use the sample mean and the meanForecast as volatility. Maybe then you get the same result. However, I'm not sure :)
May
2
awarded  Critic
Apr
24
comment GARCH model and prediction
I was able to figure it out. the command m2@sigma.t gives the values up to know. Then I can use the explicit formula and estimators to calculate $\hat{\sigma_{t+1}}$. Again many thanks
Apr
24
accepted GARCH model and prediction
Apr
24
comment GARCH model and prediction
Thanks for your patience, help and editing you answer I will accept your answer. But just one last question: You write: "It is also possible to forecast future variance, $\sigma^2_{t+k}$,as shown, using GARCH formula above." How do I get in R the past values of $\sigma^2$ (the fitted ones)?
Apr
24
comment GARCH model and prediction
Of course, what I would do is: start with ARMA process to model a time series and see which model you prefer, i.e. determine $p$ and $q$. Then check the squared residuals. If appropriate model these with GARCH, i.e. $r_t=\mu_t+\sigma_tZ_t$. Otherwise you can just use the ARMA model. I know that paper and also the particular form of an estimte of $\sigma_{t+1}$ and $\mu_{t+1}$. I just wanted to know if there is a built in function in R (like predict).
Apr
24
comment GARCH model and prediction
For example: Quantitative Risk Management - Concepts Techniques Tools by A.J. McNeil, Rüdiger Frey and Paul Embrechts page 148
Apr
24
comment GARCH model and prediction
Actually that's not true. $\mu$ depends on $t$. I model this using an ARMA process (at least in the first case, model m1). This is a general approach where you model the conditional expectation (using ARMA) and the conditional variance (GARCH).
Apr
24
comment GARCH model and prediction
thanks for your comment. Just one additional question. Assuming ARMA-GARCH means a model of the form: $r_t=\mu_t+\sigma_tZ_t$, where $\mu_t$ is modelled by the ARMA process, $\sigma$ by the GARCH and $Z_t$ is strict white noise. In this case, since $\sigma$ is so small, the forecast is more or less $r_t$ but if $\sigma$ isn't that small, then we just forecast $\mu_t$ and not $r_t$, right?
Apr
23
revised GARCH model and prediction
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Apr
23
comment GARCH model and prediction
you can find my outputs above. If it is indeed $\sigma^2$, then I would like to know how I can predict the ARMA part (in the first case) and therefore predict the returns at all.
Apr
23
revised GARCH model and prediction
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Apr
21
revised GARCH model and prediction
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