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I have found the mistake. The ugarchfit function sets automatically non negativity constraints for all coefficients- This makes sense since the alpha in our case shouldn't be negative. However, when releasing the constraint to negative values you get the right results. The only explanation I can think of is that in the course of optimisation, temporarily ...


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Assume that your stationary time series (here a daily close-to-close log-returns' series) is modelled as follows $\forall t \in \mathcal{T}=\{1,...,N\}$ \begin{align} r_t &= E_{t-1}[r_t] + \epsilon_t \\ &= E_{t-1}[r_t] + \sigma_t z_t \end{align} with $z_t \sim N(0,1)$ and $\{z_t\}_{t \in \mathcal{T}}$ are IID. The above equations suggest that, ...


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The n=100 specifies the number of periods (rolling) for the vol estimate - see the original link https://web.archive.org/web/20100326215050/http://www.sitmo.com/eq/409 where the n is referred to as Number of historical prices used for the volatility estimate An example in R: library(TTR) library(quantmod) getSymbols("AAPL") nrow(AAPL) # we have 2384 price ...


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I think the most sophisticated solutions are to be found within the R universe. One package that comes to mind is the quantmod package. You can use it to download data from Yahoo and Google finance, plot charts and filter your stocks using all kinds of technical indicators (that come with the package). It can be found on CRAN: https://cran.r-project.org/...


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I would recommend using Python because it can be downloaded for Windows or Mac and is available in almost all Linux repositories as standard. Once you have Python installed you can use any of the following links to see how to get your data https://www.quantstart.com/articles/Downloading-Historical-Intraday-US-Equities-From-DTN-IQFeed-with-Python https://...


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When calculating the simple arithmetic mean, each observation has an equal weight: $$ \hat \mu^{simple} = \frac{1}{T}\sum_{t=1}^T x_t.$$ If the observations are $i.i.d.$, $\hat \mu^{simple}$ is an efficient estimator of the population mean. When estimating the mean of a GARCH process, $\hat \mu^{simple}$ is no longer efficient. It makes sense to ...


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Try the mgarch package, it's available at CRAN. In this link you will find an example from Prof. Zivot.


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I just made things clearer hoping it would help. Let define $\mathbb{Q}_\theta$ as $$\frac{d\mathbb{Q}_\theta}{d\mathbb{P}}|_{\mathcal{F}_t}=\exp(\theta W_t -\frac{1}{2}\theta^2 t)=Z^\theta_t$$ By girsanov, if $W$ is a brownian motion under $\mathbb{P}$, then $W^\theta_t=W_t-\theta t$ is a brownian motion under $\mathbb{Q}^\theta$ $$\begin{split} \mathbb{...


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Several issues arise no matter which approach you choose (as a reference for my claims you can go through this: the covariance matrix of many assets can become instable (the more assets the more instable). Then your PCA will be based on noise. Therefore first get a good stimator of covariance. Using data of something like a year of observations worked good ...



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