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3

The ADF test assumes the DGP $$ \Delta y_t = \alpha +\beta t +\gamma y_t +\delta_1 \Delta y_{t-1}+\cdots +\delta_k \Delta y_{t-k}+\epsilon_t $$ The parameters are estimated using OLS on a sample of length $T$. You might impose $\alpha=0$ and/or $\beta=0$, this will give you different null hypotheses to test. But your test is always $\gamma=0$, and the ...


3

Usually for MLE estimation as you said we compute the residuals starting from index number of lag+1 (p+1 for AR model) in this case we obtain Conditional MLE estimates: $\hat{\theta} = \text{arg max} \sum_{p+1}^{T} \ln f(Y_{t}|\theta)$ where $f(Y_{t})$ is the marginal density of observation $Y_{t}$ and $\ln$ is employed to maximized the log likelihood. ...


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In this context, unconditional variance refers to the stationary variance level predicted by your GARCH model. This quantity need not coincide with the sample variance of the data on which the latter model has been calibrated. That being said, in an effort to reduce the complexity of the GARCH parameters' estimation process (nasty non-linear optimisation ...


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Jacob, you conclude that "The main finding is that VaR is more suited for our index portfolio GSPC than for our stock JPM." This conclusion is not surprising. However I think that is not the VaR in itself "more suited," but the underlying GARCH(1,1) model. You introduce the standardized error in section 4.6. That is the right way. I did not study your pdf ...


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You need to know what your original conditional distribution was when you fitted the AR-GARCH(1,1). Assuming that you chose a student-t distribution, the reverse transformation after step 4 in R would look as follows: step 1: Fit Garch fit <- rugarchfit step 4: Simulate points sim <- 'simulated 100 points' step 5: Convert 100 uniformly ...


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The reason is earnings and other idiosyncratic corporate actions like takeovers, major product releases, etc. There are three terms in garch(1,1), the constant, term proportional to previous day's volatility, and a term proportional to "stock noise". Earnings jump is much larger than previous "regular" volatility, and also much larger than "regular" noise. ...


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This Quandl Page provides you the informations you need: a lot of programming languages and other tools are linked to Quandl.


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You need a model which assumes that some intrinsic properties such as true overpricing is taking place but masked by the noise which has some probabilistic distribution around the true signal. The averaging of the observed data then takes advantage of the large number theorem or some version of the central limit theorem to flush out the signal. So you need ...


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You need to estimate or assume a marginal distribution of the (u,v). Lets say you assume normality (don't do this), you would be able to perform a rosenblatt-transformation, to perform the task you describe. https://en.wikipedia.org/wiki/Inverse_transform_sampling This could be a useful resource.


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You have general and specific questions, so I'll my best here. I have a forex robot that does 30% p.a. 8 years running. It's technical indicators. It's also using one set of rules that is aware of peoples-patterns. (Target prices that traders would commonly sell at). It must be people-aware because even an HFT (and some have failed in big ways) has human ...



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