# Tag Info

0

Can you not just measure the moments of your data, and then use them to find mu and v? where the second simplifies to

0

i think the fitdistrplus library in R could help you with this: fitdist(data, distr, method = c("mle", "mme", "qme", "mge"), start=NULL, fix.arg=NULL, discrete, keepdata = TRUE, keepdata.nb=100, ...) # for student t fitdistr(x, "t", start = list(m=mean(x),s=sd(x), df=3), lower=c(-1, 0.001,1))

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 ...

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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 ...

2

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. ...

1

Two comments: Normal returns should always be in $[-1,+\infty)$. I believe that the way you sample $R_i$ from Stable directly violates that. You might want to sample $\log (1+R_i)$ from Stable instead. The question is very poorly worded. For the sampling distribution of a percentile you can invoke order statistics. It will follow a transformation of Beta ...

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That all looks correct to me. It might be a bit more natural to convert the one day returns into prices and then compute the five day returns from those, but it's of course equivalent. For your final question, you are generating a sequence of random variables (the quantiles) and want to know how good your estimate of the mean is. A practical choice would ...

3

Your problem probably comes from the notations used. Let the Moment Generating Function (MGF) of a random variable $X$ be defined as $$M_X(u) := E[e^{uX}]$$ From this definition, it entails that $$E(X^n) = M_X^{(n)}(u=0) = \frac{d^{n} M_X}{ d u^{n}}(u=0)$$ Knowing this, the function $$f_{\lambda}(t,r)=E[e^{-\lambda {r_{T}}}|r_t=r]$$ can be ...

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Data to compute Tobin's Q for most other countries, particularly emerging countries, are not available. As a result, many economists have begun to use the ratio of the stock market capitalization to GDP as an approximation for Tobin's Q.

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To have an average that is statistically > 0 does NOT imply that you can NEVER have a negative daily return: it means that, on AVERAGE, you have a positive return! You can have a lot of negative days, but if the positive ones more than compensate for the losses, you end up with an AVERAGE positive return (that can or cannot be statistically significant from ...

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