Malick
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Let’s take a simple example to answer a broad but interesting question: Imagine that we have a daily return serie denoted $r_{t}$ ( which is assumed to be stationary) and let's take a little time to ...

To complement @SRKX comment ,i'll try to explain the "simple mathematical proof" beetween both formula : I assume you know the geometric or arithmetic brownian motion : Geometric: \begin{equation*} ...

The ARMA(m,p) representation of GARCH(p,q) is : \begin{align*} \left[1-\alpha(L)-\beta(L)\right]r_{t}^{2} = w + [1- \beta(L)] v_{i} \end{align*} where \begin{align} &\alpha (L) =\sum_{i=1}^...

Intuition : Lets observe the U.S. ex post real interest rates from 1961 to 1986 : At first look it is not easy to identify different states of the economy. Now lets apply an econometric model that ...

It seems to be a good question for a Community Wiki ^^ Please note this wiki is devoted to Intraday data only. If you are looking for other financial data : see What data sources are available ...

First point to consider : some banks are by nature "positive" in their account to the central banks , for instance classical saving banks tend to get more deposit than loans; conversely others are ...

The traditional way is to pre-filter the returns thanks to the a relation similar to : $r^{f}_{t} = r_{t} /\phi_{t}$ where $r_{t}$ are the squared log returns, $r^{f}_{t}$ the filtered squared ...

Yes I would recommend you to plot the log of prices instead of prices. It will re-scale the data while preserving the hierarchy of prices, and more importantly it allows to compare easily the growth ...

Yes, it is correct. Underestimation: you under-estimate the risk, so you have more VaR violations than what your model predicts. Ex: With 100 observations, and a 99% VaR, you expect 1 violation but ...

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: $\hat{\theta} = \text{arg max}... View answer Accepted answer 5 votes Two theoretical explanations regarding the long memory are given by: The mixture of distributions hypothesis of Tauchen and Pitts (1983). Essentially this hypothesis states that trading volume and ... View answer Accepted answer 5 votes Depending of$\lambda$, pasts observations will be weighted differently, if you compute the volatility at time$t$, the$t-1$observation will be weighted by$(1-\lambda)*\lambda^{0}$, the$t-2$... View answer Accepted answer 4 votes EDIT : I read more about it and I get some help with someone else, here is the correct answer : The density forecast is the predictive likelihood value of the process estimated at the realized ... View answer 4 votes No there is no way since the calculated internal rate of return$r$is by definition defined as:$0 = \sum_{i=0}^{I} \frac{C_{i}}{(1+r)^{i}} $You need to know the entire cash flow distribution ... View answer 3 votes Volatility is an unobservable continuous variable defined over a period of time (formally defined as a stochastic process over an interval) whereas Garch models deal with discrete time observations to ... View answer Accepted answer 3 votes Here are my thought, it is more an attempt to answer than a proper answer, I may be wrong : Page 54 of the book it is written : [...] What we would really like is a pay-off class that has the nice ... View answer Accepted answer 3 votes If you estimate your model via Maximum Likelihood method, you are forced to re-estimate the full model. This is due to the fact that estimates are values which maximize the full likelihood, the latter ... View answer Accepted answer 3 votes Liquidity traders have no discretion with regard to the timing of their trades. Their trades are triggered by exogenous (to the financial market) reasons and are not related to information. Then we ... View answer Accepted answer 3 votes You know that :$X \sim N(\mu,\sigma^2)$.$Z = \large\frac{X-\mu}{\sigma}$.$\text{Var}(Z) = \large\frac{1}{\sigma^2}\text{Var}(X) = \large\frac{1}{\sigma^2}\sigma^2 = 1$. So that$Z \sim N(0,1)$. ... View answer 3 votes What is the mathematical basis to say that$u^{2}_{t}/\sigma_{t}^{2}$will exhibit little auto-correlation in the series? Let's$r_{t}$be a series of returns and let's assume (Assumption I) it ... View answer 3 votes The answer can be found in the following paper (section 2.3 Distribution and quantile functions of a skewed distribution): Lambert and Laurent, 2002 Lambert, P., Laurent, S., 2002. Modeling ... View answer 3 votes I think you fail to understand Multivariate Garch model such as DCC models since they do take into account non linearity. They are interested in jointly modeling the time series behavior of multiple ... View answer Accepted answer 2 votes A negative coefficient does not necessarily entail a negative$\sigma^{2}$. Usually we do not impose positivity constraints during estimation, then we check if$\sigma^{2}$takes some negative values ... View answer 2 votes I think you are mixing the residuals versus the standardized residuals ( 0 mean and unit variance residuals) and/or the student distribution vs the standardized student distribution. The degree of ... View answer Accepted answer 2 votes Finally, thanks to Luigi's answer and by observing the examples in the testsuite I have been able to achieve it. The fake starting date is setted to today's date and the exercise date as follow : ... View answer 2 votes You can think of the fractional difference operation as a filtering procedure that "removes" the long memory feature of a serie. However the mathematics for the innovations are the same than for any ... View answer Accepted answer 2 votes A limitation of both papers is they focus on point estimates, i.e they compare$\sigma_{t}$with$h_{t}\$ in the loss functions of the SPA Tests. A possible suggestion to overcome it, is to use a loss ...

Normally distributed and that's why the two first moments are sufficient to infer their statistical significance. Proof are rather technical (and sometimes are not specific to time-series models) and ...