Malick
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How to calculate the conditional variance of a time series?
13 votes

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 ...

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How to simulate stock prices with a Geometric Brownian Motion?
13 votes

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*} ...

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Fractionally Integrated GARCH
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6 votes

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}^...

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What is a regime switch?
6 votes

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 ...

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List of Intraday stock prices API
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6 votes

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 ...

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Why banks borrow from each other
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6 votes

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 ...

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How to account for intraday seasonality in GARCH model?
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5 votes

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 ...

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Scale prices in multiple stocks for comparison
5 votes

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 ...

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Overestimating or underestimating risk?
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5 votes

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 ...

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How to obtain Standardized Residuals from a Time-Series?
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5 votes

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}...

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Why is volatility said to be persistent?
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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 ...

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RiskMetrics VaR Volatility Sample Size
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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 $t-2$ ...

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Density forecast of a GARCH model
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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 ...

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Computing Pooled IRR from the IRRs of parts
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 ...

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Criticise GARCH relative to Realized Volatility
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 ...

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Mark Joshi, C++ Design Patterns and Derivatives Pricing : Bridge Pattern vs More Simple Inheritance
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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 ...

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Streaming update of the GARCH(1,1) model
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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 ...

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Liquidity Traders
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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 ...

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Problem with obtaining densities
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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 $Z \sim N(0,1)$. ...

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Does GARCH derived variance explain the autocorrelation in a time series?
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 ...

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Value-at-Risk formula when using skewed-t distribution
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 ...

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Alternative ways to understand time-varying comovement between two time-series?
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 ...

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Negative signs in GARCH equation
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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 ...

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VaR : Student-t GARCH
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 ...

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Using the binomial-tree approach to price an option in quantlib - with time expressed as a fraction of year
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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 : ...

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Fractional Brownian motion - probability density function of the increments
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 ...

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Question regarding volatility forecasting using High Frequency Data
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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 ...

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distribution of AR, MA coefficients estimation in ARMA-GARCH models
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2 votes

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 ...

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ARMA-GARCH model, bset model selection and confidence levels calculations
2 votes

Information Criteria estimate the quality of a model based on the likelihood / the numbers of parameters (or degree of freedom) and the number of observations. It is a measure of goodness-of-fit and ...

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MSRV estimation in R
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2 votes

I'm not aware of a R package implementing the MSRV, however you can find its implementation in the Kevin Sheppard MFE Toolbox (Matlab). You’ll have to translate it for R . (the source code is ...

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