# Tag Info

6

I personally use the simple Garch(1,1) for volatility filtering in the risk management area. In fact in most cases I don't even estimate the parameters, I stick 0.94 for mean reversion, 0.04 for the squared error and I get the constant by matching the series variance. My experience is that there is no point pretending to finetune parameters when vol is ...

5

It doesn't matter if you use *100 or just pct_change, as long as you are consistent. However, in practice, due to underlying floating point numerical instabilities in the underlying optimization algorithms/default tolerances used in scipy/arch, having the returns expressed in %, i.e. multiplied by 100, will have a better chance of converging during the ...

4

Any ARCH type model always requires an additional model for the mean of the time series. If nothing is said about the mean model, then usually is simply a time average plus residual. So, if $y_t$ is your stationary time series, the mean model would be $$y_t = \bar{y} + \epsilon_t$$ where $\bar{y}$ is the average value of $y_t$. And then $\epsilon_t$ would ...

4

GARCH models are essentially white noise models with some time dependency. The reason GARCH models are used is because they have a lot of nice properties. The main being that the Conditional Volatility is time-dependent. This means that volatility can cluster. It's true that conditional vol will regress towards "normality" as a random walk process with ...

3

You can see fairly quickly that an exact answer to this question is not going to be feasible because your functional transformation is to take the square root of $\sigma_t^2$, and the square root function has a countably infinite number of derivatives. This implies that a Taylor expansion is going to leave us with a countably infinite number of terms, most ...

3

Yes, it exists and it is called ccgarch package. You can install that by simply running in R install.packages("ccgarch") and learn more about that on the CRAN relative paper. Moreover, I suggest you to read this lecture hold by the author during an R conference. Hope this help.

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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 value computed in a one step ahead way. Thus for instance for a standard arma garch process with normal errors: You forecast the mean $u^{f}_{t|t-1}$ and ...

3

You should check for autocorrelation. However, its presence does not necessarily mean your model will produce inaccurate figures. The ARCH family of models were developed to help analyze the volatility of a time-series. This data is assumed to display a degree of heteroskedasticity. Using the GARCH model, small amounts of auto-correlation (not of practical ...

3

Even though it's a straightforward extension, it took me a while (a year? yikes!); but now you can easily incorporate Bayesian ar(1) (or more generally, Bayesian regression) in joint estimation by using designmatrix = "ar(1)" as an argument to svsample. It's not well documented yet (except in the help files), but I nevertheless hope easy to use. From the ...

3

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 define main concepts : Mean Process (First moment process) The unconditional mean of $r_{t}$ denoted $u$ is just its expectation $E(r_{t})$. It is not time ...

3

To solve for $U_t$, we can proceed as follows. First, note that \begin{align*} d\left(e^{(\theta + \frac{1}{2}\xi^2)t - \xi W_t} U_t \right) &= e^{(\theta + \frac{1}{2}\xi^2)t - \xi W_t} U_t \left((\theta+\xi^2) dt -\xi dW_t\right) \\ &\qquad+ e^{(\theta + \frac{1}{2}\xi^2)t - \xi W_t} dU_t -\xi^2e^{(\theta + \frac{1}{2}\xi^2)t - \xi W_t} U_t dt\\ ...

3

$\alpha=0$ does not imply constant volatility. Consider just a simple Garch(1,1): $\sigma^2_t = \omega + \alpha \eta_t^2 + \beta \sigma^2_{t-1}$ Note that: $\sigma^2_t = \omega + (\alpha + \beta) \eta_t^2 - \beta (\eta_t^2- \sigma^2_{t-1})$ Now add $\eta_{t+1}^2$ to both sides: $\eta_{t+1}^2 = \omega + (\alpha + \beta) \eta_t^2 - \beta (\eta_t^2- ... 2 What is the mathematical basis to say that$u^{2}_{t}/\sigma_{t}^{2}$will exhibit little auto-correlation in the series? Let's$r_{t}$be a series of returns and let's assume (Assumption I) it follows a covariance stationary process defined as :$r_{t}=\sigma_{t} z_{t}$where$z_{t}$is i.i.d with$E_{t}(z_{t})=0$and$Var_{t}(z_{t})=1$; Then$ ...

2

Heston gives an expression for the characteristic function, from which option prices can be computed. Therefore it can be calibrated (statically) on a set of vanilla option prices with different strikes and maturities. Hence this produces risk neutral parameters that can be used to price other more exotic products. However, it is a pain to estimate the ...

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You find R code for seasonal ARIMA models again in the book mentioned (this chapter). Do you really need the GARCH errors?

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Just a quick fix. Looking at the wikipedia entry of EGARCH: $g(\zeta_t)$ (the unit-scale random variable) seems correct - as you say.

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PYTHON I have found this class from the statsmodels library for calculating Garch models. Unfortunately, I have not seen MGARCH class/library. Below you can see the basic information about the garch models in mentioned class from the statsmodels. Probably you have to implement it by your own in python, so this class might be used as a starting point. ...

2

Yes, you can use Multivariate GARCH model to estimate the volatility of a portfolio. For example, the Constant Conditional Correlation(CCC) GARCH model. In the CCC GARCH model, it says there is a constant correlation between portfolio and the model is defined as: Once you have estimated the correlation matrix, the the composed volatility can be computed by ...

2

Interesting question, as All the answers (including mine) could not be generalized unfortunately. As far as I am concerned, I use a univariate EGARCH for risk modelling purposes (Filtered Historical Simulation (FHS), etc.). 1 - EGARCH, merely because GARCH models do not take into account so-called leverage effects, which is crucial to me for skewed and ...

1

As far as I know, technical analysis won't work to predict intraday Forex movement. I've done so many backtest using technical analysis but it doesn't have any predictive power. The best way to predict FOREX is to find the difference of interest rates issued by both government of that currency pair. $$Pn = P_0 . e^{(r_{jpy}-r_{usd}) \Delta t }$$ $$... 1 In the very begining I advice you to model always linear effects in the time series (ARMA models). Then you add a model which investigate ARCH effects (GARCH family). When you have done the models estimation part It is advised to check if residuals of the models do not show any dependiencies ( close to normal distribution, independent). In another step you ... 1 If \log{(|R_t|)} is your first term, I'm not sure why this is a matrix. Modulus (determinant herein) applied to a matrix R_t gives a scalar. If your implementation in python produces a matrix, that's likely because modulus is treated as an element-wise abs() function for each element of a matrix. It may be easier and faster to use rugarch (univariate ... 1 As regards the point (1), you do not have to include the exogenous variables in the garch model, but, as described in the paper (IV. Methodology, p. 7), you must estimate the following models and steps: Get residuals vector \epsilon_t by running: RetJP_t = ... 1 Few comments on your questions: 1) Yes, Arch and Garch are suitable for equities volatility, please see: http://onlinelibrary.wiley.com/doi/10.1002/jae.800/pdf 2) No. These are models of volatility. To model interest rates use CIR, Vasicek or similar. 3) and 4) Check paper above. 1 Garch models are not good to predict "many" periods ahead, but for "very short" times. If you want to predict 2 months from here, maybe you should be working with monthly data. I did a similar exercise with some indexes (symb=c("^BVSP","^MERV","^DJA","^N225")) using daily returns from="1991/01/01", look the incredible predictions. 1 So you are asking whether the function Box.test requires standardized or raw residuals as input? I do not know this function but as you mention that the results change based on your input it should be such that the function requires standardized values. In case a standardization is implemented directly the output should not differ because you either plug-in ... 1 This should follow from the properties of the forecast - for example the GARCH(1,1) forecast for h steps is computing the conditional expectation of \sigma^2_{t+h} based on the information set-up in t. This can be computed recursively by$$ V(\varepsilon_{t+h}|F_t)=\omega+\alpha\varepsilon_{t+h-1|F_t}+\beta\sigma^2_{t+h-1|F_t}\\ ...

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My 2 Zimbabwe cents: A few years ago developing new ARCH like models became almost a fad and large numbers of them were published without a clear justification in my humble opinion. However there is an important distinction I do think. Some markets are symmetric, while others (such as Stock Indexes) show a Leverage Effect where the volatility rises when ...

1

HF data have a lot of auto correlation so common models to deal with this problems are ARFIMA, FIGARCH, Fractional Integrated GARCH. Engle recently propose the multiplicative components GARCH for high frequency data, which can include a mean model like and ARMA. In this post they explain how to implement it in R with the rugarch package, it takes some time ...

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You are right - GARCH model models volatility. They write: " The GARCH [27] can be used to model changes in the variance of the errors as a function of time." What people often do is to fit an ARIMA model (that can be used to forecast a time series) and apply a GARCH model to the errors (which gives you a feeling for the forecast error). See Hyndman and ...

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