# Tag Info

3

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 ...

3

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.

3

You can use Matlab too, that, in my humble opinion, is simpler than R from a syntax point of view. The model you need for is run by the Matlab function arima that can be used with seasonality option to do what you have to do. Here you can find an example and a brief explanation of the model. Type ctrl + F and search for: "Specify a seasonal ARIMA model" ...

3

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 ...

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In the case of application in finance, usually, GARCH is used in estimating realized volatility of returns based on the weight we would like to give to each past observation. Ultimately after estimating (calibrating) the parameters of the model to an existing time-series, GARCH is used for forecasting multi-step ahead return (future) volatility. Different ...

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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.

1

alpha + beta < 1 is the stationary condition for GARCH. If alpha and beta are low that means volatility of the stock does not have clustering behaviors. I think you can have a look at ADF and PACF of Return^2 time series first. If the first order autocorrelation is very significant but alpha is not, then perhaps you can check on the parameter calibration. ...

1

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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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

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

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 ...

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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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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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The mean equation specification for ARIMAX(8,0,0)(5,0,1)[7] (as in the R code above): $$(1 - \phi_1L^1 - \ldots - \phi_8L^8)(1-\Phi_1L^7 - \Phi_2L^{14} - \ldots - \Phi_5L^{35})y_t = \beta x_t + (1 + \Theta_1L^7)\varepsilon_t$$ where $x_t$ is the holiday dummy variable. Equivalent ARIMA fit in Matlab (+ GARCH and forecasting): % specify seasonal ...

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You can pass in the parameters are you estimating with EWMA or GARCH using the mu (mean), sigma (co/variance) m3 (co/skewness) and m4(co/kurtosis) arguments. e.g. blahblah = EWMA(my_time_series) VaR(my_time_series,mu=blahblah)

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I have the same problem as you. Up to my knowledge, there is no package allowing to combine seasonal ARIMA process with GARCH effects.

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If log returns have a symmetric distribution, prices will have a positively skewed distribution, since exponentiating induces positive skew.

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Did you try rmgarch package of R ? http://cran.r-project.org/web/packages/rmgarch/index.html http://unstarched.net/r-examples/rmgarch/mgarch-comparison-using-the-hong-li-misspecification-test/

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