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4

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 returns and $\phi_{t}$ the periodicity component. $\phi_{t}$ is a deterministic intraday component (the seasonal effect at time $t$). We estimate the GARCH model on ...


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When you model log-returns $(Y_t)$ by $Y_t=\varepsilon_t$ where $\varepsilon_t|\mathcal{F}_{t-1}\sim N(0,\sigma^2_t)$ and a standard GARCH($p,q$) model with $$\sigma_t^2=\omega+\sum_{i=1}^p \alpha_{i}\varepsilon^2_{t-i}+\sum_{i=1}^q \beta_i \sigma^2_{t-i},$$ where $\omega>0, \alpha_i,\beta_i\geq0$. This model assumes indeed a constant mean of zero for the ...


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GARCH models are usually used to predict volatility, not returns.


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An external regressor in the mean specification can be added to the mean specification, i.e. $$r_t = \mu + \varepsilon_t + \theta x_t $$. An external regressor in the variance specification can be added to the variance specification, i.e. $$\sigma^2_t = \omega + \alpha \sigma_{t-1}^2 + \beta \varepsilon_{t-1}^2 + \theta x_{t}$$


2

The error arises because the first element of rets is NA (which is expected behavior as ROC calculates the rate of change of a series, but a previous value prior to the first element is naturally not available). To avoid this, add the optional argument na.pad = FALSE, i.e. rets = ROC(SPY$SPY.Close, na.pad = FALSE): > rets=ROC(SPY$SPY.Close) > head(...


2

I guess its possible if you employ some kind of GARCH with an intraday component. In general, it should not be too difficult to alter my R-package mfGARCH for estimating it. Maybe http://www.unstarched.net/2013/03/20/high-frequency-garch-the-multiplicative-component-garch-mcsgarch-model/ could be a start for modeling intraday seasonality. Best, Onno


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Found the answer. The rescale=True is used when the model fails to converge to a result. So rescale could be a solution for the problem. If the model doesn't need rescale, even if the parameter is True, it will not do anything. Point of Attempion: If the rescale=True and, in fact, rescaled the series. It's necessary to adjust the outputs. In my question I ...


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https://medium.com/auquan/time-series-analysis-for-finance-arch-garch-models-822f87f1d755 This would get you started. I would suggest reading some time series books (ex. Ruey S Tsay) for a better grasp of subject.


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library(fGarch) fit = garchFit(~ arma(1,0)+garch(1,1), data = y,include.mean=FALSE) summary(fit) please see here (page 11) for more details


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Your function returning (minus) the log-likelihood seems weird to me, I would go with function y = findGARCH_LLy(params,S,rf) % Finds log-likelihood for the GARCH option pricing model. alpha0 = params(1); alpha1 = params(2); beta1 = params(3); lambda = params(4); N = length(S); % Define the returns (pad first return with zero) r = [0, diff(log(S))]; % ...


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In general for stock data, classical GARCH models are designed to model daily volatilities, but not the intraday ones, because, for instance, they do not capture diurnal patterns. So, I would say that models you are estimating are not valid for the 1-minutes returns. And of course, the presence of the microstructure noise makes them even less valid. As a ...


1

If you are using the "rugarch" package in R, you can include these terms via the argument external.regressors within the argument mean.model in the ugarchspec function. From CRAN: external.regressors A matrix object containing the external regressors to include in the mean equation with as many rows as will be included in the data (which is passed in the ...


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You have to use a multivariate Garch indeed. Search for mGARCH versions like GARCH-BEKK or VECH GARCH or DCC.


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Yes. We should indeed say that the Garch part of the model does not help to predict the Direction of the movement (this is given by the expected drift of the Arma, which gives the conditional mean of the return process) but helps to predict the size of the deviation of the next period return from the expected Arma drift. It is a measure of the squared size ...


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I traced the error. It is a C language routine implemented in R that appears to have been functionally obsolesced, so it is called by other routines, but I don't think it is still implemented as its own routine. Some information on it is at ftp://cran.r-project.org/pub/R/doc/manuals/r-devel/R-exts.html Given the underlying math, there is one of three ...


1

It is a good idea indeed to use GARCH for intraday volatility because it is as clustered as daily volatility. Moreover, if you want to account for autocorrelations, you should consider using other variables like the bid-ask spread, the traded volume and the volume of the book at first limits. It is done in Endogeneous Dynamics of Intraday Liquidity by ...


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