search for: sigma_t

...s" by Ruey S. Tsay, and I was succesfull, but I had to use "for" loop, which is quite slow. The loop is necessary, since you need to calculate recursive sequence. Is there a faster way to do this in R, without using loops? The model is such: r_t = \mu + \alpha_2 r_{t-2} + a_t a_t = \sigma_t\varepsilon_t \sigma_t^2 = \beta_1a_{t-1}^2+\beta_2\sigma_{t-1}^2+ 1_{\{a_{t-1}>0\}}(\gamma_0+ \gamma_1a_{t-1}^2+\gamma_2\sigma^2_{t-1}) It is asummed that \varepsilon_t are iid and normal with zero mean and variance one. The data given is r_t, and you have to estimate variables, \mu, \alpha, \...

...because there are obviously a lot of very bright people on this list. Suppose I had a time series of data and at each point in time t, I was calculating x bar + plus minus sigma where x bar was based on a moving window of size n and so was sigma. So, if I was at time t , then x bar t plus minus sigma_t would be based on the values of x_t-n+1 through x_t. This is the hard part : Is there a way to back out what the next value(s), x_t+1 would have to be in order to for that value to be either greater than x bar_t+1 plus Z*sigma_t+1 or less than x bar_t+1 plus minus Z*sigma_t+1. where Z i...

...in case of a normal distribution, this would be very easy, I assume the returns to follow a normal distribution and calculate a volatility forecast for each day, so I have sigma_1,sigma_2,...,sigma_n,. I can calculate the VaR via (mu constant, z_alpha quantile of standard normal): VaR_(alpha,t)=mu+sigma_t * z_alpha. This is in case, I have losses, so I look at the right tail. So for each day I have a normal density with a constant mu but a different sigma corrensponding to the volatility model. Let's assume a very simple volatility model, e.g. (empirical) standard deviation of the last 10 days a...

Hello - Here's what I'm trying to do. I want to fit a time series y with ARMA(1,1) + GARCH(1,1), there are also an exogeneous variable x which I wish to include, so the whole equation looks like: y_t - \phi y_{t-1} = \sigma_t \epsilon_t + \theta \sigma_{t-1} \epsilon_{t-1} + c x_t where \epsilon_t are i.i.d. random variables \sigma_t^2 = omega + \alpha \sigma_{t-1}^2 + \beta y_{t-1}^2 I looked through documentation of garchFit() from the fGarch library but didn't find a way to include exogeneous variable...

Hi, I want to fit a mean and variance model jointly. For example I might want to fit an AR(2)-GARCH(1,1) model i.e. r_t = constant_term1 + b*r_t-1 + c*r_t-2 + a_t where a_t = sigma_t*epsilon_t where sigma^2_t = constant_term2 + p*sigma^2_t-1 + q*a^2_t-1 i.e. R estimates a constant_term1, b, c, constant_term2, p, q TIA Aditya

...63328 0.01566420 0.01565676 6 0.001263328 0.01574062 0.01573312 7 0.001263328 0.01582800 0.01582047 8 0.001263328 0.01590372 0.01589614 9 0.001263328 0.01598779 0.01598018 10 0.001263328 0.01606258 0.01605493 I am modelling this Y_t-mean=e_t=sigma_t*Z_t however, my question is ,the prediction for the return itself is the mean forecast? if this is the case my prediction for the price would be equal to (1+.001451401)*110.41 =110.57 but i think this is not a good prediction, because the volatility is not affecting so much , in addition...

...ch') Regards Liviu On Mon, Aug 23, 2010 at 5:59 AM, Aditya Damani wrote: > Hi, > > I want to fit a mean and variance model jointly. > > For example I might want to fit an AR(2)-GARCH(1,1) model i.e. > > r_t = constant_term1 + b*r_t-1 + c*r_t-2 + a_t > > where a_t = sigma_t*epsilon_t > > where sigma^2_t = constant_term2 + p*sigma^2_t-1 + q*a^2_t-1 > > i.e. R estimates a constant_term1, b, c, constant_term2, p, q > > TIA > Aditya > > ______________________________________________ > R-help at r-project.org mailing list > https://stat.eth...