# Tag Info

10

You may want to first broadly categorize volatility models before comparing between them within each class, it does not make sense to compare standard deviation models with an implied vol model. I would broadly classify as follows: Historical realized volatility: Those include standard deviation (sum of squared deviations), realized range volatility ...

4

You want to set the parameter n.roll to the number of n.ahead, n.roll rolling forecasts you want. (The n.ahead parameter controls how many steps ahead you want to forecast for each roll date.) Thus by setting n.roll to a number almost equal to your sample size, and critically setting the out.sample parameter almost equal to your sample size, you're telling ...

4

There is no one right answer to this question, but a common starting place is to compare the bias and variance of the forecast vs. the realized variance. Take your forecasted variance $\hat y$ and regress them against the realized variance: $y = \beta_0 + \beta_1 \hat y + \epsilon$ A few things that you want to see: The forecast should be unbiased, ...

4

Basically he's just saying that you don't have to estimate parameters assuming they're the same in every period. Arch and Garch parameters are typically estimated via maximum likelihood. In MLE, parameters are estimated by $$\theta \equiv argmax\left\{ \sum_{t=1}^{T}ln\left(f\left(x_{t}|\theta\right)\right)\right\}$$ where $\theta$ are some parameters ...

3

The return equation is just an econometric equation that models stock returns (or other asset returns) as a function of: (i) intercept (i.e. the average return), (ii) some independent variables/features, (iii) noise that has zero mean and time-varying variance. There are sometimes other things in the return equation too that form more advanced models. The ...

3

Squaring normally distributed variables results chi-square distributions, which (as you imply) is why the chi-square distribution is used in hypothesis tests for the variance. If you estimate a Garch model and obtain the conditional variance at every point in time, you could use a chi-squared hypothesis test to ask a question like is the variance in a ...

2

1.Is it correct, that the coefficients are now different to the coefficients of the arima output? It seems right that the ARMA coefficients are different. Indeed, in the second model, the GARCH component will capture fluctuations that the ARMA component will not have to capture, resulting in different ARMA parameter estimates. 2.This is the acf of ...

2

Fitting a time series on a given stock is really trade off between statistical risk and model error. If your time series is too short then your statistical error will be high. If your time series is too long, then the distribution of the market will probably have changed, and the your model error will be high. 5000 days is about 20 trading years. There is ...

1

I would confirm it. For time series forecasting, one can use 3 versions of random walk: RW model 1 (basic geometric random walk): stock returns in different periods are statistically independent (uncorrelated) and identically distributed (constant volatility) RW model 2: stock returns in different periods are statistically independent bot not identically ...

1

Since you are talking about using volatility of stocks you could just use the straddle strategy both on long or short. I will answer only with theory about trading strategies. If you are 100% certain (we know this is not possible, but let´s take this as an assumption just for the sake of theory matter) of the volatily you can go two ways: High Volatility: ...

1

Annualized volatility is not calculated generally by forecasting the volatility n days ahead. what is done is that the next period volatility is calculated and then it is multiplied by square root of n where n is the number of the periods contained in the year as the scaling factor. so if you calculate daily volatility and the number of trading days is 250 ...

1

fopen,fscan are in stdio.h but it looks like Ox has their own include file. For some reason it's commented out in garchOxModelling.ox, uncomment that line only. #include <oxstd.h> //#include <packages/gnudraw/gnudraw.h> I remember I had to change this line as well since I used a newer G@rch distro. It was /Garch42/ , I changed it to ...

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I would suggest writing the joint density as the product of the conditional densities then estimate parameters using an optimization package. The joint density is given by $$f(r_0, \ldots, r_T) = f(r_0) \prod_{t=1}^T f(r_t|r_0, \ldots, r_{t-1})$$ then the log likelihood function is L = \log(f(r_0)) + \sum_{t=1}^T \log(f(r_t | r_0, \ldots, r_{t-1}) ...

1

"How can I understand if the volatility is not constant reading ARCH/GARCH model ": By analyzing the error terms/residuals. There is not much more magic going on than just this and the following rather introductory level paper should get you started: http://archive.nyu.edu/bitstream/2451/26577/2/FIN-01-030.pdf Garch models essentially add conditional ...

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