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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

Ah, this is becoming a common question, just in R now. Please look at this [question] (GARCH model and prediction), it has R code to do the prediction. In brief, you keep predicting one day ahead. $\sigma_{t+k}^2 =w+\alpha u_{t+k-1}^2+\beta \sigma_{t+k-1}^2$. You already know $ w,\space \alpha \space and \space \beta $ the starting values are the last ...


4

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

$$ E\left[ {{y_t}|{{\cal F}_{t - 1}}} \right] = E\left[ {{\sigma _t}{z_t}|{{\cal F}_{t - 1}}} \right] = {\sigma _t}E\left[ {{z_t}} \right] = 0 $$ $$ {\mathop{\rm var}} \left[ {{y_t}|{{\cal F}_{t - 1}}} \right] = {\mathop{\rm var}} \left[ {{\sigma _t}{z_t}|{{\cal F}_{t - 1}}} \right] = \sigma _t^2{\mathop{\rm var}} \left[ {{z_t}} \right] = \sigma _t^2 $$ $$ ...


3

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

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 ...


2

The interface from R to Ox is no longer supported by Rmetrics. You could look into the Rugarch package from CRAN instead. It supports a number of Garch specifications.


2

work you way from GARCH(4,4) to GARCH(0,0) removing the intercept too. 5*5*2-1 = 49 estimations Make sure your coefficients are all statistically significant at least to 95% confidence. Make sure you have no autocorrelation in your error terms. pacf and acf should be clean. Likelihood ratio tests assess whether you lose explaining power from ...


1

The mean could be the long run variance which is sig2 = fit.Constant/(1-fit.GARCH{1}-fit.ARCH{1}); I hope this explains. If not, note I ran this model through Matlab, I get different values. you can paste your m1 and m2 values and some other intermediate results so I can see why Matlab differs. EDIT: The question refers to forecasting the returns. ...


1

For the question in your title, The mean reversion of the volatility is due to the Moving Average part of the volatility process. The solution would be to set $\beta = 0$. In other words you have to use an AR process for the volatility (so an ARCH model for price). The restriction in p and q come from the estimation process of the parameters. You test ...


1

Perhaps not the most encouraging answer, but: I would think that it is contingent upon the specific implementation, magnitude, regularity, and transiency of arbitrage available as well as the volatility estimate time-scale. In a very simple case, the existence of arbitrage opportunities would likely result in larger fraction of informed traders (relative to ...


1

If you look at it from a mathematical point of view - presence of arbitrage should not matter for volatility estimates. Absence of arbitrage can be associated with the existence of an equivalent martingale measure for the bank account numeraire. (first fundamental theorem of asset pricing) Let's assume the real world process is something like ...


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

My guess would be most people approach this using rolling regressions. My approach would be to generate a matrix using all the lookbacks that you want to predict the present on each row and a corresponding squared return, then subsample the two.


1

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

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

should be price returns, transforming your series as return=ln(Pt/Pt-1), in words, it means the natural logarithmic transformation of the ratio of price at time t to price at time t-1


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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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