# Tag Info

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 ...

3

$$E\left[ {{y_t}|{{\cal F}_{t - 1}}} \right] = E\left[ {{\sigma _t}{z_t}|{{\cal F}_{t - 1}}} \right] = {\sigma _t}E\left[ {{z_t}} \right] = 0$$ $${\mathop{\rm var}} \left[ {{y_t}|{{\cal F}_{t - 1}}} \right] = {\mathop{\rm var}} \left[ {{\sigma _t}{z_t}|{{\cal F}_{t - 1}}} \right] = \sigma _t^2{\mathop{\rm var}} \left[ {{z_t}} \right] = \sigma _t^2$$ $$... 3 You can use Matlab too, that, in my humble opinion, is simpler than R from a syntax point of view. The model you need for is run by the Matlab function arima that can be used with seasonality option to do what you have to do. Here you can find an example and a brief explanation of the model. Type ctrl + F and search for: "Specify a seasonal ARIMA model" ... 2 work you way from GARCH(4,4) to GARCH(0,0) removing the intercept too. 5*5*2-1 = 49 estimations Make sure your coefficients are all statistically significant at least to 95% confidence. Make sure you have no autocorrelation in your error terms. pacf and acf should be clean. Likelihood ratio tests assess whether you lose explaining power from ... 2 In the case of application in finance, usually, GARCH is used in estimating realized volatility of returns based on the weight we would like to give to each past observation. Ultimately after estimating (calibrating) the parameters of the model to an existing time-series, GARCH is used for forecasting multi-step ahead return (future) volatility. Different ... 2 There is no guarantee that the optimization method always converges! In an introduction the author of the package recommends using the "hybrid" solver, which starts out with the "solnp" and goes through the other solvers, if it doesn't converge. According to him, this should at least guarantee convergence in 90 % of the cases. ... 1 The mean equation specification for ARIMAX(8,0,0)(5,0,1)[7] (as in the R code above):$$ (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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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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Concidering 22 days of trading per month you have approximatly 132 days of trading. I highly doubt that this will be sufficient for any forecasting. The sample might be too small. Have a look here: http://research.stlouisfed.org/wp/2012/2012-008.pdf Erdemlioglu, Laurent and Neely used the data of ~10 years to conduct their survey.

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You can use the known result, that when $X\sim N(0,1)$, then $aX\sim N(0,a^2)$ where $a=\sigma_t$ is conditionally constant.

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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

Some models do use ln(r_t), like Black–Derman–Toy and the Black–Karasinski models. Mainly to avoid negative interest rates in low rates / high volatility environments through the use of the log-normal distribution. Negative rates can wreak havoc in option premiums for example. They are interest rates indeed, that we call short rates, not yield on ...

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These are not yield. They are instantaneous short rates which are not directly observable in the market.

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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. ...

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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 ...

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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 ...

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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 ...

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