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To test for model misspeicfication: First ensure that auto correlation of standardized residuals resulted from the ARMA-GARCH model are not significant. Further, you can use Box-Ljung test. It test joint significance of auto correlation upto lag $K$. Leverage effect is tested by sign bias test. If $p$ value is less than .05 (assumed significance level) ...

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The first part has already been answer by @Uditg_ucla, so I am only providing answer of your 2nd part. Rewriting your SDE in more sophisticated way: $$dS=k(b-S)dt+\sigma S dz$$ You want SDE for $S^2$. Using Taylor series, it can be written as: $$df(S)=f'(S)dS + \frac{1}{2!}f''(S)(dS)^2+\cdots$$ $$df(S)=2SdS+(dS)^2$$ df(S)=2S[k(b-S)dt+\sigma S ...

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While I've never used SIT, I have used quantstrat quite a bit and can attest to its strength. It has a solid developer community backing it (7 contributors on Github), is part of the TradeAnalytics project on R-Forge, and while it's still technically in beta, it should provide plenty of functionality. There is admittedly a pretty steep learning curve when ...

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