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http://bluemountaincapital.github.io/Deedle/ Disclaimer: I haven't used this.


Mean reversion speed $\kappa$ is better interpreted with the concept of half-life, which can be calculated from $\text{HL} = \ln(2) / \kappa$. For example, if the mean reversion coefficient is $\kappa = 1.5$, then the half-life of the process is $\ln(2) / 1.5 = 0.46209812$ years, or about 6 months. Let's assume that the current interest rate is 1% and the ...


In the Mean-Reverting Models like C.I.R \begin{align} &dr_t=\kappa(\theta-r_t)dt+\sigma\sqrt {r_t} dW_t \end{align} speed of mean reversion ($\kappa$) is not negative.If the condition $2\kappa\theta> \sigma^2$ holds, then the drift is sufficiently large for the process to be guaranteed positive and not reach zero. This condition is known as the Feller ...


Few comments on your questions: 1) Yes, Arch and Garch are suitable for equities volatility, please see: http://onlinelibrary.wiley.com/doi/10.1002/jae.800/pdf 2) No. These are models of volatility. To model interest rates use CIR, Vasicek or similar. 3) and 4) Check paper above.


In practice, for heavily traded assets (above 60% quantile of average daily dollar volume), individual asset return is pretty scalable across different time frame by a factor of $\sqrt{T}$. However, for covariance among different assets, moving between different time frame is not linearly scalable (although it should be in math). This is known as "Epps ...


Yes, these are the fundamental building blocks for a money making strategy. To partially solve the issues you mention (small/low positive means/profits with large standard errors), you can investigate on many assets simultaneously. The idea is to take the advantage of Central Limit Theorem. Assuming the signal for each asset are i.i.d., and each signal ...


You estimate a model $$ Y_t = \beta X_t + \epsilon_t. $$ which is just time-series regression. Concerning your question 1): One usually looks at the beta of a single security w.r.t. a stock index (see the CAPM). High beta (above 1)will indicate that the stock would rise and fall more than the market. Other approaches where one estimates a beta is in ...


This paper states that heteroskedasticity is a stylized fact in daily as well as intra-day returns: https://statistik.econ.kit.edu/download/doc_secure1/HandbookITandFinan.pdf


Approach 1 is parametric regression, whereas approach 2 is non-parametric regression. How are they related: non-parametric regression models the entire distribution of all possible function forms, and then do the integration to calculate a single value E[Y|X]. It is function-form free. In contrast, parametric linear regression ASSUMES that the function ...


look at the econometrics literature on "total Least squares" (van huffel has a text out by that name)...or more generally think about what principal components does (hint: it's minimizing the distance to a regression line as in #2..it's not minimizing just the "vertical" distance)


For time-frames of >21 days you can just compute the standard deviation of daily returns over that time period and then annualize it to make it comparable. For the 5 days realized volatility the best option is really to use intraday data and sum the squared intraday returns.

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