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This is seen as a bit of a niche field, which is likely why there are not so many books and these issues are not covered in standard econometrics texts. Options pricing models are usually fitted to options data rather than estimated econometrically from historical data. For statistical models, it is often more convenient to start from a discrete model as the ...


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The simplest example might be Y= realized variance of a stock and X= return on the stock. Clearly these are dependent since they are both calculated from daily stock prices. X can be positive or negative , but Y is always positive. If large moves in the stock occur (up or down) , we would expect to measure high realized volatility. This might give a ...


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A correlation and a dependence cannot be interchanged. The dependence is more general term that two radnom variables are somehow linked. The correlation concerns linear dependence only. So, in your example variables $X$ and $Y$ are dependent because $Y=X^2$. As you pointed out, this is a quadratic dependency, not linear, hence there is no correlation. A ...


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Economics question yes. Also fairly easy to google. However, unless you are familiar with econ, finance etc it may not be clear where to search first. FED chairman Paul Volker was responsible for these high interest rates. This was at a time of Stagflation, high inflation and slow growth. The link has some basic explanations but generally this is difficult ...


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Normality of returns follows from the fact that the Brownian increments are normal distributed (property 3), $W(t_i)-W(t_{i-1}) \sim N(0,t_i-t_{i-1})$, and furthermore that $t_i-t_{i-1}=T(\frac{i}{n}-\frac{i-1}{n})=\frac{T}{n}$. See that: \begin{align} r(t_i)&=p(t_i)-p(t_{i-1})\\ &=\left[p(0)+\mu\cdot t_i + \sigma W(t_i) \right] - \left[p(0)+\mu\cdot ...


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It is an old thread. Just pointing out that capability is available in ARCH package now for the benefit of future readers. https://pypi.org/project/arch/ Volatility models ARCH GARCH TARCH EGARCH EWMA/RiskMetrics


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An Evaluation of Change Point Detection Algorithms might be of use.


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