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Twelve Days 2013: LASSO Regression

December 19, 2013
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Day Eight: LASSO RegressionTL/DRLASSO regression (least absolute shrinkage and selection operator) is a modified form of least squares regression that penalizes model complexity via a regularization parameter. It does so by including a term proportional to $||\beta||_{l_1}$ in the objective function which shrinks coefficients towards zero, and can even eliminate them entirely. In that light, LASSO is a...

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Twelve Days 2013: Sensor Fusion

December 18, 2013
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Twelve Days 2013: Sensor Fusion

Day Seven: Sensor FusionTL/DRSensor fusion is a generic term for techniques that address the issue of combining multiple noisy estimates of state in an optimal fashion. There’s a straight forward view of it as the gain on a Kalman–Bucy filter, and an even simpler interpretation under the central limit theorem.A Primer on Stochastic ControlControl theory is...

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Dynasty Meets the Central Limit Theorem

November 20, 2013
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Dynasty Meets the Central Limit Theorem

There’s a classic probability problem/brainteaser popularized by google that states:In a country in which people only want boys, every family continues to have children until they have a boy. If they have a girl, they have another child. If they have a boy, they stop. What is the proportion of boys to girls in the country?It seems...

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Measuring Randomness in Capital Markets

September 29, 2013
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Measuring Randomness in Capital Markets

What is Random?As previously discussed, there’s no universal measure of randomness. Randomness implies the lack of pattern and the inability to predict future outcomes. However, The lack of an obvious model doesn’t imply randomness anymore than a curve fit one implies order. So what actually constitutes randomness, how can we quantify it, and why do we care?Randomness $\neq$ Volatility, and Predictability $\neq$ ProfitFirst...

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‘Tis the Season for September Bearishness?

August 22, 2013
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‘Tis the Season for September Bearishness?

Is September Bearish?Traders love discussing seasonality, and September declines in US equity markets are a favorite topic. Historically September has underperformed every other month of the year, offering a mean return of -.56% on the S&P 500 index from 1950 to 2012; 54% of Septembers were bearish over the same period – more than any other month. Empirically, September...

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