Volatility forecast evaluation in R

In portfolio management, risk management and derivative pricing, volatility plays an important role. So important in fact that you can find more volatility models than you can handle (Wikipedia link). What follows is to check how well each model performs, in and out of sample. Here are three simple things you can do:

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Intraday volatility measures

In the last few decades there has been tremendous progress in the realm of volatility estimation. A major step is the additional use of intraday price path. It has been shown that estimates which consider intraday information are more accurate. Which is to say they converge faster to the real unobserved value of the true volatility.

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Bootstrapping time series – R code

Bootstrapping in its general form (“ordinary” bootstrap) relies on IID observations which staples the theory backing it. However, time series are a different animal and bootstrapping time series requires somewhat different procedure to preserve dependency structure.

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Better summary function in R

The summary function in R returns:

For the univariate case I wrote what I consider to be a better summary function which returns:

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Random books

It seems like a very long while since my bachelor. Checking my bookshelf the other day I was thinking to flag some of those books which helped or inspired me along the way. Here they are in no particular order.

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Forecasting the Eurozone Misery index

Is Miss Stagflation coming to visit?
The Misery index is the sum of inflation and unemployment rate. We would like them both to stay naturally low, and we are miserable when they are not. The index is currently floating in it’s record scratching levels. In this post I demonstrate the use of the nice FitAR package in R to fit an AR model and see what we can expect accordingly. Inflation and unemployment numbers concerning the Eurozone (17 countries) can be found here.
Have a look at the index over time:

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Stock market Kurtosis over time

In the last decade we have observed an increase in computational power, information availability, speed of execution and stock market competition in general. One might think that, as a result, we are prone to larger shocks that occur faster than what was common in the past. I crunched some numbers and was surprised to see that this is not the case.

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Kurtosis Interpretation

When you google “Kurtosis”, you encounter many formulas to help you calculate it, talk about how this measure is used to evaluate the “peakedness” of your data, maybe some other measures to help you do so, maybe all of a sudden a side step towards Skewness, and how both Skewness and Kurtosis are higher moments of the distribution. This is all very true, but maybe you just want to understand what does Kurtosis mean and how to interpret this measure. Similarly to the way you interpret standard deviation (the average distance from the average). Here I take a shot at giving a more intuitive interpretation.

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Marriage is good for your income

For those of you who are into machine learning, here you can find a cool collection of databases to play around with your favorite algorithm. I choose one out of the available 200 and fit a logistic regression model. The idea is to see what kind of properties are common for those who earn above 50K a year. Our data is such that the “y” variable is binary. A value of 1 is given if the individual earns above 50K and 0 if below. We know many things about the individual. Level of education in years, age, is she married, where from, which sector is she working in, how many working hours per week, race, and more. We can fit logistic regression, which is quite standard for a binary dependent variable, and see which variables are important.

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Most profitable hedge fund style

This is not an investment advice!!

Couple of weeks back, during amst-R-dam user group talk on backtesting trading strategies using R, I mentioned the most effective style for hedge funds is relative value statistical arbitrage, I read it somewhere. After the talk was over, I was not sure anymore if it was correct to say it and decided to check it.

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Bootstrap example

Bootstrap your way into robust inference. Wow, that was fun to write..

Introduction
Say you made a simple regression, now you have your  \widehat{\beta} . You wish to know if it is significantly different from (say) zero. In general, people look at the statistic or p.value reported by their software of choice, (heRe). Thing is, this p.value calculation relies on the distribution of your dependent variable. Your software assumes normal distribution if not told differently, how so? for example, the (95%) confidence interval is  \widehat{\beta} \pm 1.96 \times sd( \widehat{\beta}) , the 1.96 comes from the normal distribution.
It is advisable not to do that, the beauty in bootstrapping* is that it is distribution untroubled, it’s valid for dependent which is Gaussian, Cauchy, or whatever. You can defend yourself against misspecification, and\or use the tool for inference when the underlying distribution is unknown.

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