Density Confidence Interval

Density estimation belongs with the literature of non-parametric statistics. Using simple bootstrapping techniques we can obtain confidence intervals (CI) for the whole density curve. Here is a quick and easy way to obtain CI’s for different risk measures (VaR, expected shortfall) and using what follows, you can answer all kind of relevant questions.

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Why statistical bootstrap

I often write about bootstrap (here an example and here a critique). I refer to it here as one of the most consequential advances in modern statistics. When I wrote that last post I was searching the web for a simple explanation to quickly show how useful bootstrap is, without boring the reader with the underlying math. Since I was not content with anything I could find, I decided to write it up, so here we go.

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The case for Regime-Switching GARCH

GARCH models are very responsive in the sense that they allow the fit of the model to adjust rather quickly with incoming observations. However, this adjustment depends on the parameters of the model, and those may not be constant. Parameters’ estimation of a GARCH process is not as quick as those of say, simple regression, especially for a multivariate case. Because of that, I think, the literature on time-varying GARCH is not yet at its full speed. This post makes the point that there is a need for such a class of models. I demonstrate this by looking at the parameters of Threshold-GARCH model (aka GJR GARCH), before and after the 2008 crisis. In addition, you can learn how to make inference on GARCH parameters without relying on asymptotic normality, i.e. using bootstrap.

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Bayesian vs. Frequentist in Practice

Rivers of ink have been spilled over the ‘Bayesian vs. Frequentist’ dispute. Most of us were trained as Frequentists. Probably because the computational power needed for Bayesian analysis was not around when the syllabus of your statistical/econometric courses was formed. In this age of tablets and fast internet connection, your training does not matter much, you can easily transform between the two approaches, engaging the right webpages/communities. I will not talk about the ideological differences between the two, or which approach is more appealing and why. Larry Wasserman already gave an excellent review.

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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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