Author Archives: Georg

ForeCA: Forecastable Component Analysis

Forecastable component analysis (ForeCA) is a novel dimension reduction (DR) technique to find optimally forecastable signals from multivariate time series (published at JMLR).

See this video for my ForeCA talk at ICML 2013.

ForeCA works similar to PCA or ICA, but instead of finding high-variance or statistically independent components, it finds forecastable linear combinations.

ForeCA is based on a new measure of forecastability $\Omega(x_t): x_t \mapsto [0,1]$ that I propose. It is defined as

$\Omega(x_t) = 1 - \frac{H_s(x_t)}{\log 2 \pi}$

where

$H_s(x_t) = \int_{-\pi}^{\pi} f_x(\lambda) \log f_x(\lambda) d \lambda$

is the entropy of the spectral density of the process $x_t$ . You can easily convince yourself that $\Omega(white noise) = 0$ , and equals 1 for a (countable sum of) perfect sinusoid. Thus larger values mean that the signal is easier to forecast. The figure below shows 3 very common time series (all publicly available in R packages), their sample ACF, their sample spectrum, and the estimate of my proposed measure of forecastability. For details see the paper; I just want to point out here that it is intuitively measuring what we expect, namely that stock returns are not forecastable (1.5%), tree ring data is a bit more (15.86%), and monthly temperature is very much forecastable (46.12%). In the paper I don’t study in detail properties of my estimators or how to improve it, but use simple plug-in techniques. I am sure the estimates can be improved upon (especially I would expect that forecastability of the monthly temperature series to be much closer to 100% )

Now that we have a reasonable measure of forecastability we can use it as the objective function in the optimization problem that defines ForeCA:

$\boldsymbol{w}^{*} = arg \max_{\boldsymbol{w}} \Omega(\boldsymbol{w}' \boldsymbol{X}_t)$

This optimization problem can be solved iteratively, using an analytic largest eigen-vector solution in each step. Voila, this is ForeCA! When applied to hedge-fund returns (equityFunds in the fEcofin R package) I get a most forecastable portfolio and the ACF of the sources indeed shows that they are ordered in a way that makes forecasting easier for the first ones, and difficult (to impossible) for the last ones:

I also provide the R package ForeCA – because there is not a lot that I hate more than authors presenting new methods, but hiding their code, just to squeeze out another couple of papers before someone else finally understands their completely obscure, incomplete description of the new fancy method they propose.

All good things come in threes: 3rd time student paper competition winner (JSM 2012)

Driven by my competitive side I digged up a manuscript hidden for a long time on my hard drive entitled Testing for white noise against locally stationary alternatives. After some days polishing it, I submitted it to the 2012 JSM student paper competition held by the Section of Statistical Learning and Data Mining, sponsored by the journal with the same name (SAM). And to my – positive – surprise it was selected as one of five winners – just like last year and 2007.

San Diego here I come.

Update: pdf at academia.edu. A more polished updated version has been published in SAM.

Oops I did it again: winner of the JSM 2011 student paper competition

My paper “A Frequency Domain EM Algorithm to Detect Similar Dynamics in Time Series with Applications to Spike Sorting and Macro-Economics” was selected as (one out of three) major winners in the JSM 2011 student paper competition on Statistical Learning and Data Mining. Arxiv: 1103.3300.

This is the second time after my 2007 JSM award on the time varying long memory paper.

Lambert W Random Variables forthcoming in AoAS

My paper on ”Lambert W Random Variables – A New Family of Generalized Skewed Distributions with Applications to Risk Estimation” was accepted by the Annals of Applied Statistics (AoAS). Slightly older version on arxiv.

Gaussianize Cauchy in R the Lambert Way

Here I show you how you can make a random Cauchy sample look like a Gaussian (and here is the accompanying paper with theory and methodology). The data is transformed by a non-linear, but bijective transformation – thus you can go back and forth between Cauchy and Gaussian-like.

library(LambertW)
set.seed(10)
nn <- 100
yy <- rcauchy(n = nn)
normfit(yy) # definitely not Gaussian
xx <- Gaussianize(yy, method="MLE")
Consumption of big amounts of carbohydrates should be also avoided mainly because they increase the level of serotonin in the blood to show cheapest viagra no prescription  its action. Immediately seek medical help if you suffer from any unwanted side effects, then immediately seek medical assistance for the same.* Prolonged erection of your male organ can be one of the best medicine available for erectile dysfunction.  bulk generic viagra There can be problems of erectile dysfunction sildenafil wholesale find my link and, not confusing cause and effect here, there can be depression. There are two possible reasons for which you should definitely seek levitra on line amerikabulteni.com doctor help in case of erection problems. normfit(xx) # Gaussian

# what does the Lambert W x Gaussian model look like?
mod <- MLE_LambertW(yy, type="h")
summary(mod)
plot(mod)

Hans Rosling – just wow!

… and he even topped it a year later with this …