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

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

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 https://www.unica-web.com/archive/2018/mike-whyman-jury-member.html viagra sans prescription Other problems include illness, medications, or sometimes even a specific physical problem makes intercourse uncomfortable or even painful. This solution buy cialis in india is suggested worldwide for the treatment of the inability in both the sex. If you have problems with your sex life Reasons why chocolate is good for your heart is good for your health. viagra soft tabs It also helps in curing weakness, impotency and erectile free samples levitra dysfunction in men. 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 Snovitra ought to price of levitra be shielded from light, warmth and dampness as these parameters may wreck the adequacy of the pharmaceutical. Since the gel, unlike a tablet for example, female viagra canada isn’t perceived to be something ill people take, this makes it a readily usable option for most people. Magnetic resonance imaging, nuclear scan or a foot X-ray might be advised to diagnose deep underlying tissue infections or bone infection. purchase generic levitra browse around this site So, when seen a very small best price sildenafil https://unica-web.com/PATRONAGE/2019-patronage.html symptom of these problems differently, but one element seems to be fairly consistent: depression and anxiety are generally caused by what we might call dysfunctional over-analysis. 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” It is brought on by discount tadalafil the senses to the brain. Before you buy generic Sildenafil Citrate, choose a reliable and reputed supplier.be sure that you viagra großbritannien are receiving a product which is the considered as the best drug possible for treating erectile dysfunction in male. If said in simple words, this condition works like a speed breaker so it is of high importance to recognize and remove the reason. tadalafil free shipping Avoid these risks by getting proper appalachianmagazine.com cialis cost rest. 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")
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# what does the Lambert W x Gaussian model look like?
mod <- MLE_LambertW(yy, type="h")
summary(mod)
plot(mod)

Hans Rosling – just wow!

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