Day of the week and the cross-section of returns

I just finished reading an interesting paper by Justin Birru titled: “Day of the week and the cross-section of returns” (reference below). The story is much too simple to be true, but it looks to be so. In fact, I would probably altogether skip it without the highly ranked Journal of Financial Economics stamp of approval. However, by the end of the paper I was as convinced as one can be without actually running the analysis.

More

R Journal publication

The R Journal is the open access, refereed journal of the R project for statistical computing. It features short to medium length articles covering topics that should be of interest to users or developers of R.

Christoph Weiss, Gernot Roetzer and myself have joined forces to write an R package and the accompanied paper: Forecast Combinations in R using the ForecastComb Package, which is now published in the R journal. Below you can find a few of my thoughts about the journey towards publication in the R journal, and a few words about working with a small team of three, from three different locations.

More

Most popular machine learning R packages – part 2

In a previous post: Most popular machine learning R packages, trying to hash out what are the most frequently used machine learning packages, I simply chose few names from my own memory. However, there is a CRAN task views web page which “aims to provide some guidance which packages on CRAN are relevant for tasks related to a certain topic.” So instead of relying on my own experience, in this post I correct for the bias by simply looking at the topic
Machine Learning & Statistical Learning. There are currently around 100 of those packages on CRAN.

More

R tips and tricks – higher-order functions

A higher-order function is a function that takes one or more functions as arguments, and\or returns a function as its result. This can be super handy in programming when you want to tilt your code towards readability and still keep it concise.

More

Most popular posts – 2018

2019 is well underway. 2018 was personally difficult, so I am happy it’s behind us. Without further ado, here is what my analytics report shows to be the three most popular posts for 2018:

More

Create own Recession Indicator using Mixture Models

Context

Broadly speaking, we can classify financial markets conditions into two categories: Bull and Bear. The first is a “todo bien” market, tranquil and generally upward sloping. The second describes a market with a downturn trend, usually more volatile. It is thought that those bull\bear terms originate from the way those animals supposedly attack. Bull thrusts its horns up while a bear swipe its paws down. At any given moment, we can only guess the state in which we are in, there is no way of telling really; simply because those two states don’t have a uniformly exact definitions. So basically we never actually observe a membership of an observation. In this post we are going to use (finite) mixture models to try and assign daily equity returns to their bull\bear subgroups. It is essentially an unsupervised clustering exercise. We will create our own recession indicator to help us quantify if the equity market is contracting or not. We use minimal inputs, nothing but equity return data. Starting with a short description of Finite Mixture Models and moving on to give a hands-on practical example.

More

Test of Equality Between Two Densities

Are returns this year actually different than what can be expected from a typical year? Is the variance actually different than what can be expected from a typical year? Those are fairly light, easy to answer questions. We can use tests for equality of means or equality of variances.
But how about the following question:

is the profile\behavior of returns this year different than what can be expected in a typical year?

This is a more general and important question, since it encompasses all moments and tail behavior. And it is not as trivial to answer.

In this post I am scratching an itch I had since I wrote Understanding Kullback – Leibler Divergence. In the Kullback – Leibler Divergence post we saw how to quantify the difference between densities, exemplified using SPY return density per year. Once I was done with that post I was thinking there must be a way to test the difference formally, rather than just quantify, visualize and eyeball. And indeed there is. This post aim is to show to formally test for equality between densities.

More

Orthogonality in Statistics

Orthogonality in mathematics

The word Orthogonality originates from a combination of two words in ancient Greek: orthos (upright), and gonia (angle). It has a geometrical meaning. It means two lines create a 90 degrees angle between them. So one line is perpendicular to the other line. Like so:

Perpendicular
Source: Wikipedia

Even though Orthogonality is a geometrical term, it appears very often in statistics. You probably know that in a statistical context orthogonality means uncorrelated, or linearly independent. But why?

Why use a geometrical term to describe a statistical relation between random variables? By extension, why does the word angle appears in the incredibly common regression method least-angle regression (LARS)? Enough losing sleep over it (as you undoubtedly do), an extensive answer below.

More

Visualizing Time series Data

This post has two goals. I hope to make you think about your graphics, and think about the future of data-visualization. An example is given using some simulated time series data. A very quick read.

More

Kaggle Experience

At least in part, a typical data-scientist is busy with forecasting and prediction. Kaggle is a platform which hosts a slew of competitions. Those who have the time, energy and know-how to combat real-life problems, are huddling together to test their talent. I highly recommend this experience. A side effect of tackling actual problems (rather than those which appear in textbooks), is that most of the time you are not at all enjoying new wonderful insights or exploring fascinating unfamiliar, ground-breaking algos. Rather, you are handling\wrangling\manipulating data, which is.. ugly and boring, but necessary and useful.

I tried my powers few years ago, and again about 6 months ago in one of those competitions called Toxic Comment Classification Challenge. Here are my thoughts on that short experience and some insight from scraping the results of that competition.

More

Market intraday momentum

I recently spotted the following intriguing paper: Market intraday momentum.
From the abstract of that paper:

Based on high frequency S&P 500 exchange-traded fund (ETF) data from 1993–2013, we show an intraday momentum pattern: the first half-hour return on the market as measured from the previous day’s market close predicts the last half-hour return. This predictability, which is both statistically and economically significant is stronger on more volatile days, on higher volume days, on recession days, and on major macroeconomic news release days.

Nice! Looks like we can all become rich now. I mean, given how it’s written, it should be quite easy for any individual with a trading account and a mouse to leverage up and start accumulating. Maybe this is so, but let’s have an informal closer look, with as little effort as possible, and see if there is anything we can say about this idea.

More