This blog is just a personal hobby. When I’m extra busy as I was this year the blog is a front-line casualty. This is why 2023 saw a weaker posting stream. Nonetheless I am pleased with just over 30K visits this year, with an average of roughly one minute per visit (engagement time, whatever

A common issue encountered in modern statistics involves the inversion of a matrix. For example, when your data is sick with multicollinearity your estimates for the regression coefficient can bounce all over the place. In finance we use the covariance matrix as an input for portfolio construction.

Imagine you’re picking from 1,000 money managers. If you test just one, there’s a 5% chance you might wrongly think they’re great. But test 10, and your error chance jumps to 40%. To keep your error rate at 5%, you need to control the “family-wise error rate.” One method is to set higher

During 2017 I blogged about Statistical Shrinkage. At the end of that post I mentioned the important role signal-to-noise ratio (SNR) plays when it comes to the need for shrinkage. This post shares some recent related empirical results published in the Journal of Machine Learning Research from the

As per usual this point in time, I check my blog’s traffic-analytics to see which were the most popular pieces last year. Without further ado.. First: Correlation and Correlation Structure (6) – Distance Correlation (08:33 minutes average time on page) Second: Similarity and Dissimilarity

The word spurious refers to “outwardly similar or corresponding to something without having its genuine qualities.” Fake. While the meanings of spurious correlation and spurious regression are common knowledge nowadays, much less is understood about spurious factors. This post draws your

While linear correlation (aka Pearson correlation) is by far the most common type of dependence measure there are few arguably better ways to characterize\estimate the degree of dependence between variables. This is a fascinating topic I keep coming back to. There is so much for a typical geek to

Kind of sad, but the same intro which served last year, befits this year also. Littered with Corona, this year was not easy. But looking around me, I feel grateful. The following quote by Socrates comes to mind: “If all our misfortunes were laid in one common heap whence everyone must take an

In volatility modelling, a typical challenge is to keep the covariance matrix estimate valid, meaning (1) symmetric and (2) positive semi definite*. A new paper published in Econometrica (citing from the paper) “introduces a novel parametrization of the correlation matrix. The reparametrization

This post is inspired by Leo Breiman’s opinion piece “No Bayesians in foxholes”. The saying “there are no atheists in foxholes” refers to the fact that if you are in the foxhole (being bombarded..), you pray! Leo’s paraphrase indicates that when complex, real problems are present, there

Every form of strength is also a form of weakness*. I love statistics, but I focus to much on methodology, which is not for everyone. Some people (right or wrong) question: “wonderful sir, but what can I do with it?”. A new paper titled “Beta in the tails” is a showcase application for why

This is the fifth post which is concerned with quantifying the dependence between variables. When talking correlations one usually thinks about linear correlation, aka Pearson’s correlation. One serious limitation of linear correlation is that it’s, well.. linear. By construction it’s not

Principal component analysis (PCA from here on) is performed via linear algebra functions called eigen decomposition or singular value decomposition. Since you are actually reading this, you may well have used PCA in the past, at school or where you work. There is a strong link between PCA and the

Littered with Corona, this year was not easy. But looking around me, I feel grateful. The following quote by Socrates comes to mind: “If all our misfortunes were laid in one common heap whence everyone must take an equal portion, most people would be content to take their own and depart.” On

If you regularly read this blog then you know I am not one to jump on the “AI Bandwagon”, being quickly weary of anyone flashing the “It’s Artificial Intelligence” joker card. Don’t get me wrong, I understand it is a sexy term I, but to me it always feels a bit like a sales pitch. If the

Here I share a refreshing idea from the paper “Asymmetric correlations of equity portfolios” which was published in the Journal of financial Economics, a top tier journal in this field. The question is how much the observed conditional correlation on the downside (say) differs from the

Density estimation is now a trivial one-liner script in all modern software. What is not so easy is to become comfortable with the result, how well is is my density estimated? we rarely know. One reason is the lack of ground-truth. Density estimation falls under unsupervised learning, we don’t

Enough! Enough with that pointless R versus Python debate. I find it almost as pointless as the Bayesian vs Frequentist “dispute”. I advocate here what I advocated there (“..don’t be a Bayesian, nor be a Frequenist, be opportunist“). Nowadays even marginally tedious computation is being

Another opinion piece. If you can’t explain it simply you don’t understand it well enough. (Albert Einstein) Rant in progress A bit on Deep Learning What is so deep about deep learning? Nothing. There is nothing deep about it. If you read through the excellent Deep Learning book you can see (p.

Many machine learning algorithms rely on distances between data points as their input, sometimes the only input, especially so for clustering and ranking algorithms. The celebrated k-nearest neighbors (KNN) algorithm is our example chief, but distances are also frequently used as an input in the

The term mutual information is drawn from the field of information theory. Information theory is busy with the quantification of information. For example, a central concept in this field is entropy, which we have discussed before. If you google the term “mutual information” you will land at some

As every year, I checked my analytics so that I can let you know what was popular. This year I have also experimented with a survey where I asked one question at the end of each relevant post. About 120 replies recieved, but the free Survey Monkey account (the survey provider I went with) only lets

I have recently been reading about more modern ways to decompose a matrix. Singular value decomposition is a popular way, but there are more. I went down the rabbit whole. After a couple of “see references therein” I found something which looks to justify spending time on this. An excellent

Principal component analysis (PCA) is one of the earliest multivariate techniques. Yet not only it survived but it is arguably the most common way of reducing the dimension of multivariate data, with countless applications in almost all sciences. Mathematically, PCA is performed via linear algebra

Moving average is one of the most commonly used smoothing method, basically the go-to. It helps us detect trend in the data by smoothing out short term fluctuations. The computation is trivial: take the most recent k points and simple-average them. Here is how it looks: Moving average example with

When you build your portfolio you must decide what is your risk profile. A pension fund’s risk profile is different than that of a hedge fund, which is different than that of a family office. Everyone’s goal is to maximize returns given the risk. Sinfully but commonly risk is defined as the

Many years ago, when I was still trying to beat the market, I used to pair-trade. In principle it is quite straightforward to estimate the correlation between two stocks. The estimator for beta is very important since it determines how much you should long the one and how much you should short the

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

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

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. Consider the following code: # Generate some fake data

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: – Create own Recession Indicator using Mixture Models (3:53 minutes average time on page) – Portfolio

Reproducible Finance with R is a clever book, with modern treatment of classical concepts. Here below is what I liked- and disliked about the book. Back when I was practicing Judo, there was a guy in my group who mastered that one exercise (called Uchi Mata). He could go fighting 20 consecutive

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

Just finished reading the paper Stock Market’s Price Movement Prediction With LSTM Neural Networks. The abstract attractively reads: “The results that were obtained are promising, getting up to an average of 55.9% of accuracy when predicting if the price of a particular stock is going to go up

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

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. In visualization, like in programming, presenting or any other skill, there is much to learn. Also

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

The yearly R in Finance conference is one of my favorites: 1. Titans of the R community are there every year. This year the founder of Rstudio (but much more really), JJ Allaire was a keynote speaker. He gave a talk about Machine Learning with TensorFlow and R. 2. Single track. I like everything,

Higher moments such as Skewness and Kurtosis are not as explored as they should be. These moments are crucial for managing portfolio risk. At least as important as volatility, if not more. Skewness relates to asymmetry risk and Kurtosis relates to tail risk. Despite their great importance, those

Constructing a portfolio means allocating your money between few chosen assets. The simplest thing you can do is evenly split your money between few chosen assets. Simple as it is, good research shows it is just fine, and even better than other more sophisticated methods (for example Optimal Versus

Note: I usually write more technical posts, this is an opinion piece. And you know what they say: opinions are like feet, everybody’s got a couple. Machine learning is simply statistics A lot of buzz words nowadays. Data Science, business intelligence, machine learning, deep learning, statistical

Is bitcoin a bubble? I don’t know. What defines a bubble? The price should drastically overestimate the underlying fundamentals. I simply don’t know much about blockchain to have an opinion there. A related characteristic is a run-away price. Going up fast just because it is going up fast. How

Writing this, I can’t believe how quickly the year 2017 has gone by. Also weird, we are already three weeks into 2018, unreal. Time flies when you’re having fun I guess. The analytics report shows that the three most popular posts for 2017 are: – Understanding False Discovery Rate (4 minutes

This is another comparison between R and MATLAB (Python also in the mix this time). In previous rounds we discussed the differences in 3d visualization, differences in syntax and input-output differences. Today is about computational speed. Spoiler alert: MATLAB wins by a knockout. A genuinely fair

Tail risk conventionally refers to the risk of a large and sharp draw down of the portfolio. How large is subjective and depends on how you define what is a tail. A lot of research is directed towards having a good estimate of the tail risk. Some fairly new research also now indicates that investors

LASSO stands for Least Absolute Shrinkage and Selection Operator. It was first introduced 21 years ago by Robert Tibshirani (Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B). In 2004 the four statistical masters: Efron, Hastie, Johnstone and

Density estimation using regression? Yes we can! I like regression. It is one of those simple yet powerful statistical methods. You always know exactly what you are doing. This post is about density estimation, and how to get an estimate of the density using (Poisson) regression. The “go-to”

If you consider yourself Econometrician\Statistician or one of those numerous buzz word synonyms that are floating around these days, Computer Age Statistical Inference: Algorithms, Evidence and Data Science by Bradley Efron and Trevor Hastie is a book you can’t miss, and now nor should you. You

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. Risk: Elements of Financial Risk Management Clear and to the point, 5 stars. Value at

Shrinkage in statistics has increased in popularity over the decades. Now statistical shrinkage is commonplace, explicitly or implicitly. But when is it that we need to make use of shrinkage? At least partly it depends on signal-to-noise ratio. Introduction The term shrinkage, I think, is the most