Introduction to Quantifying

Introduction

This blog is going to be about everything quantitative, focusing on applications of mathematical and statistical modelling. Not cool eh? Well, hopefully you'll find otherwise. Mathematics has been around for millennia and was first used for essentials such as counting things. More exciting applications soon developed in geometry and astronomy. This happened because people observed the regularity of the movements of the moon and the stars. Useful things came out of that very early such as the ability to navigate. But the ability to develop statistical models was a long time coming and wasn't to do with the lack of data. Conceptually statistics seems difficult and many ideas, even as simple as the mean, took a long time to gain acceptance. A great article on this is "An average understanding" by Simon Raper in the Royal Statistical Society's Significance magazine which you can find online. We take this concept for granted but it was only in the nineteenth century that it became widely accepted. To use statistical modelling effectively requires the application of concepts such as the mean but also the ability to corral and wrangle the data. I'll be using Python to do that with its modules such as matplotlib which are so useful to produce good graphics. You can see an example at the top of this page. There is a great variety of more sophisticated statistical techniques which go beyond the use of averages or well known methods such as linear regression. I'll be investigating these as this blog grows. Many of these can be used to investigate and model data sets with many fields so as to uncover unexpected relationships or gain confidence in known relationships. Wherever this blog goes I'm expecting the journey to be an exciting one!     

Who is it for?

This blog is for scientists, researchers and students with an interest in applying statistics and mathematics to real world problems. Many of the posts will be on finance and economics but many of the techniques I'll be using can be applied anywhere.  

Quantitative Finance

Some posts will complement material that I've written about in my book "Quantitative Finance for Dummies" published by John Wiley in July 2016. Inevitably when writing a book some subjects don't quite make it in but are important nonetheless, so this is a chance for me to expand on the book contents. For example, the book covers conventional bonds but has nothing on index linked bonds despite a quarter of the UK government debt being in that form. It's also a chance for me to expand on some of the more difficult subjects such as Brownian motion and multi-variate analysis

Yield Curves

I'm fascinated by the yield curve and what you can predict using it. Many central banks provide excellent data and so this is an arena for testing quite complex statistical models. The chart below shows just such data from the Japanese Ministry of Finance. Each line on the chart shows how the yields of bonds of a given maturity evolved in time. Mostly the longer maturity bonds have higher yields than the short maturity bonds. The overall trend for all maturities is downward with some going negative in recent times. There are some features in the chart particularly around 2008 and 2016 which reflect economic events. I created the chart using Pandas and data downloaded from Quandl which is a great source for financial data.

Python

In my the book I deliberately avoided writing anything about programming languages except to say that it's a key step in learning quantitative finance. In these posts I'll be showing you how to do quantitative finance with the Python language. There are many advantages to using Python. Firstly you can download it free of charge from the Python Software Foundation. Secondly, there are many tools available to work with it especially NumPy which allows you to do key numerical tasks such as matrix inversion or least squares optimisation. For more complex model fitting you can also use SciPy . An equally useful tool is Pandas which is a powerful environment for the time series analysis that's ubiquitous in financial trading. Another great toolkit is scikit-learn which enables you to do machine learning with Python.

Machine Learning

Machine learning is a new science that has emerged from the fusion of statistical analysis with data science. I'll be looking at some trending topics such as random forests which are so easy to implement using Python but incorporate many subtle ideas.

Technology

Do we live in exceptional times of technology development? I'll be looking at technology development throughout time. How significant is the so called fourth industrial revolution compared with previous technological changes such as the invention of the wheel? How might society develop with such powerful corporations as Facebook and Google having research budgets well in excess of what many countries could afford?