# quantitative analysis

What if you had a tool that could help you decide when to apply mean reversion strategies and when to apply momentum to a particular time series? That's the promise of the Hurst exponent, which helps characterise a time series as mean reverting, trending, or a random walk. For a brief introduction to Hurst, including some Python code for its calculation, check out our previous post. Even if you have read this post previously, it is worth checking out again as we have updated our method for calculating Hurst and believe this new implementation is more accurate. It would be great if we could plug some historical time series data into the Hurst algorithm and know whether we expect the time series to mean revert or trend. But as is usually the case when we apply such tools to the financial domain, it isn't quite that straightforward. In the last post, we noted that Hurst gives different results depending on how it is calculated; this begs the question of how to choose a calculation method intelligently so that we avoid choosing...

This post comes to you from Dr Tom Starke, a good friend of Robot Wealth. Tom is a physicist, quant developer and experienced algo trader with keen interests in machine learning and quantum computing. I am thrilled that Tom is sharing his knowledge and expertise with the Robot Wealth community. Over to you, Tom. Unlike most other businesses, algorithmic trading has the advantage of giving you almost instant feedback on how good you are in your business. For anyone who is numerically inclined this is a very attractive proposition. I have seen articles written about this subject but they have never really addressed a lot of the issues I have come across on my journey. In this post I would like to talk about this a little as an inspiration or perhaps a deterrent for all the people who read this and consider making money that way. Nothing could be more amazing, a system that runs by itself and consistently spits out cash to finance prolonged stays in Bali, South America or with your mom if that’s what you’re after. However,...

In the first Mean Reversion and Cointegration post, I explored mean reversion of individual financial time series using techniques such as the Augmented Dickey-Fuller test, the Hurst exponent and the Ornstein-Uhlenbeck equation for a mean reverting stochastic process. I also presented a simple linear mean reversion strategy as a proof of concept. In this post, I’ll explore artificial stationary time series and will present a more practical trading strategy for exploiting mean reversion. Again this work is based on Ernie Chan's Algorithmic Trading, which I highly recommend and have used as inspiration for a great deal of my own research. Go easy on my design abilities... In presenting my results, I have purposefully shown equity curves from mean reversion strategies that go through periods of stellar performance as well as periods so bad that they would send most traders broke. Rather than cherry pick the good performance, I want to demonstrate what I think is of utmost importance in this type of trading, namely that the nature of mean reversion for any financial time series is constantly changing. At times this dynamism can...

In the last article, I described an application of the k-means clustering algorithm for classifying candlesticks based on the relative position of their open, high, low and close. This was a simple enough exercise, but now I tackle something more challenging: isolating information that is both useful and practical to real trading. I'll initially try two approaches: Investigate whether there are any statistically significant patterns in certain clusters following others Investigate the distribution of next day returns following the appearance of a candle from each cluster The insights gained from this analysis will hopefully inform the next direction of this research. Data preliminaries In the last article, I classified twelve months of daily candles (June 2014 - July 2015) into eight clusters. To simplify the analysis and ensure that enough instances of each cluster are observed, I'll reduce the number of clusters to four and extend the history to cover 2008-2015. I'll exclude my 2015 data for now in case I need a final, unseen test set at some point in the future. Here's a subset of the candles over the entire price history (2008-2014, 2015...

This post builds on work done by jcl over at his blog, The Financial Hacker. He proposes the Cold Blood Index as a means of objectively deciding whether to continue trading a system through a drawdown. I was recently looking for a solution like this and actually settled on a modification of jcl's second example, where an allowance is made for the drawdown to grow with time. The modification I made was to use the confidence intervals for the maximum drawdown calculated by Zorro’s Monte Carlo engine rather than the maximum drawdown of the backtest. The limitation is that the confidence intervals for the maximum drawdown length are unknown – only those for the maximum drawdown depth are known. I used the maximum drawdown length calculated for the backtest and considered where the backtest drawdown depth lay in relation to the confidence intervals calculated via Monte Carlo to get a feel for whether it was a reasonable value. Below is a chart of the minimum profit for a strategy I recently took live plotted out to the end of 2015, created using the method...

In the first part of this article, I described a procedure for empirically testing whether a trading strategy has predictive power by comparing its performance to the distribution of the performance of a large number of random strategies with similar trade distributions. In this post, I will present the results of the simple example described by the code in the previous post in order to illustrate how susceptible trading strategies are to the vagaries of randomness. I will also illustrate by way of example my thought process when it comes to deciding whether to include a particular component in my live portfolio or discard it. I tested one particular trading system on a number of markets separately in both directions. I picked out three instances where the out of sample performance was good as candidates for live trading. The markets, trade directions and profit factors obtained from the out of sample backtest are as follows: USD/CAD - Short - Profit Factor = 1.79 GBP/USD - Long - Profit Factor = 1.20 GBP/JPY - Long - Profit Factor = 1.31 Next, I estimated the performance of...