Thursday, June 10, 2010

Quantitative Candlestick Pattern Recognition (HMM, Baum Welch, and all that)

Fig 1. Clustering based approach to candlestick Pattern Recognition.

I've been reading a book titled, 'the Quants,' that I'm sure will tantalize many traders with some of the ideas embedded within. Most notably (IMO), the notion that Renaissance's James Simons, hired a battery of cryptographers and speech recognition experts to decipher the code of the markets. Most notable of the hired experts was, leonard Baum, co-developer of the Baum-Welch algorithm; an algorithm used to model hidden markov models. Now while I don't plan to divulge full details of my own work in this area; I do want to give a brief example of some methods to possibly apply with respect to these ideas.

Now most practitioners of classical TA have built up an enormous amount of literature around candlesticks, the japanese symbols used to denote a symbolic formation around open, high, low, and close daily data. The problem as I see it, is that most of the literature that is available only deals with qualitative recognition of patterns, rather than quantitative.

We might want to utilize a more quantitative approach to analyzing the information, as it holds much more potential than single closing price data (i.e. the information in each candle contains four dimensions of information). The question is, how do we do this in a quantitative manner?

One method to recognizing patterns that is well known is the supervised method.  In supervised learning, we feed the learner a correct list of responses to learn and configure itself from; over many iterations, it comes up with the most optimal configuration to minimize errors between the data it learns to identify, and the data we feed as examples.  For instance, we might look at a set of hand-written characters and build a black box to recognize each letter by training via a neural net, support vector machine, or other supervised learning device. However, you probably don't want to spend hours classifying the types of candlesticks by name. Those familiar with candlesticks, might recognize numerous different symbols; shooting star, hammer, doji, etc... Each connotating a unique symbolic harbinger of the future to come. From a quantitative perspective, we might be more interested in understanding the bayesian perspective; I.e. P(upday|hammer)=P(upday,hammer)/P(hammer), for instance.

But how could we learn the corpus of symbols, without the tedious method of identifying each individual symbol by hand? This is a problem that may better be approached by unsupervised learning. In unsupervised learning, we don't need to train a learner; it finds relationships by itself. Typically, the relationships are established as a function of distance between exemplars. Please see the data mining text (Witten/Frank) in my recommended list in order to examine the concepts in more detail.  In this case I am going to train using a very common unsupervised learner called k-means clustering.

 Fig 2. Graph of arbitrary window of QQQQ data

Notice the common time ordered candlestick form of plotting is displayed in Fig 2.  Now using k-means clustering, with a goal of identifying 6 clusters, I tried to automatically learn 6 unique candlestick forms based on H,L,Cl data relative to Open in this example. The idea being that similar candlestick archetypes will tend to cluster by distance.

Fig 3. Candlestick symbols sorted by 6 Clusters

Notice in Figure 3, that we can clearly see the k-means clustering approach automatically recognized large red bodies, green bodies, and even more interestingly, there are a preponderance of hammers that were automatically recognized in cluster number 5.

So given that we have identified a corpus of 6 symbols in our language, of what use might this be? Well, we can take and run a cross tabulation of our symbol states using a program like R.

Fig 4. Cross Tabulation of Clustered States.

One of the things that strikes me right away is that there are an overwhelming number of pairs with state 1s following state 5; Notice the 57% frequency trounces all other dependent states.  Now what is interesting about this? Remember we established that state 5 corresponds to a hammer candlestick? Well, common intuition (at least from my years of reading) expects that a hammer is a turning point that is followed by an up move. Yet, in our table we see it is overwhelmingly followed by state 1, which if you look back, at the sorted by cluster diagram, is a very big red down candlestick. This is completely opposite to what our common body of knowledge and intuition tells us.

In case it might seem unbelievable to fathom, we can resort the data again, this time in original time order, but with clusters identified.

Fig 5.  Visual Inspection of hammer (state5) likely followed by down candle (state 1)

We can go back and resort the data and identify the states via the resorted cluster ID staircase level(5), or use labels to more simply identify the case of hammer(5) and its following symbol. Notice that contrary to common knowledge, our automatic recognition process and tabulated probability matrix, found good corroboration with our visual inspection. In the simple window sample (resized to improve visibility), 4 of the 5 instances of the hammer (state 5) were followed by a big red down candle (state 1). Now one other comment to make is that in case the state 5 is not followed by state 1 (say, we bet on expecting a down move), it has a 14.3% chance of landing in state 6 on the next move, which brings our likelihood of a decent sized down move to 71.4% overall.

We can take these simple quantitative ideas and extend them to MCMC dynamic models, Baum Welch and Viterbi algorithms, and all that sophisticated stuff. Perhaps one day even mimicking the mighty Renaissance itself?  I don't know, but any edge we can add to our arsenal will surely help.

Take some time to read the Quants, if you want a great laymen's view of many related quant approaches.

There may be some bugs in this post, as google just seemed to update their editing platform, and I'm trying to iron out some of the kinks.