The role and importance of time series analysis in finance was recognized in 2003 by awarding the Nobel Prize of economics to Robert Engle for his work on the Autoregressive Conditional Heteroscedastic (ARCH) model, pioneered in 1982. However, detecting trends and patterns in financial time-series has been of great interest to the finance world for decades. So far, the primary means of detecting trends and patterns has involved statistical methods such as statistical clustering and regression analysis and more recently the Autoregressive Conditional Heteroscedastic (ARCH) model, as mentioned above, and Generalized ARCH (GARCH) model which are considered today the most often applied time-varying model. The mathematical models associated with these methods for economical forecasting, however, are linear and may fail to forecast the turning points in economic cycles because in many cases the data they model may be highly nonlinear.

Time series analysis is the fitting of stochastic processes to time series. Any associative array of times and numbers can be viewed as a time series. The times may not necessarily be of a regular interval length. For example, the historical fluctuations in the price of a NYMEX Gold Contract can be said to be the time series for NYMEX Gold. Analysts throughout the economy will use the tools outlined here to aid in the management of their corresponding businesses. Energy traders, for example, will often attempt to forecast power consumption based upon both weather normals and short term weather forecasts.

This usually entails statistical analyses, but it is not a straightforward application of statistics. A stochastic process may seem similar to a sample , and a time series may seem similar to a realization of a sample, but there is a profound difference. A sample—the province of statistics—comprises random variables that are assumed independent and identically distributed (IID). While it is possible that the terms of a stochastic process might be IID—in which case, time series analysis reduces to statistics—this is not a particularly interesting case. The purpose of time series analysis is to study the more interesting case in which terms corresponding to different points in time have interdependencies.

A “renaissance” in Computational Intelligence is occurring, including neural networks, and genetic algorithms, and has re-attracted attention form analyst and quants of trends and patterns. Mainly due to the fact that we now have the computational scale to simulate these methods. In particular, neural networks are being used extensively for financial forecasting with stock markets, foreign exchange trading, commodity future trading and bond yields.

Stock market prediction is an area of financial forecasting which attracts a great deal of attention. In financial theory, the efficient market hypothesis (EMH), in its weak form, predicts that analysis of time series data alone will provide no excess return over a simple buy and hold strategy and the data contained in the time-series has no economic value unless the data leads to a transaction. However, it does not deny that such prediction is possible from inside information. Predictive success with neural networks and univariate time series would be contrary to this form of the EMH. Research on using neural networks has been carried out to retrieve trends and patterns of stock markets. Application of neural networks in time series forecasting is based on the ability of neural networks to approximate nonlinear functions very quickly, possibility in real-time, if they are implemented correctly.

I am currently conducting research in the area and will share some results as they come in.

The literature on time series analysis documents numerous standard models for stationary processes. The simplest of these are white noise processes. From white noise processes can be constructed moving average, autoregressive and autoregressive-moving-average processes, which are generally used to model conditionally homoskedastic autocorrelated processes. Other processes are used to model conditionally heteroskedastic processes. Techniques for fitting these processes to actual time series tend to be specific to the particular models. Some more interesting topics are as follows:

• ARCH A category of conditionally heteroskedastic stochastic processes.
• Autoregressive moving-average process A type of stochastic process.
• Autoregressive process A type of stochastic process.
• Brownian motion A simple continuous stochastic process that is widely used in physics and finance for modeling random behavior that evolves over time.
• Heteroskedasticity A condition where a stochastic process has non-constant second moments.
• Martingale A type of stochastic process that has zero drift.
• Moving-average process A type of stochastic process. random walk A discrete stochastic process whose increments form a white noise.
• Stochastic volatility model A category of conditionally heteroskedastic stochastic processes. volatility A metric of variability in a stochastic process.
• Volatility clustering A property of some stochastic processes that they experience periods of high and low variance.
• Volatility skew A condition where implied volatilities vary by strike. white noise A simple form of stochastic process.

Intelligent Agents have been used in the financial industry for a variety of applications, from Simple Network Management Protocol-based (SNMP) monitoring tools for operational infrastructure management to more sophisticated functions like sorting, sifting and digesting the mountains of information that will surround consumers. In the ‘Always On Real Time Access’  Networks of the future, these agents pick out relevant information as they autonomously roam around the always-connected network autonomously.

In computer science, an intelligent agent (IA) is a software agent that exhibits some form of artificial intelligence that assists the user and will act on their behalf, in performing repetitive computer-related tasks. While the working of software agents used for operator assistance or data mining (sometimes referred to as bots) is often based on fixed pre-programmed rules, “intelligent” here implies the ability to adapt and learn.In some literature IAs are also referred to as autonomous intelligent agents, which means they act independently, and will learn and adapt to changing circumstances. –Wikipedia

One of the most notable and interesting use of agents is the Santa Fe Instute’s Artificial Stock Exchange. The Santa Fe Artificial Stock Market’s objective was to use agent-based technology to model an entire market and to get an understanding of the dynamics in relatively traditional economic models. It is these models for which economists often invoke the heroic assumption of convergence to rational expectations equilibrium where agents’ beliefs and behavior have converged to a self-consistent world view. Obviously, this would be a nice place to getto, but the dynamics of this journey are rarely spelled out. Given that financial markets appear to thrive on diverse opinions and behavior, a first level test of rational expectations from a heterogeneous learning perspective was always needed.

The Santa Fe Institute (or SFI) is a non-profit research institute in Santa Fe, New Mexico founded by George Cowan, David Pines, Sterling Colgate, Murray Gell-Mann, Nick Metropolis, Herb Anderson, Peter Caruthers, and Richard Stansky in 1984 to study complex systems.

–Wikipedia

While the Santa Fe Instute’s Artificial Stock Exchange was seminal work on exploring the use of agents to simulate a complex social networks, my scope is a wee bit narrower but I think equally of interest. What I propose is to model a smaller social network; that of an Artificial Trading Room. Imagine, if you will, a hyperspace room filled with autonomous agents buying and selling the same security. the room is filled with posts, similar to specialist stations, but more to just act as the book, and another function as we will see later, but not a market maker. The room is filled with x posts the represent different time horizons that an agent is interested in relative to the stock. Around each post will be ytrading agents that are truly intelligent in the “artificial” sense. They all have a hyper-cortex (Artificial Brains not just rules) that are self-organising neural networks that continuously adapts to incoming market data, recent transactional data, Quote data, and have also been trained on massive amounts of historical market data. The y agents that gather around a trading post are unique entities, they have been trained using a different sub-set of historical data, their neurons were randomized during training using different seed numbers and it is even possible to use different neural network topologies. All these variations will result in agents with differnt dispostions.

This may all seem obvious form a theoretical point of view so far. But what I suggest next is to put a second layer of adaptivity on top of the computational agents hyper-cortex. Most market participants know from empirical “pain” that as quickly as one places a trading strategy into the market its performance begins to decay. Just for the simple fact that the massive social network that make up the other market participants eventually catch on. The computational agents hyper-cortex adapt well but in some cases they may not adapt quickly enough because they have so much historical data to biases them towards a quick change.

I propose that the second layer of adaptivity is a simple strategy that is already employed in the “real trading rooms”. For each trading post we have y agents that buys and sells securities, attempting to out perform the market relative to all others agents;

The Survival of the fittest will drive the best Aston Martin…or more fittingly, in our case,  relegated to the highest performing processing unit!!

A “Post Agent” will monitor the performance of all agents during a fixed period of time, most likely proportional to the trading horizon but not necessarily. At the end of that fixed period the “Post Agent” will rank the agents in terms of market performance. The top performer is left to “his” own business; he is the “cock of the walk” for the day. The bottom performer is “fired”, well actually a little worse, kill -9. More interestingly the “Post Agents” then are responsible to become genetic scientists and mutate the remaining agents in different degrees dependant on their ranking; the over-performers mutate less then the under-performers. This genetic mutation can be implemented by randomly adjusting selected neural connections (Synapses) which will change the disposition of the agent and “may” accelerate the agents adaptivity to sudden market changes. This mutation method is crucial in the success of the evolution. Mutation may also create even poorer performers, but the algorithm of selection is based on survival of the fittest, so it should converge to the dominate spices (Oh yea, Intelligent Agent).

The computational scale and implementation of just one trading room is challenging and probably was not even possible only 1 or 2 years ago. Just the market data alone in terms of level II historical quotes were not available; and even if they were available to store them would be prohibitively expensive. Technologiclly, things have changed and now we have more of the enabling technologies we require.

Let’s look at what would make up a virtual trading room; (i) Many agents acting as traders (ii) several different strategies being implemented by the traders, like pairs, SUE and so on, (iIi) different time horizons for each strategy, (iv) several trading agents for each horizon and (v) and a Post Agent. To be modest, lets say we are using 10 strategies with 1min, 5min, 15min, 30min, 1hour, 2hour, 4, hour and 6 1/2 hour horizons, and we have 10 agents per post. This is just for ONE symbol, not even the entire NASDAQ. The scale becomes massively complex.

Computationally this will be very intense. but with advances in computing and the ability to capture and process massive volumes of meaningful data we have never had a better opportunity. We never before have had the processing power to analysis such a thing. This in conjunction with the advances in computational methods, we have been recently equipped to examine financial data in real-time and more efficiently than anytime previously. With the convergence of four advanced and diverse fields of; (i) model-driven trading, (ii) computational intelligence, (iii) the availability of high frequency market data, and (iv) the evolution of enabling technologies; such as available 64-bit processors, high performance data managers and grid computing we can attemp to model this. 

These rooms will be possible and will be able to analysis the entire NASDAQ cash equity market by loading and committing inhomogeneous time-series market data into cache memory. The market data can then be applied to continuously adaptive and biologically-inspired intelligent agents that will conduct high speed pattern recognition. The resultant patterns will indicate market anomalies and will form stylized facts that in turn can be used to supply a paradigm for model-driven trading. Because of the technology barriers to entry and a high level of domain specific knowledge required the method described here has not been attempted by any known large non-bank entities and is truly ground breaking.

More to Come.

Computational Intelligence has promised many things over the last three decades; automated stock picking, portfolio optimization, neural prosthesis, predictive models for complex systems and many more. To say the very least, these methods have come up short on all fronts. There are furious debates in academia why this is so, I’m only concerned with moving this field forward and delivery some of the computational scalability these methods show in theory. So instead of tackling all the different reasons why they do not deliver theoretical scale, I’m going to concentrate on some obvious whys how to improve these methods.

I have done a lot of work with the Self-organizing Kohonen Feature map (SOM); which is a neural network that resembles the way in which the visual cortex self-organizes the features it is presented by the visual system. These neural networks have proven to be very useful in simulation mode or low data frequency. I initially used the computational method to reverse engineer 500 KLOC of COBOL code into and object-oriented representation for the European Space Agency. The system performed extremely well and recognized 80% of the objects that human engineers agreed to. But it was very slow. And what I want to do now needs high performance: the analysis of Level II quotes in real time for the full NASDAQ Market.

One of the fundamental problems with computational intelligence, and neural networks in general, is that they gain almost all there scale from being massively parallel. The ironic bit about this is we have spent almost all of our research time on neural network topology, learning methods and applications. And relegated experimental platforms to what we call Artificial Neural Networks; which is where we transform highly parallel computations into linear computations so the instructions can be “corralled” through a single pipe on a processor (maybe two if you’re lucky). Transforming what 4 billion neurons do simultaneously into a purposely-built linear processor is counter intuitive. And the scale required by the SOM will never be reached to do anything meaningful in real-time in this manner. Attempts have been made to build purposely-build parallel machines with very simple processing units (e.g. Thinking Machines) but this approach failed seemingly due to the cost of the machine and the limited of use. Hybrid approaches are now being explored that use simpler micro-controllers as processing units but this approach is still expensive to get to scale. At the other end of the scale is grid computing where you use a grid of many fully functional, sophisticated processors. To simulate a sizable neural network using a grid, the grid would need to be unreasonable massive and very expensive.

I proposed to a colleague, Damien Morton a highly motivated and innovative consultant, that what I really need is an “out of the box” approach for simulating a neural network that would at least get me an order of magnitude performance over the main processing unit of any machine. This type of performance would get me close to analyzing real-time Level II Quotes.

Damien Morton, a highly motivated and innovative consultant living in Australia, has been the sole implementer of the SOM on the GPU and has been key in the demonstration and theory of this approach.

To Be Continued…

Advances in computing have profoundly changed our society. It has provided us with the ability to capture and process massive volumes of meaningful data. We never before have had the amount of financial data available for analysis nor have had the processing power to analysis a complete market in real-time. This in conjunction with the advances in computational methods, we have been recently equipped to examine financial data in real-time and more efficiently than anytime previously.

It is proposed that thier is a large scientific and commercial relevance exposed as a result of the convergence of four advanced and diverse fields of; (i) model-driven trading, (ii) computational intelligence, (iii) the availability of high frequency market data, and (iv) the evolution of enabling technologies; such as available 64-bit processors, high performance data managers and grid computing.

We sould be able demonstrate the unique power of this technology convergence by analyzing quote depth, which is still not commercially available in historic form, in real-time and identifying important non-seasonal patterns. One can examine the BID-ASK depth of the NASDAQ cash equity market by loading and committing inhomogeneous time-series market data into cache memory. By applying the dataset to a continuously adaptive and biologically-inspired computational method high speed pattern recognition can be conducted. The resultant identified patterns should indicate market anomalies and will form stylized facts that in turn can be used to supply a paradigm for model-driven trading. Because of the technology barriers to entry and a high level of domain specific knowledge required the method described here has not been attempted by any known large non-bank entities and is truly ground breaking.