Computational Intelligence within Finance

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.