FIGURE 17.7 PREDICTED SQUARED ERROR MODELING CRITERION. THE PSE PRODUCES ROBUST MODELS THAT WORK WELL WITH NOISY DATA.

Model Performance Error

Increasing Model Complexity

with the best (i.e., least) score is selected as the best for a particular database. The PSE performs a trade-off between network complexity and accuracy to find the simplest network that best models training and independent data. It gives an analytic estimate of the network for independent data. The PSE is:

PSE = FSE + KP = PSE + CPM [(2K/N) sp2]

where

PSE is the fitting squared error of the network on the training data

KP penalizes more complex netwotks, as they ate mote likely to ovetfit training

data and therefore not perform well on independent data

CPM is a Complexity Penalty Multiplier used to vary the emphasis of the KP term

K\s the total number of network coefficients in the network model

Wis the number of training observations

s2 is an a priori estimate of the optimal models error variance

The PSE produces networks that avoid modeling noise and overfitting training data. The network synthesis process begins at the left of the PSE curve shown in Figure 17.7. As the complexity of hypothesized networks increases, the PSE of those

networks decreases until the network with the minimum PSE is found. The learning process ends when certain "stopping criteria" are met (see Figure 17.7). These criteria include heuristics that recognize when the learning process is taking place on the upward slope of the PSE curve, indicating the best network has already been found.

Statistical Network Advantages

While Statistical Networks are parametric at the node level, the hypothesis heuristics and modeling criterion at the network level create an automated nonpara-metric process. Therefore, the modeler is not required to be an integral part of the learning algorithm as is required by other approaches. This allows the modeler to focus limited resources on other issues, such as data collection, problem analysis, approach design, model evaluation, and trading system development. Compared with traditional neural network technology, Statistical Networks excel at estimating continuous parameters and are much more practical to develop. Because the process is nonparametric, resulting models generally outperform those developed with linear regression.

Example of a Statistical Network Trading Application

To demonstrate the application of Statistical Networks data mining to market modeling, we chose to model daily price and volume data from the Dow Jones 30 Industrials (DJIA) as of January 31, 1997. We used High, Low, Open, Close, and Volume data from the period January 1, 1987, to January 31, 1997, which includes 2,548 trading days. Our goal was to create a model that accurately produces Buy and Sell indicators.

Technical Indicator Descriptions

One of the distinct advantages of Statistical Networks is that inputs that do not provide useful information for modeling the output variables will not be used in the final network produced by the Statistical Network learning algorithm. This ontogenic characteristic allows considerable freedom in selecting input variables; it allows one to include any and all variables that may contain useful information. The Statistical Network learning algorithm will automatically determine which variables should be used, and in what way.

For this problem, we chose a diverse set of technical indicators.10 Each is a function of Open, High, Low, Close, and/or Volume data. We did not use indicators that are functions of broad market indicators such as indices, new Highs/Lows, Put/Call ratios, and Up/Down Volume.

Each technical indicator is useful for characterizing certain market characteristics. The challenge is determining how to combine the many different characterizations

Table 17.1 Technical indicator descriptions

Indicator Name Abbreviation Time Windows

Open, High, Low, Close, Volume Open, High, Low, Close, Vol. None Description

Daily Open, High, Low, and Close prices, and the trading Volume of the issue on a particular day. Accumulationion/Distribution Accumulation/Distribution None

Description

A cumulative momentum indicator which associates changes in price and volume.

Average True Range TrueRangeXX 5, 10, 14, 20, 30, 60, 90, 180

Description

The moving window average (typically 14 days) of the True Range, providing a measure of volatility. Chaikin Oscillator ChaikinOscXXl-XX2 3/10,5/10,3/15, 10/30, 10/45,

30/90

Description

An oscillator based on a function of two exponential moving averages of the Accumulation/Distribution indicator.

Chaikins Volatility ChaikinVolatilityXXl-XX2 3/10, 3/15, 5/10, 10/20, 10/30,

10/45, 30/90

Description

A quantification of the spread between High and Low price, involving a function of the percentage

change over a time period (Xl) of a moving average of period (X2).

Ease of Movement EaseofMovement None

Description

Characterizes the relationship between price and volume changes; showing how much volume is required to move price.

Exponential Moving Average ExponMWAXXX 5, 9, 12, 14, 20, 21, 26, 30, 45, 90

Description

A moving average that places more emphasis on recent prices.

Negative Volume Index NegVolIndex None

Description

Indicates when volume decreases, presumes "smart money" takes positions when volume decreases. On Balance Volume OnBalanceVolume None

Description

A momentum indicator relating price and volume change.

Positive Volume Index PosVolIndex None

Description

Indicates when volume increases, premised on the hypothesis that the "crowd" takes positions when volume increases.

Price Oscillator PriceOscXXl-XX2 10/30, 12/26