Momentum, Direction, and Divergence

by William Blau

Quick Summary

William Blau presents a mathematically rigorous framework for constructing momentum indicators through double and triple smoothing of price data using exponential moving averages. The book develops original oscillators and signal lines for measuring trend direction, momentum strength, and divergence, providing precise formulas suitable for programming into trading systems. This is a technical indicators construction manual rather than a trading strategy book.

Detailed Summary

William Blau's "Momentum, Direction, and Divergence," part of the Wiley Trading series edited by Perry J. Kaufman, is a specialized work on the mathematical construction of smoothed momentum indicators. The book's central innovation is the systematic application of double and triple exponential smoothing to raw momentum data, producing indicators with superior signal-to-noise characteristics compared to conventional single-smoothed oscillators.

Blau begins by defining momentum as the difference between today's closing price and the closing price q periods ago. He then demonstrates how applying successive rounds of exponential moving average smoothing to this raw momentum reduces noise while preserving the essential directional signal. The double-smoothed momentum and triple-smoothed momentum indicators serve as the building blocks for all subsequent constructions in the book.

The True Strength Index (TSI) normalizes the double-smoothed momentum by dividing it by double-smoothed absolute momentum, producing a bounded oscillator that measures the percentage of total momentum that is directional. Blau shows how to add signal lines (exponential smoothing of the TSI itself) and construct histogram divergence indicators from the difference between the TSI and its signal.

The Ergodic concept extends these ideas to candlestick-based momentum, using the difference between close and open prices. Blau develops ergodic oscillators and their associated signal lines and histograms, creating a family of interrelated indicators.

The book also addresses stochastic indicators, applying the double-smoothing framework to George Lane's original stochastic oscillator to create smoothed stochastic versions with reduced whipsaw. Blau further develops the concept of the stochastic applied to the TSI, creating a second-order indicator that measures whether the TSI itself is near the top or bottom of its recent range.

Throughout, Blau provides exact mathematical formulas and brief pseudocode suitable for implementation in TradeStation, MetaStock, or any programming environment. Charts illustrate each indicator applied to real market data, showing how the smoothed versions filter out noise while still responding promptly to genuine trend changes.

This is not a book for casual readers. It demands comfort with mathematical notation and iterative computational procedures. Its value lies in providing a principled, parameterizable framework for indicator construction that a systematic trader can customize and integrate into quantitative trading systems.