This is a technical resource book written for self-directed traders who want to understand the scientific underpinnings of the filters and indicators they use in their trading decisions. There is plenty of theory and years of research behind the unique solutions provided in this book, but the emphasis is on simplicity rather than mathematical purity. In particular, the solutions use a pragmatic approach to attain effective trading results. Cycle Analytics for Traders will allow traders to think of their indicators and trading strategies in the frequency domain as well as their motions in the time domain. This new viewpoint will enable them to select the most efficient filter lengths for the job at hand.

• Shows an awareness of Spectral Dilation, and how to eliminate it or to use it to your advantage
• Discusses how to use Automatic Gain Control (AGC) to normalize indicator amplitude swings
• Explains thinking of prices in the frequency domain as well as in the time domain
• Creates an awareness that all indicators are statistical rather than absolute, as implied by their single line displays
• Sheds light on several advanced cookbook filters
• Showcases new advanced indicators like the Even Better Sinewave and Decycler Indicators
• Explains how to use transforms to improve the display and interpretation of indicators

John F. Ehlers worked as an electrical engineer at one of the largest aerospace companies in the industry before retiring as a senior engineering fellow. A graduate of the University of Missouri, he has been a private trader since 1976, specializing in technical analysis. The discoverer of Maximum Entropy Spectrum Analysis, he writes extensively on technical trading and speaks internationally on the subject.

Preface ix

About the Author xiii

Chapter 1 Unified Filter Theory 1

Transfer Response 1

Nonrecursive Filters 3

Recursive Filters 8

Generalized Filters 10

Programming the Filters 11

Wave Amplitude, Power, and Decibels (dB) 13

Key Points to Remember 13

Chapter 2 SMAs, EMAs, or Other? 15

Simple Moving Averages (SMAs) 15

Exponential Moving Averages (EMAs) 18

Weighted Moving Averages (WMAs) 21

Median Filter 22

Key Points to Remember 23

Chapter 3 Smoothing Filters on Steroids 25

Nonrecursive Filters 25

Modified Simple Moving Averages 29

Modified Least-Squares Quadratics 30

SuperSmoother 31

SuperSmoother Filter Applications 34

Key Points to Remember 36

Chapter 4 Decyclers 39

Decycler Construction 39

Decycler Application 41

Decycler Oscillator 43

Key Points to Remember 45

Chapter 5 Band-Pass Filters 47

Band-Pass Filter 47

Band-Pass Filter Q 51

Automatic Gain Control (AGC) 54

Spectral Dilation Removal 56

Band-Pass Filter 56

Measuring the Cycle Period 58

Key Points to Remember 61

Chapter 6 Market Structure and the Hurst Coefficient 63

Fractal Dimension 65

Computing the Hurst Coefficient 67

The Hurst Coefficient in Action 68

Drunkard’s Walk Hypothesis for Market Structure 70

Key Points to Remember 74

Chapter 7 Spectral Dilation 77

Frequency Content of Indicator Outputs 77

Roofing Filter as an Indicator 80

Impact of Spectral Dilation on

Conventional Indicators 83

Key Points to Remember 88

Chapter 8 Autocorrelation 91

Background 91

Autocorrelation 93

Autocorrelation Periodogram 102

Autocorrelation Reversals 110

Key Points to Remember 113

Chapter 9 Fourier Transforms 115

Spectral Dilation 116

Discrete Fourier Transform (DFT) 117

Key Points to Remember 124

Chapter 10 Comb Filter Spectral Estimates 125

Spectral Dilation 125

Computing a Comb Filter Spectral Estimate 126

Key Points to Remember 133

Chapter 11 Adaptive Filters 135

Adaptive Relative Strength Index (RSI) 135

Adaptive Stochastic Indicator 142

Adaptive CCI (Commodity Channel Index) 147

Adaptive Band-Pass Filter 152

Adaptive Indicator Comparison 157

Key Points to Remember 158

Chapter 12 The Even Better Sinewave Indicator 159

Even Better Sinewave Approach 160

Even Better Sinewave Description 160

Using the Even Better Sinewave Indicator 162

Key Points to Remember 164

Chapter 13 Convolution 165

Theoretical Foundation 165

Heat Map Display 168

Computing Convolution 169

Key Points to Remember 174

Chapter 14 The Hilbert Transformer 175

Analytic Signals 176

Hilbert Transformer Mathematics 177

Computing the Hilbert Transformer 181

The Hilbert Transformer Indicator 183

Using the Hilbert Transformer to

Compute the Dominant Cycle 186

Dual Differentiator 187

Phase Accumulation 189

Homodyne 192

Key Points to Remember 194

Chapter 15 Indicator Transforms 195

Fisher Transform 195

Inverse Fisher Transform 198

Cube Transform 200

Key Points to Remember 202

Chapter 16 SwamiCharts 203

SwamiCharts Overview 204

SwamiCharts RSI 205

SwamiCharts Stochastic 210

Roll Your Own SwamiCharts 216

Key Points to Remember 216

Chapter 17 Swing-Trading Strategies 217

Conventional Wisdom 219

Anticipating the Turning Point 220

Sine Wave Uniqueness 221

Safety Valve 224

Exiting a Trade 225

Stop Loss 225

Evaluating a Trading Strategy 226

Monte Carlo Evaluation 227

Stockspotter.com 228

Key Points to Remember 229

About the Website 231

Index 233