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3

APPENDICES

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1. THE NOT-TO-BE-EXPECTED "ORDER" OF SPECTRAL RELATIONSHIPS IN STOCK PRICE DATA .............................188

The Implications of Fourier Analysis of Stock Prices 188

Course Frequency Structure 190

Fine Frequency Structure 190

Amplitude-Frequency Relationships 191

The Use of Comb Filters 191

The Variables Involved 196

Best EstinfKte of Spectral Line Spacing 196

The Line Spectral Model 199

II. EXTENSION OF "AVERAGE" RESULTS TO INDIVIDUAL ISSUES ... .201 A Basis For the Principle of Commonality 201 Spectral Signatures, Fundamentals, and Time Synchroniration 201

. THE SOURCE AND NATURE OF TRANSACTION INTERVAL

EFFECTS ............................................. 204

Theoretical Yield-Rate Maximums vs. Transaction Interval 204

The Impact of Compounding 204

The Effect of Sinusoidal Rate Summation 206

IV. FREQUENCY RESPONSE CHARACTERISTICS OF A CENTERED

MOVING AVERAGE .......................................207

Response Derivation 207 Response Characteristics 207 Application Implications 207

11. SPECTRAL ANALYSIS - HOW TO DO IT AND WHAT IT MEANS ......168

Why Numerical Analysis 169

The Meaning of a Frequency Spectrum 169

How to Do Fourier Analysis 171

Assembling Your Data 171

Separating Your Data Into Two Sequences 172

Determining the Frequencies in Your Analysis 172

Now Compute the Corresponding Amplitudes 173

How to Get Composite Amplitudes 175

The Kind of Results You Can Expect 175

How Numerical Filters Can Help You 175

VWiat You Must Know About Filter Operation 176

The Part of "Weits" in Numerical Filters 177

How to Design Your Own Numerical Filters 178

Applying Your Numerical Filter to Stock Prices 182

Take Advan tage of Curve Fitting 183

Fit Your Data With a Straight line 184

How to Use Other Kinds of Curve Fitting 185

Summarizing Numerical Analy sis 185



Response of the Inverse Centered Moving Average 210

V. PARABOUC INTERPOLATION ................................212

Three-Point Interpolation 212 Equation Derivation 213

VI. TRIGONOMETRIC CURVE FITTING ...........................215

Generalized Least-Square-Error Methods 215

Solving for Frequency 216

Computing Amplitudes 217

Determining Composity Amplitudes and Phases 217

BIBLIOGRAPHY ...........................................218

INDEX ....................................................220



List of illustrations

Figure I-l. Typical Weekly "High-Low" Chart • 24

Figure 1-2. Ideal Transaction Timing 25

Figure II-l. The Magnitude-Duration Relationship • 34

Figure II-2. Price Fluctuations in The Dow Average • 36

Figure II-3. A Constant-Width Envelope: The Starting Point in

Observational Analysis • 37

Figure IW. Nesting Envelopes • 39

Figure II-5. Another Envelope Technique • 40

Figure 11-6. An Example of Short-Duration Cyclicality • 41

Figure II-7. The Longer Duration Cycles Require Monthly Data • 42

Figure II-8. The Infamous "Bull-Bear" Cycle • 43

Figure II-9. The Time-Persistence of Cyclicality • 44

Figure IMO. The Principle of Variation at Work • 45

Figure -1 ]. Cyclicality and Numerical Analysis • 46

Figure 11-12. Before Envelope Analysis • 46

Figure II-l 3. Envelopes and Standard Packaging • 47

Figure 11-14. Nesting Down • 47

Figure 11-15. Nesting Up 48

Figure 11-16. Commonality and Standard Packaging • 49

Figure 111-1. Channel Formation • 53

Figure III-2. Adding Another Component • 54

Figure 1-3. The Summation Principle Applied • 54

Figure III-4. How Head and Shoulder Patterns Form • 55

Figure 1II-5. True Channels Are Curvilinear • 56

Figure -6. The Effect of Cycle Timing Change • 57

Figure III-7. How Double Tops (and Bottoms) Are Formed 58

Figure 1 -8. How Triangles Come About • 58

Figure -9. Triangle Analysis in Perkin-EImer • 60

Figure 111-10. Moving Averages Versus Time-Span - 63

Figure III-l 1. "Centering" a Moving Average 66

Figure IV-1. Plotting Helps - But Not Enough • 73

Figure IV-2. A First Envelope Adds Visibility • 74

Figure IV-3, A Second Envelope Clarifies the Picture Further • 75

Figure IV-4. Rough Prediction Using Envelopes * 76

Figure lV-5. How Resuks Compare With Prediction 77

Figure IV-6. Refining Predictions - By Going to Daily Data • 80



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