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59 Spectral Anafym-How to Do It and WhatltMeans 185 By replacing "A" and "B" in yoiir basic equation with the corresponding values you have just derived, you tablish the equation of the best-fitting straight line to your original data points. Now you may select any two values of "t" that you wish, put them one at a time into your equation and solve for the corresponding "oj." This gives you two points to plot on the graph of the original data. Draw a straight Une through them and see for yourself how well your best-fit line describes your data! HOW TO USE OTHER KINDS OF CURVE FTmNG You can find a way in the references to fit nearly any kind of curve you wish through data. However, two additional kinds of fits will handle 99% of all your market research work. Each of these requires somewhat more extensive arithmetic manipulation than that used for the straight-line fit, so the basic technique is located m the Appendix. Here we will discuss the need and use of these methods. You recall that stock price data spacing became a design parameter for numerical filters. This means that you will probably find yourself faced from time to time with a situation like tills; • You have designed one filter using a given data spacing. The filter output then has this spacing also, say five weeks. • You have designed another filter using a different data spacing. Lets say this one is three weeks. • You desire to compare directly {or sum, or difference, or otherwise operate with) the outputs of the two filters. But the outputs will not compare directly because of the difference in the spacing of points where the values of each are known. You can solve this problem by use of curve fitting techniques. What you must do is to fit a section of a curve such as a parabola through each possible consecutive set of three filter output data points. The resulting equations can then be solved to give you "in-between" values for both filter outputs which are associated vrith common times, and can therefore be directly compared. For the charts m this book, all filter results have been interpolated in this manner down to a common interval of one week. The technique for doing this you will find in the Appendix. The third exceptionally useful data-fitting technique derives its utility from the nature of the results you get in analyzing stock price data. This is the Prony method of fitting curves to sine waves. The application Is obvious in the analysis of filter results to determine objectively the frequency, amplitude, and phase of resulting sine waves. This technique is also described in the Appendix. SUMMARIZING NUMERICAL ANALYSIS You now have at hand, or know where to go to get, the basic tools you need to research stock price data from the frequency spectrum standpoint. There are many
other powerful aids available to you through numerical analysis, and as you pursue the references you will start to see their applicability to your own special problems. As you dig further into this field you should bear in mind the following: • There are a number of ways in which you can analyze "spaced" or "sampled" data (aich as stock prices) that can get you into trouble regarding conclusions. Always search the references for these stumbling blocks before applying a new method. • Fourier analysis is a powerful tool for stock market research. However, the results achieved should always be verified and expanded by other ectral analysis methods before conclusive decisions are reached. • Digital or numerical filters are a natural next step in the spectral analysis process. • The disciplines of statistical analysis and the methods of curve fitting provide additional tools with which to work. • The tools of numerical analysis are widely applied at universities and research institutes to help find solutions to a great variety of problems. They do not appear to have been used with equal vigor in the analysis of stock price motions. Why dont you try them for yoursdf-perhaps it will make the "competitive edge" difference youve been looking for in your stock market operations!
APPENDICES appendix one appendix two The Not-To-Be-Expected "Order" of Spectral Re(at nshfp$ in Stock Price Data Extension of "Average** Results to Individual Issues appendix three The Source and Nature of Transaction Interval Effects appendix four Frequency Response Characteristics of a Centered Moving Average appendix five Parabolic Interpolation appendix six Trigonometric Curve Fitting
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