Cycle Analytics for Traders, + Downloadable Software : Advanced Technical Trading Concepts by John F Ehlers 2013, Hardcover for sale online

Band-pass filters would pass only cycle components centered at the critical cycle period. Band-stop filters would reject only cycle components also centered at the critical cycle period. If that is the only term used in the filter, the filter is said to be nonrecursive.

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Low-pass filters are data smoothers that remove the higher-frequency jitter in the input data that often makes the data hard to interpret. The penalty traders pay for this smoothing is the lag introduced in the transfer response. Though technical in nature, Cycle Analytics for Traders emphasizes simplicity rather than mathematical purity, taking a pragmatic real-world approach to attaining effective trading results. It allows traders to think of indicators and trading strategies in the frequency domain as well as their motions in the time domain, letting them select the most efficient filter lengths for the job at hand. One of the most important filter characteristics to a trader is how much lag the filter introduces at the output relative to the input. A nonrecursive filter whose coefficients are symmetrical about the center of the filter ­always has a lag equal to the degree of the filter divided by two.

• Additionally, market cycles are ephemeral and are often buried in pure noise.
• By thinking in terms of the transfer responses, you will easily make the transition between filter theory and programming the filters in your trading platform.
• The horizontal axis is plotted in terms of frequency rather than the cycle period that is most familiar to traders.
• The interesting thing about this equation is that we have now written the transfer response as a generalized algebraic polynomial.

Cycle Analytics for Traders: Advanced Technical Trading Concepts

EasyLanguage computer code is used to calculate and display the indicators. From my viewpoint, Easy Language is just a dialect of Pascal with key words for trading. The important conclusion from this discussion is that we can think of the transfer response with equal validity in the time domain or in the frequency domain. SMA filters are a special case of moving average filters where all the filter coefficients have the same value.

■ Generalized Filters

However, it is much more efficient to ­create the band-pass filter response simply by selecting the proper ­coefficients in ­Equation 1-3. This equation can be true only when the frequency is half the sampling frequency. Half the sampling frequency is the highest frequency that is allowable in sampled data systems without aliasing, and is called the Nyquist frequency. In our case, the sampling is done uniformly at once per bar, so the highest possible frequency we can filter is 0.5 cycles per bar, or a period of two bars.

We can see the frequency characteristic of the transfer response by starting with a five-element SMA and then generalizing. 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. A “file MD5” is a hash that gets computed from the file contents, and is reasonably unique based on that content. All shadow libraries that we have indexed on here primarily use MD5s to identify files.

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In addition, you will find that the responses in the time domain and in the frequency domain are intimately connected. When designing filters for trading, it is beneficial to consider the response in both of these domains. It is important to remember that no filter is predictive—filter responses are computed on the basis of historical data samples. It is most convenient to consider filters as stonewall filters that have only a pass band and a stop band with the boundary between them located at a critical cycle period.

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.

• The descriptions are written for understanding at several different levels.
• Half the sampling frequency is the highest frequency that is allowable in sampled data systems without aliasing, and is called the Nyquist frequency.
• One of the most important filter characteristics to a trader is how much lag the filter introduces at the output relative to the input.

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The second part, the denominator term, consists of previously computed values of the output. Filters using any previously computed values of the output are said to be recursive. The distinction is important because it is difficult to create recursive filters in some computer languages used for trading. Parenthetically, the coefficient a0 is usually unity to keep things simple.

One of the first realizations that a trader must make is that cycles cannot be the basis of trades all the time. Sometimes the cycle swings are swamped by trends, and it is folly to try to fight the trend. However, the cyclic swings can be helpful to know when to buy on a dip in the direction of the trend. This equation completely describes the transfer response of any filter. The only thing that differentiates one filter from another is the selection of the coefficients of the polynomials. It is immediately apparent that the more fancy and complex the filter becomes, the more input data is required.

Rather than simply using cycle analytics on blind faith, this book explores and explains the how and why of cycles. Cycles are unique because they are one of the few characteristics of market data that can be scientifically measured. In the most general sense, there is a triple infinity of parameters–period, phase, and amplitude–that must be identified simultaneously to completely describe the cycles. Additionally, market cycles are ephemeral and are often buried in pure noise.

The equality of the exponential expressions and the sine equivalent will be recognized by readers familiar with complex variables as DeMoivre's theorem. For information about the various datasets that we have compiled, see the Datasets page. When we plot the response of the four-element SMA as a function of frequency in cycle analytics for traders Figure 1.1, we see that we not only have a zero at the Nyquist frequency, but also at a frequency of 0.25.

This is really bad for filters used in trading because using more data means the filter necessarily has more lag. Minimizing lag in trading filters is almost more important than the smoothing that is realized by using the filter. Therefore, filters used for trading best use a relatively small amount of input data and should be not be complex. In this chapter you will find the difference between nonrecursive filters and recursive filters, and combinations of the two, enabling you to select the best filter for each application.

For ­example, a nonrecursive filter of degree six will have a three-bar delay. Since lag is very important, and since lag is directly related to filter degree, filters used for trading most generally are simple and are of low degree. Further, that delay will be exactly half the degree of the transfer response polynomial. The horizontal axis is plotted in terms of frequency rather than the cycle period that is most familiar to traders. Frequency and period have a reciprocal relationship, so a frequency of 0.25 cycles per bar corresponds to a four-bar period.