The output divided by the input is the transfer response of the system. It is this transfer response that describes the action of the system. The concepts are presented so they can be understood with only a background in algebra. The writing style in the book is intentionally terse so the reader doesn’t need to wade through a mountain of words to find the ideas being presented.
The concept of thinking of how a filter works in the frequency domain as well as how it works in the time domain is central to the understanding of the indicators that will be developed. Low frequencies near zero are passed from input to output with little or no attenuation. Since higher frequencies are blocked from being passed to the output, the SMA is a type of low-pass filter—passing low frequencies and blocking higher frequencies.
- The distinction is important because it is difficult to create recursive filters in some computer languages used for trading.
- Figure 1.1 shows that there are zeros in the filter transfer response in the frequency domain as well as in the time domain.
- When designing filters for trading, it is beneficial to consider the response in both of these domains.
- With this practical and informative book as a guide, any trader can master cycle analytics, letting statistics and science light the way to long-term trading success.
Equation 1-7 shows that the zero in the transfer response occurs exactly at the Nyquist frequency. We have succeeded in completely canceling out the highest possible frequency in the four-bar SMA. In this case, the roots of the polynomial are called the poles of the transfer response because a zero in the denominator of the transfer response causes the transfer response to go to infinity at that point. One can visualize the transfer response as the canvas of a circus tent in the context of complex numbers, and the poles in the transfer response are analogous to the tent poles. While it is possible to choose coefficients that cause the transfer function to blow up, frequencies are constrained to be real numbers, and therefore it is relatively easy to avoid the complex pole locations. In this case, the higher frequencies are passed, and the lower frequencies are severely attenuated by the filter.
Book Description
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.
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.
- Band-pass filters would pass only cycle components centered at the critical cycle period.
- The equality of the exponential expressions and the sine equivalent will be recognized by readers familiar with complex variables as DeMoivre’s theorem.
- 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.
- Input data are supplied to the system, and the system provides the resultant as an output.
Markets Served
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 rather than to use the trading tools on blind faith. CyCycle 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. The descriptions are written for understanding at several different levels. Traders with little mathematical background will be able to assess general market conditions to their advantage. More technically advanced traders will be able to create indicators and strategies that automatically adapt to measured market conditions by using combinations of computer code that are described.
■ 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.
Advanced Technical Trading Concepts ·
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.
Since trends can be viewed as pieces of a very long cycle, a high-pass filter is basically a detrender because the low-trend frequencies are rejected in its transfer response. Equation 1-12 is exactly the equation for an exponential moving average (EMA). Note that the sum of all of the coefficients on the right-hand side of Equation 1-11 sum to 1 so that the filter has no noise gain. 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. Cycle Analytics for Traders shows traders how to approach trading as a statistical process that should be judged from the long-term view, rather than a small sample set of just a few trades—no matter how profitable those few are. With this practical and informative book as a guide, any trader can master cycle analytics, letting statistics and science light the way to long-term trading success.
The vertical axis is the amplitude of the output relative to the amplitude of the input data in decibels. Figure 1.1 shows that there are zeros in the filter transfer response in the frequency domain as well as in the time domain. Cycles are a unique kind of trading analytics, being one of the few types of market data that can be accurately measured. But understanding what the cycles mean and which trades to make based on them is an extremely complex process. Cycle Analytics for Traders is a technical resource for self-directed traders that explains the scientific underpinnings of the filters and indicators used to make effective and profitable trading decisions.
About this book
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.
■ Nonrecursive Filters
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.
The interesting thing about this equation is that we have now written the transfer response as a generalized algebraic polynomial. Input data are supplied to the system, and the system provides the resultant as an output. However, the system between the input and cycle analytics for traders output can be as complex as desired.
