CycleTools for CQG - Overview

Transcription

1 CycleTools for CQG - Overview by Brian R. Bell Introduction Do you want to trade short-term market cycles? Have you ever wished you had a way to measure them, a logical way to trade a cycling market? CycleTools for CQG are state-of-the-art indicators implemented for use on the CQG for Windows platform. These studies are designed to help the user make money regardless of whether the market is trending or cycling, and to help the user stay out when the market is simply wandering. Many of the studies in this package were originally conceived by John Ehlers, worldfamous for his development of the MESA trading software. Some of these have been refined and/or expanded by Brian R. Bell, President of Custom Trading Solutions. Others are the product of Brian R. Bell s own research. CycleTools for CQG indicators can be roughly classified as: Instantaneous frequency measurement, Instantaneous trendlines, Oscillators, Detrenders, Low-lag tracking filters, and Miscellaneous indicators. This overview will examine some of the theoretical basis behind CycleTools for CQG, then each of the groups of indicators will be briefly examined. CycleTools for CQG also includes a number of logical conditions for the trader to use as starting points in creating alerts or building trading systems. Trending and Cycling The basis of CycleTools for CQG is a model of the market in which there is a trending component and a cycling component.[1] Each component may be active or inactive at any time. The market may be trending, cycling, trending and cycling, or neither trending nor cycling. CycleTools for CQG gives the trader tools to help detect these conditions. For example, consider Figure 1. In the earlier part of the chart, the market was clearly in a cycling mode, as indicated by the Cosine Indicator having a nicely formed sine-wave shape over several cycles. Trend-following trading techniques would have gotten chopped to pieces during this time. This would be the time to use oscillator-type indicators for timing entries and exits. The market then broke out of the cycling mode and started a nice tradable up-trend. The bars are colored purple when CycleTools is detecting a trending market. The market stayed above the instantaneous trendline and remained in trending mode for the duration of the upward move. Prices and Signals Most of the indicators in CycleTools for CQG consist of applying signal-analysis techniques and algorithms to a price series. Signal analysis is a mature engineering field, and many techniques and algorithms for estimation, prediction, and noise reduction have been developed. Figure 1 Cycling and trending. In performing these calculations, we often treat a sequence of prices as a signal, such as a radio signal. For this reason I will often refer to the price signal. The price signal is nothing more than a normal series of prices.

2 Instantaneous Frequency Measurement and Dominant Cycle Periods Every cyclical signal has a frequency. The frequency of a cycle is the number of times it recurs in a given period of time. For example, the A below middle C on a piano has a frequency of 440 Hz. This means that the string vibrates though one complete cycle 440 times per second. The reciprocal of frequency is period. The period of a cycle is the amount of time it takes to complete one cycle. Continuing the above example, the period of the note is 1/440 seconds, or approximately 2.3 milliseconds. Most signals are composed of many different frequencies of different strengths, or amplitudes. Spectral analysis is a mathematical technique via which the relative strengths of each frequency present in a signal can be measured. There are many different algorithms for performing spectral analysis. The fast Fourier transform is probably the most well-known. John Ehlers is famous for his development of the MESA trading software package, which implements another spectral analysis techniqe, the maximum-entropy method. Figure 2 shows a typical spectral analysis plot. The horizontal axis is frequency, while the vertical axis the amount of power in the signal at that particular frequency. Thus the term power spectrum is often used to describe this plot. Note how in Figure 2 there is a a peak at frequency f 0. Since there is more power in the signal at this frequency than at any other, we can say that this frequency is the dominant cycle. CycleTools for CQG offers three different algorithms for measuring the period of the dominant cycle. All three were originally described by Mr. Ehlers. It is important to note that these algorithms do not detect the dominant cycle by means of calculating a power spectrum. Instead, two of them analyze the price signal indirectly using the Hilbert transform. The third analyzes the signal directly using techniques drawn from trigonometry. There is a discrepancy in terminology here of which you should be aware. The studies that measure the dominant cycle are all called instantaneous frequency measurement (IFM) studies. In fact, however, the numbers provided by these studies are the periods of the dominant cycle, not the frequency. Of course, given one, the other can always be calculated. Mr. Ehlers presented the studies as IFM studies, and in the interest of continuity, I have decide to retain his terminology in CycleTools for CQG. The basic IFM study was described by Mr. Ehlers in [7]. The other two are described in a paper by Mr. Ehlers that can be found on his Figure 3 - Three different IFM algorithms applied to a sine wave with slowly varying frequency. Figure 2 A typical power-spectrum plot. website [2]. The three different IFM algorithms applied to a sine wave that is slowly decreasing in frequency are shown in Figure 3. Although the three algorithms provide similar results under these conditions, it has been my experience that the IFMCos algorithm generally gives rather different results than the other two when applied to actual market data. 2

3 Instantaneous Trendlines The market may be modeled as a being a combination of a trending component and a cyclic component. (CycleTools for CQG is concerned with detection and analysis of shortterm cycles of 8 to 50 bars in length. Seasonal cycles are not included.) As shown by John Ehlers in [1], applying a simple moving average to a cyclical signal (i.e., a sine wave) will remove the cyclical component of the signal when the period of the moving average is the same as the period of the signal. Thus, if we know the period of the cyclical content in the price signal, we can use a moving average of that same period to remove the cyclical content, leaving only the trending component of the price signal. This is the idea behind Instantaneous Trendlines (ITLs). The ITL studies are used the same way as conventional trendlines. When the market is in trending mode, the ITL can be expected to provide a very smooth line that reflects the trending component of the market. The market will often find support in the area of this line. Depending on the strategy of the trader, this line can also be used for setting stops. CycleTools for CQG offers two different ITL studies. The first is an ITL calculation based on a simple moving average. At each bar, the IFM is calculated, giving the period of the dominant cycle. Then a simple moving average is calculated, using dominant cycle period as its period. The other ITL study is based on an exponential moving average. In 1984, Jack Hutson related the exponential moving average to a simple moving average with the following relationship [7]: α = 2, (1) ( P + 1) where P is the period of the simple moving average and the EMA is calculated as: E i = Pi + ( 1 α ) Ei 1 α. (2) Using (1), this exponential ITL study converts the period of the dominant cycle to an α value to be used in an exponential moving average at each point in the curve. It then calculates the EMA using the equation in (2). Figure 4 The ITL studies. The red curve (top) is an ITL based on the simple moving average; the purple one (bottom) is based on the exponential moving average. Generally, the exponential ITL is much slower than the simple ITL. Figure 4 shows both of the ITL studies in action. Trend Mode Detection Knowing the period of the dominant cycle and using the instantaneous trend line, we can use this information to define when the market is trending. The idea is this. When the market is not trending, we assume that prices will cross over the ITL each half-period of the dominant cycle. If prices haven t crossed over the ITL in this period of time, we say that the market is trending. We can define a trending market to be one in which the prices haven t crossed over the ITL for more than one half-cycle of the dominant period. 3

4 There are two trend mode detection conditions supplied with CycleTools for CQG. One is based on the simple ITL, while the other is based Figure 5 Trendmode detection using the simple ITL. The purple bars indicate that the market is trending, while the dark blue bars indicate a possible cyclical market. poorly. The use of oscillator-type indicators is called for when the market is cycling. CycleTools for CQG provides two oscillators for you to use, the Cosine Indicator and the RawC. Each has different characteristics, suited to different traders. The Cosine Indicator Trading a consolidating market is notoriously difficult. The cosine indicator is a tool that helps the trader time entries and exits in a market that is cycling. A cyclical signal can be represented as a phasor (an arrow) on a two-dimensional plot. As discussed above, the horizontal axis is the real part of the signal and the vertical axis is the imaginary component. As the signal progresses through a cycle, the phasor that represents the signal goes around in a circle. Refer to Figure 7. The angle a is called the phase of the signal. Using the Hilbert transform (discussed below), Figure 6 Trendmode detection using the exponential ITL. The purple bars indicate that the market is trending. Figure 7 A phasor representing a cyclical signal goes counter-clockwise around the origin as the signal makes a complete cycle. The angle a is the phase of the signal. on the slower exponential ITL. Figure 5 and Figure 6 show each of these conditions in practice. Oscillators When the market is in a cycling mode, trendfollowing techniques based on tracking indicators like moving averages will work very the price signal can be separated into its real and imaginary components. These components can then be used to continuously calculate the phase of the signal. CycleTools for CQG includes a phase study, although, like the Hilbert transform, this study is not intended to be used on its own. 4

5 Instead, the phase study is used as input to the Cosine Indicator. The cosine indicator has two curves. The first curve is the cosine of the phase. This curve is a reconstruction of the cyclical part of the price signal. The second curve is also the cosine of the phase, except that it is advanced by some adjustable amount. The CycleTools for CQG Cosine Indicator was inspired by and is largely the same as John Ehlers Sinwave Indicator. The Cosine Indicator is obtained by taking the cosine of a phase quantity that is calculated slightly differently than Mr. Ehlers study. Thus I have chosen to name it the Cosine Indicator rather than the Sinwave Indicator, which is Mr. Ehler s term. As stated above, however, the two indicators are largely similar and serve the same purpose. When the cyclical component of the market is strong, the turning points of the Cosine Indicator can help you time your entries and exits. Crossover points, where the leading curve of the Cosine Indicator crosses above or below the cosine curve, serve as warnings that a turning point is approaching. Figure 8 shows the Cosine Indicator applied to a chart. The blue and red diamonds indicate points where the indicator changed direction. CycleTools for CQG includes the conditions to detect the crossovers and turning points, allowing you to set alerts on these conditions. Figure 9 The RawC indicator applied to 5-tick SP constant-volume-bars. parameter values and find the values that work best for the types of markets you like to trade. I will examine the Cosine Indicator in more depth in another article, explaining some of the ways it can be used and patterns to watch. The RawC Indicator The RawC indicator is a result of my own research, inspired by the work of Mr. Ehlers. The RawC indicator is an oscillator that is actually very useful in both cycling and trending markets. Figure 10 shows a 13-period RawC applied to a daily continuation of dollar index futures. The blue and red squares show buy and sell signals generated by the RawC crossing above 0.5 and below 0.5, respectively. Figure 8 The Cosine Indicator and turning point signals applied to a chart. As with all of the studies included in CycleTools for CQG, I suggest that you experiment with the Figure 10 RawC indicator daily continuation chart of dollar index futures. 5

6 The RawC indicator seems to be very effective on very short-term charts, as well. Figure 9 shows the indicator and signals applied to a 5- tick constant-volume-bar chart of S&P futures. Detrenders Although these studies could be considered oscillators, I have put them in a different category. This is due to their special nature and their usefulness as building blocks in other studies. Before the cyclical content of a signal can be measured and analyzed, the signal must detrended. Detrending is the process of removing any constant value of a signal (the low-frequency components) and leaving only the variable part (the high-frequency components). Many of the conventional oscillators in use today could be considered to be detrenders momentum, rate-of-change, and the plain old oscillator. CycleTools for CQG offers two detrender studies. The first serves as the basis for all of the cyclical analysis algorithms performed in CycleTools for CQG. It is named CY_DetrendedPrices. By supplying appropriate parameter values, this study will calculate momentum, smoothed momentum, a simple moving average oscillator, or the optimal detrending algorithm, discussed below. The second detrending study is the optimal detrender, explained by John Ehlers in [3]. Conventional methods of detrending, such as the momentum study, have poor frequency-response and delay characteristics. For example, using a momentum study with a period of 6 will completely remove cyclical components with a period of 6, 12, or any other multiple of 6! The optimal detrender overcomes these problems, introducing much less distortion in the detrended signal. Low-lag Tracking Indicators CycleTools for CQG includes several low-lag tracking indicators, which can be used in combination with the other indicators. The Zero- Lag Moving Average (ZMA), Zero-Lag Exponential Moving Average (ZEMA), and Optimal Tracking Filter indicators are state-ofthe-art indicators developed by John Ehlers that allow a varying degree of smoothing while introducing very little lag. In addition, CycleTools for CQG includes the Frequency-Adjusted ZMA, another result of my own research. One of my favorite uses for these indicators is to use them as a proxy for price. In most of the indicators that John Ehlers has developed and published in EasyLanguage, he uses the midpoint of the bar (halfway between the high and low) as the price series. This generally yields a smoother price signal than simply using the closing prices. The indicators in CycleTools for CQG, on the other hand, always use the closes when applied to a price series. (This limitation is a result of certain factors in CQG for Windows, not of CycleTools for CQG.) In order to duplicate Mr. Ehlers results, it is necessary to first apply a 1- period moving average that is configured to use the Mid as the input price series. Then the CycleTools for CQG indicator can be applied to the moving average, instead of the prices themselves. Instead of doing this, I prefer to use one of the low-lag tracking indicators applied to the closing prices and then apply the CycleTools for CQG indicators to the low-lag tracking indicator. This results in a greater degree of smoothing, with very little lag introduced. Zero-lag Moving Averages In [7], John Ehlers described a zero-lag moving average, and in [4] he described a zero-lag Figure 11 Zero-lag moving average (ZMA) and zerolag exponential moving average (ZEMA). exponential moving average. Both of these indicators are available in CycleTools for CQG, and are shown in Figure 11. 6

7 Figure 12 The Optimal Tracking Filter Indicator. Optimal Tracking Filter In [4], John Ehlers describes the Optimal Tracking Filter, which is a simplified version of a Kalman filter. CycleTools for CQG includes the Optimal Tracking Filter Indicator, shown in Figure 12. This indicator has excellent abilities to accelerate and catch a large part of a quick market move, yet it will also flatten very quickly in a consolidation to reduce or eliminate whipsaws. Frequency-Adjusted ZMA The Frequency-Adjusted ZMA (FAZMA) is another result of my own research. The FAZMA could be considered another type of instantaneous trendline. This study builds on Ehlers ZMA by continuously adjusting the period of the calculation based on the frequency of the dominant cycle, as measured by the IFM studies within CycleTools for CQG. This technique leads to a superior movingaverage type of study, which tracks trending movements very closely and then slows down to prevent whipsaws when the market consolidates. An example of this behavior is shown in Figure 13. Note how closely the indicator tracks prices throughout the upward move, then slows down when the move is over, preventing whipsaws. Miscellaneous Indicators CycleTools for CQG includes several indicators that aren t easily categorized into any of the Figure 13 The frequency-adjusted ZMA applied to daily bond futures. preceding categories. These are the Hilbert transforms, the signal-to-noise ratio, and the phase indicator. Hilbert Transforms A Hilbert transform is a mathematical transformation used in signal processing applications. It is also sometimes known as a 90-degree phase shifter. The mathematics underlying Hilbert transforms will not be discussed here. The interested (and mathematically inclined) reader may find more information in any good textbook on digital signal processing.[5,6] The Hilbert transform is used in CycleTools for CQG to compute the real and imaginary components of the price signal. Signals are often represented by engineers as phasors in a twodimensional plane (see Figure 7). The horizontal axis represents the real part of the signal, while the vertical axis is the imaginary component. CycleTools for CQG includes three different algorithms for Hilbert transforms. John Ehlers has recently described two different algorithms for computing the Hilbert transform; these are included.[7,8] Additionally, an algorithm described by Charles Rader is included.[9] See the section below on Common Parameters for information on how to select the algorithm you wish to use. 7

8 Figure 14 The three different Hilbert transform algorithms. The three Hilbert transforms give slightly different results, as can be seen in Figure 14. In this figure, all three Hilbert transform algorithms are applied to a sin wave, which has a slowly increasing period (decreasing frequency). In each case, the real part of the signal is drawn in red, while the imaginary part is in blue. The top Hilbert transform study is the algorithm described in [7]. The second one down is the algorithm described in [8], while the bottom one is the Rader algorithm [9]. The Hilbert transform study is not intended to be used on its own. Instead, the Hilbert transform serves as a basis for many other studies in CycleTools for CQG. Whenever a study accepts a parameter named HilbertType, that study uses the Hilbert transform in its calculations. When using these studies, please experiment with the Hilbert algorithms and parameters to see what works best in the types of markets you like to trade. Signal-to-Noise Ratio (SNR) In signal processing, one of the primary considerations is that of detecting a signal in the presence of noise. In the real world, all analog signals are corrupted with some amount of noise. The amount of noise may be very little, or it may be so much as to render the signal useless. Likewise, price signals have a noisy component. If the noise is great enough, the noise will drown-out the signal and technical analysis techniques will break down and stop working. Mr. Ehlers has described a study to calculate the signal-to-noise ratio (SNR).[7] CycleTools for CQG includes a modified version of this indicator, shown in Figure 15. This indicator compares the amplitude of the price signal to the amount of corrupting noise. The high-low range is considered to be noise, while the price signal amplitude is calculated from Hilbert transform real and imaginary components. A horizontal threshold line can be placed on the indicator. When the indicator is above the threshold, the SNR is high enough to allow trading. Otherwise, the noise is overwhelming the signal and the conservative trader might want to stand aside. In the example shown, the noisy market in the left portion of the chart would be difficult to trade. It is exhibiting a very low SNR. More recently, the SNR has improved, making trading easier. Although the experienced trader may not derive much benefit from this indicator in real-time, it Algorithm DetrendType Period1 HilbertType Ehlers March [3] Ehlers May [4] Rader [5] Table 1 Parameter values for studies shown in Figure 14. Figure 15 The Signal-to-Noise Ratio (SNR). 8

9 could prove to be a great help in developing effective scans and trading systems. The Phase Indicator The Phase Indicator is included in CycleTools for CQG as an item of interest, rather than a standalone tool to help you trade. At the same time, there is no group of people on the planet more resourceful than traders, and if you find that you can indeed use this indicator to increase your profits, good for you! The Phase Indicator is the basis for the Cosine Indicator. The Cosine Indicator has two curves the first is simply the cosine of the phase, while the second is the cosine of the phase plus some leading angle. The calculations leading to the Phase Indicator were described by John Ehlers in his May, 2000 article in Technical Analysis of Stocks & Commodities [8]. Figure 16 The phase indicator and the cosine indicator applied to a chart. 9

10 CycleTools for CQG Reference Quick-Reference Table Indicator CQG Study Name CQG Study Abbreviation Cosine CY_Cos CY_Cos Detrended Prices CY_DetrendedPrices CY_Detr Frequency-adjusted ZMA CY_FAZMA CY_FAZM Hilbert Transform CY_Hilbert CY_Hilb Instantaneous Frequency Measurement Basic Algorithm CY_IFM CY_IFM Instantaneous Frequency Measurement Cosine Algorithm CY_IFMCos CY_IFMC Instantaneous Frequency Measurement IQ Algorithm CY_IFMIQ CY_IFMI Instantaneous Trend Line Exponential CY_ITLExp CY_ITLE Instantaneous Trend Line Simple CY_ITLSim CY_ITLS Optimal Detrend CY_OptimalDetrend CY_OptD Optimal Smooth CY_OptimalSmooth CY_OptS Optimal Tracking Filter CY_OTF CY_OTF Phase CY_Phase CY_Phas RawC CY_RawC CY_RawC Signal-to-noise Ratio CY_SNR CY_SNR Zero-lag Exponential Moving Average CY_ZEMA CY_ZEMA Zero-lag Simple Moving Average CY_ZMA CY_ZMA Common Parameters Some parameters are used in many different studies and formulas. These parameters are: DetrendType: When detrended prices may be used as an input, this parameters denotes the type of detrending to be used. The following values are allowed. If a value other than those described here is used, it will be treated as having a value of 1. 0 No detrending performed. 1 Momentum, calculated using a period of Period1. 2 Smoothed momentum. The momentum is calculated using a period of Period1. It is then smoothed with an exponential moving average using a period of Period2. 3 Exponential moving average oscillator. The first moving average is calculated using a period of Period1, the second using a period of Period2. 4 Optimal detrending, as described in [3]. Period1: A floating point value used as described above. Period2: A floating point value used as described above. IFMType: Some studies require a dominant cycle period as an input. In these cases, this parameter denotes the type of instantaneous frequency measurement to be used. The following values are allowed. If a value other than those described here is used, it will be treated as having a value of 1. 1 Basic IFM. 10

11 2 IQ IFM. 3 Cosine IFM. HilbertType: Many of the studies are based on a calculation of the Hilbert transform. There are many algorithms available for this calculation. This parameter denotes the algorithm used in the calculation. The following values are allowed. If a value other than those described here is used, it will be treated as having a value of 1. 1 The Hilbert transform algorithm given by John Ehlers in the March 2000 issue of Technical Analysis of Stocks & Commodities. [7] 2 The Hilbert transform algorithm given by John Ehlers in the May 2000 issue of Technical Analysis of Stocks & Commodities. [8] 3 The Hilbert transform algorithm given by Charles Rader in the November 1984 issue of IEEE Transactions on Aerospace and Electronic Systems. [9] Smooth: This is always a floating-point smoothing constant. It is used as the period of an exponential moving average. The individual descriptions below will explain what it being smoothed. A value of 1.0 indicates no smoothing. A value of 0.0 is not allowed and will cause the study not to display. Offset: The tracking indicators, such as ZMA and OTF, has this parameter, which allows the user to offset the study some number of bars into the future or past. Negative values indicate shifting the curve into the future. This is what is commonly done with displaced moving averages. Positive values shift the curve into the past. Study: CY_Cos The Studies Summary: The cosine indicator. Displays the cosine of the phase of the price signal and the cosine of the phase advanced by some user-settable amount. Abbreviation: CY_Cos^ CY_Cos.Cos^: The cosine of the phase of the price signal. CY_Cos.CosLead^: The cosine of the phase of the price signal plus an amount specified by the Lead parameter. IFMType: See Common Parameters. Smooth: See Common Parameters. Used to smooth the raw period measurement that is an input to the phase calculation. Lead: The amount to add to the phase when the CosLead curve is calculated. A value of 0.78 represents 1/8 of a cycle (45 degrees), 1.57 is equivalent to ¼ of a cycle (90 degrees). Remarks The Hilbert transform calculates the real and imaginary components of the detrended price series. Using these values and the period of the dominant cycle, it is possible to calculate the phase of the signal represented by the prices. This study calculates the cosine of the phase. When the market is in cycle mode, the turns in this value will often closely correspond to the short-term swings in the market. Depending on the amount of lead specified, the crossovers of this study will provide some warning that a turning point is imminent. 11

12 These calculations are optimized for use with DetrendType = 1, Period1 = 6, and HilbertType = 3. Study: CY_Detrended Prices Summary: Detrends a price series by one of several techniques. Abbreviation: CY_Detr^ CY_Detr.DP^: The detrended price series. The calculations for this study are obtained from the user value of the same name. All of the studies in CycleTools for CQG that use the Hilbert transform use these calculations for the initial detrending phase. Study: CY_FAZMA Summary: Plots the frequency-adjusted zero-lag moving average (ZMA). Abbreviation: CY_FAZM^ CY_FAZM.FAZMA^: The frequency-adjusted ZMA. IFMType: See Common Parameters. Offset: See Common Parameters. This is one of my favorite indicators in CycleTools for CQG. When the market makes a move, it is much quicker than the CY_ITLSim study, making it better for catching short, sharp moves. At the same time, it will often go almost dead flat in a consolidating market, sometimes completely above or below the consolidation, minimizing whipsaws. Study: CY_Hilbert Summary: Plots the Hilbert transform of the input signal. Abbreviation: CY_Hilb^ CY_Hilb.Real^: The real component of the transformed signal. CY_Hilb.Imag^: The imaginary component of the transformed signal. IFMType: See Common Parameters. 12

13 The Hilbert transform serves as the basis for all the indicators in CycleTools for CQG that calculate or use the dominant cycle period. The mathematically inclined reader may learn more about it in [5] and [6]. The Hilbert transform is included in study form for educational purposes only I don t believe it is really useful on its own as an indicator. All of the studies in CycleTools for CQG that depend on Hilbert transform values use the user values CY_HilbertReal and CY_HilbertImag. Study: CY_IFM Summary: Basic Instantaneous Frequency Measurement. Abbreviation: CY_IFM^ CY_IFM.IFM^: The period of the dominant cycle of the input. Remarks This study returns the period of the dominant cycle of the input. It is measured as described in [7]. The term instantaneous frequency measurement here is a misnomer, since the study actually measures the period of the dominant cycle, which is the inverse of the frequency. I have retained the original terminology use in John Ehlers article. The raw period measurement is smoothed by an exponential moving average of period smooth. Setting smooth equal to one eliminates the smoothing altogether. Study: CY_IFMCos Summary: Cosine method of Instantaneous Frequency Measurement. Abbreviation: CY_IFMC^ CY_IFMC.IFMCos^: The period of the dominant cycle of the input. 13

14 Remarks This study returns the period of the dominant cycle of the input. It is measured using the cosine technique as described in [2]. The term instantaneous frequency measurement here is a misnomer, since the study actually measures the period of the dominant cycle, which is the inverse of the frequency. I have retained the original terminology use in John Ehlers article. The raw period measurement is smoothed by an exponential moving average of period smooth. Setting smooth equal to one eliminates the smoothing altogether. NOTE: It has been my experience that this study gives very different results than the the other two types of IFM, the basic IFM and IFMIQ algorithms. I will be investigating this in the near future, to determine if there is a problem with the algorithm or the implementation, or if this is just a property of the algorithm. In the meantime, I suggest that you treat the results of this study with caution, unless you see evidence that the results are valid for your particular application. Study: CY_IFMIQ Summary: IQ method of Instantaneous Frequency Measurement. Abbreviation: CY_IFMI^ CY_IFMI.IFM^: The period of the dominant cycle of the input. Remarks This study returns the period of the dominant cycle of the input. It is measured using the IQ technique as described in [2]. The term instantaneous frequency measurement here is a misnomer, since the study actually measures the period of the dominant cycle, which is the inverse of the frequency. I have retained the original terminology use in John Ehlers article. The raw period measurement is smoothed by an exponential moving average of period Smooth. Setting Smooth equal to one eliminates the smoothing altogether. Study: CY_ITLExp Summary: The instantaneous trendline study, calculated using an exponential moving average algorithm. Abbreviation: CY_ITLE^ CY_ITLE.ITL^: The instantaneous trendline. 14

15 This study calculates an exponential moving average of prices, continuously adjusting the moving average parameters based on the instantaneous frequency measurement. At each step, the period of the dominant cycle is converted to an exponential moving average smoothing parameter, then the moving average is calculated using that value. The study parameters allow the user to change the method used to measure the dominant cycle period. This study is generally significantly slower than the CY_ITLSim study. Study: CY_ITLSim Summary: The instantaneous trendline study, calculated using a simple moving average algorithm. Abbreviation: CY_ITLS^ CY_ITLS.ITL^: The instantaneous trendline. This study calculates a simple moving average of prices, continuously adjusting the moving average period based on the instantaneous frequency measurement. At each step, the average of the last n prices is calculated, where n is the period of the dominant cycle. The study parameters allow the user to change the method used to measure the dominant cycle period. This study is generally significantly faster than the CY_ITLExp study, although not as fast as the CY_FAZMA study. Study: CY_OptimalDetrend Summary: Returns the input price series detrended using the optimal detrending algorithm described by John Ehlers in [3]. Abbreviation: CY_OptD^ CY_OptD.Detrend^: The detrended price series. (no parameters) The detrending algorithm used in this study is taken from radar technology, as explained by Mr. Ehlers in [3]. It displays much better frequency characteristics than conventional methods of detrending, such as the simple N-bar momentum function. This indicator is included in displayable form for education purposes only. The real advantage to this algorithm is to use it as a building block for other indicators. For these purposes, use the user value CY_OptimalDetrend. 15

16 The optimal detrending algorithm may be selected for any CycleTools for CQG indicator or function that allows such selection by setting the DetrendType parameter to 4. Study: CY_OptimalSmooth Summary: Returns the input price series smoothed using the optimal smoothing algorithm described by John Ehlers in [3]. Abbreviation: CY_OptS^ CY_OptS.Smooth^: The smoothed price series. (no parameters) The smoothing algorithm used in this study a modified elliptic filter, as explained by Mr. Ehlers in [3]. It displays no more than one bar of lag over the full frequency spectrum. I believe that the real advantage to this algorithm is to use it as a building block for other indicators. For these purposes, use the user value CY_OptimalSmooth. Study: CY_OTF Summary: Plots the optimal tracking filter described by John Ehlers in [4]. Abbreviation: CY_OTF CY_OTF.OTF^: The optimal tracking filter. Smooth: See Common Parameters. Used to smooth the raw OTF calculation. Offset: See Common Parameters. The optimal tracking filter behaves similarly to the CY_FAZMA study, which itself is similar to Kaufman s adaptive moving average. With the Smooth parameter set to appropriate values (start with 0.1 and experiment from there), this indicator shows excellent abilities to catch a very large part of a fast market move and then quickly flatten out, reducing whipsaws in a consolidating market. Study: CY_Phase Summary: Plots the phase of the price signal. Abbreviation: CY_Phas CY_Phas.Phase^: The phase of the price signal. 16

17 Remarks The Hilbert transform calculates the real and imaginary components of the detrended price series. Using these values and the period of the dominant cycle, it is possible to calculate the phase of the signal represented by the prices. The phase calculations are optimized for use with DetrendType = 1 and Period1 = 6. This indicator is included for education purposes only, and is not intended to be used on its own for market analysis. These values are used in calculating the Cosine Indicator. Study: CY_RawC Summary: Plots the RawC indicator. Abbreviation: CY_RawC CY_RawC.RawC^: The RawC indicator. CY_RawC.Signal^: A smoothed (trailing) version of the RawC curve. Smooth: See Common Parameters. Used to calculate the Signal curve. Remarks The RawC calculation is closely related to the Cosine Indicator, in that it is calculated based on Hilbert transform values. A quick estimate of the signal phase is obtained from the Hilbert transform values, then the cosine of this estimate is calculated. Unlike the Cosine Indicator, the RawC will go overbought or oversold and stay there in a trending market. Study: CY_SNR Summary: Plots the signal-to-noise ratio. Abbreviation: CY_SNR CY_SNR.SNR^: The signal-to-noise ratio. The signal-to-noise ratio indicator in CycleTools for CQG is a modified version of the study that John Ehlers revealed in [7]. When the value of the study is high, it indicates that the amplitude of the price signal is large relative to the noise in the signal. The range of the bars is used as a proxy for noise. 17

18 When the SNR ratio is high, it indicates a high level of tradeability for the market. Conversely, when the SNR is low, it indicates that noise is overwhelming the price signal, and trading at that time frame will be more difficult. Study: CY_ZEMA Summary: Plots the zero-lag exponential moving average. Abbreviation: CY_ZEMA CY_ZEMA.ZEMA^: The zero-lag exponential moving average. Period: The ZEMA uses a smoothed estimate of the velocity of the market in its calculations. The velocity is estimated as being equal to the n-bar momentum function, Close Close[n]. This parameter specifies the value of n. Alpha: The smoothing constant of the exponential moving average portion of the calculation. Beta: The smoothing constant used to smooth the velocity estimate. The n-bar momentum is smoothed using an exponential moving average with a constant of Beta. K: A gain factor, used to increase or decrease the effect of the velocity estimate. Offset: See Common Parameters. Remarks John Ehlers described this indicator in [4]. This indicator provides excellent smoothing abilities with very low lag. It is a precursor to the optimal tracking filter. Setting K = 0 results in a normal exponential moving average. Experiment with the parameters. Generally, increasing the value of either K or Beta will increase the fidelity of the indicator (decrease the smoothing). Increasing the value of K beyond 1.0 will cause the indicator to become unstable, leading to overshoots. Study: CY_ZMA Summary: Plots the zero-lag moving average. Abbreviation: CY_ZMA CY_ZMA.ZMA^: The zero-lag moving average. Alpha: The smoothing constant of the exponential moving average. Offset: See Common Parameters. Remarks John Ehlers described this indicator in [7]. It is an exponential moving average with a correction term to reduce the lag. While it doesn t have the fidelity capabilities of the ZEMA, it provides excellent smoothing with very little lag. The Conditions Condition: CY_CosTurnsUp Summary: True when CY_Cos.Cos^ turns up. 18

19 IFMType: See Common Parameters. Smooth: See Common Parameters. Used to smooth the raw period measurement that is an input to the phase calculation. Use this condition to get alerts or mark bars when the Cosine Indicator actually makes an upturn. The condition should only be considered valid when the market is in cycle mode. Condition: CY_CosTurnsDown Summary: True when CY_Cos.Cos^ turns down. IFMType: See Common Parameters. Smooth: See Common Parameters. Used to smooth the raw period measurement that is an input to the phase calculation. Use this condition to get alerts or mark bars when the Cosine Indicator actually makes a downturn. The condition should only be considered valid when the market is in cycle mode. Condition: CY_CosXA Summary: True when CY_Cos.CosLead^ crosses above CY_Cos.Cos^. IFMType: See Common Parameters. Smooth: See Common Parameters. Used to smooth the raw period measurement that is an input to the phase calculation. Lead: The amount to add to the phase when the CosLead curve is calculated. A value of 0.78 represents 1/8 of a cycle (45 degrees), 1.57 is equivalent to ¼ of a cycle (90 degrees). Use this condition to get alerts or mark bars when the Cosine Indicator warns of an upturn. The condition should only be considered valid when the market is in cycle mode. Condition: CY_CosXB Summary: True when CY_Cos.CosLead^ crosses below CY_Cos.Cos^. 19

20 IFMType: See Common Parameters. Smooth: See Common Parameters. Used to smooth the raw period measurement that is an input to the phase calculation. Lead: The amount to add to the phase when the CosLead curve is calculated. A value of 0.78 represents 1/8 of a cycle (45 degrees), 1.57 is equivalent to ¼ of a cycle (90 degrees). Use this condition to get alerts or mark bars when the Cosine Indicator warns of an downturn. The condition should only be considered valid when the market is in cycle mode. Condition: CY_RawCXA Summary: True when CY_RawC.RawC^ crosses above CY_RawC.Signal^. Smooth: See Common Parameters. The Signal curve is the exponential moving average of the RawC curve. The value of this parameter is the smoothing constant of the moving average. Use this condition to get alerts or mark bars when the RawC curve crosses above its moving average. Condition: CY_RawCXALevel Summary: True when CY_RawC.RawC^ crosses above a specified level. Level: The threshold value. Use this condition to get alerts or mark bars when the RawC curve crosses above the specified level. NOTE: There is a bug in some versions of CQG for Windows that prevents the condition CY_RawCXALevel from working properly when the specified threshold is negative. If this is a problem, use the condition CY_RawCXALevelBugFix and specify the absolute value of the threshold. 20

21 Condition: CY_RawCXALevelBugFix Summary: True when CY_RawC.RawC^ crosses above the negative of the specified level. Level: The negative of the threshold value. Use this condition to get alerts or mark bars when the RawC curve crosses above the negative of the specified level. NOTE: There is a bug in some versions of CQG for Windows that prevents the condition CY_RawCXALevel from working properly when the specified threshold is negative. If this is a problem, use the condition CY_RawCXALevelBugFix and specify the absolute value of the threshold. Condition: CY_RawCXB Summary: True when CY_RawC.RawC^ crosses below CY_RawC.Signal^. Smooth: See Common Parameters. The Signal curve is the exponential moving average of the RawC curve. The value of this parameter is the smoothing constant of the moving average. Use this condition to get alerts or mark bars when the RawC curve crosses below its moving average. Condition: CY_RawCXBLevel Summary: True when CY_RawC.RawC^ crosses below a specified level. Level: The threshold value. Use this condition to get alerts or mark bars when the RawC curve crosses below the specified level. NOTE: There is a bug in some versions of CQG for Windows that prevents the condition CY_RawCXBLevel from working properly when the specified threshold is negative. If this is a problem, use the condition CY_RawCXBLevelBugFix and specify the absolute value of the threshold. 21

22 Condition: CY_RawCXBLevelBugFix Summary: True when CY_RawC.RawC^ crosses below the negative of the specified level. Level: The negative of the threshold value. Use this condition to get alerts or mark bars when the RawC curve crosses below the negative of the specified level. NOTE: There is a bug in some versions of CQG for Windows that prevents the condition CY_RawCXBLevel from working properly when the specified threshold is negative. If this is a problem, use the condition CY_RawCXBLevelBugFix and specify the absolute value of the threshold. Condition: CY_TrendmodeExp Summary: True when the market is in trendmode, based on the exponential ITL. IFMType: See Common Parameters. Smooth: See Common Parameters. Used to smooth the raw IFM measurement. Use this condition to get alerts or mark bars when the market enters trendmode. When the market is cycling, we expect it to cross over the instantaneous trendline every half-period of the dominant cycle. Thus we can define the market to be in trendmode when the closing price has not crossed over the ITL for a period of more than half of the dominant cycle period. This condition uses the exponential ITL. Condition: CY_TrendmodeSim Summary: True when the market is in trendmode, based on the simple ITL. IFMType: See Common Parameters. 22

23 Smooth: See Common Parameters. Used to smooth the raw IFM measurement. Use this condition to get alerts or mark bars when the market enters trendmode. When the market is cycling, we expect it to cross over the instantaneous trendline every half-period of the dominant cycle. Thus we can define the market to be in trendmode when the closing price has not crossed over the ITL for a period of more than half of the dominant cycle period. This condition uses the exponential ITL. The User Values Almost all of the studies and conditions in CycleTools for CQG are built from CQG user values. These are formulas that you can use in creating your own conditions and studies. User Value: CY_Cos Summary: Calculates the cosine of the phase of the price signal. IFMType: See Common Parameters. Smooth: See Common Parameters. Used to smooth the raw period measurement that is an input to the phase calculation. Remarks The Hilbert transform calculates the real and imaginary components of the detrended price series. Using these values and the period of the dominant cycle, it is possible to calculate the phase of the signal represented by the prices. This user value calculates the cosine of the phase. These calculations are optimized for use with DetrendType = 1, Period1 = 6, and HilbertType = 3. User Value: CY_CosLead Summary: Calculates the cosine of the phase of the price signal plus some specified lead amount. IFMType: See Common Parameters. Smooth: See Common Parameters. Used to smooth the raw period measurement that is an input to the phase calculation. Lead: The amount (in radians) added to the phase. A value of 0.78 represents 1/8 of a cycle (45 degrees), 1.57 is equivalent to ¼ of a cycle (90 degrees). Remarks 23

24 The Hilbert transform calculates the real and imaginary components of the detrended price series. Using these values and the period of the dominant cycle, it is possible to calculate the phase of the signal represented by the prices. This user value calculates the cosine of the phase, advanced by some specified amount. These calculations are optimized for use with DetrendType = 1, Period1 = 6, and HilbertType = 3. User Value: CY_Detrended Prices Summary: Calculates a detrended price series. The algorithm used for detrending is selectable via the DetrendType parameter. This user value is meant to be used as the basis for other studies that require a detrended input. User Value: CY_DominantCycle Summary: Calculates the period of the dominant cycle. IFMType: See Common Parameters. The algorithm used for calculating the dominant cycle period is selectable via the IFMType parameter. This user value is meant to be used as the basis for other studies that require the period of the dominant cycle as an input. User Value: CY_FAZMA Summary: Calculates the frequency-adjusted zero-lag moving average (ZMA). IFMType: See Common Parameters. User Value: CY_HilbertImag Summary: Calculates the imaginary part of the Hilbert transform. 24

25 IFMType: See Common Parameters. The Hilbert transform serves as the basis for all the indicators in CycleTools for CQG that calculate or use the dominant cycle period. The mathematically inclined reader may learn more about it in [5] and [6]. This user value returns the imaginary part of the Hilbert transform of the input. User Value: CY_HilbertReal Summary: Calculates the real part of the Hilbert transform. IFMType: See Common Parameters. The Hilbert transform serves as the basis for all the indicators in CycleTools for CQG that calculate or use the dominant cycle period. The mathematically inclined reader may learn more about it in [5] and [6]. This user value returns the real part of the Hilbert transform of the input. User Value: CY_IFM Summary: Calculates the dominant cycle period, using the basic Instantaneous Frequency Measurement algorithm. Remarks This user value returns the period of the dominant cycle of the input. It is calculated as described in [7]. The term instantaneous frequency measurement here is a misnomer, since the calculation actually measures the period of the dominant cycle, which is the inverse of the frequency. I have retained the original terminology use in John Ehlers article. The raw period measurement is smoothed by an exponential moving average of period smooth. Setting smooth equal to one eliminates the smoothing altogether. 25

26 User Value: CY_IFMCos Summary: Calculates the dominant cycle period, using the cosine algorithm for Instantaneous Frequency Measurement. Remarks This user value returns the period of the dominant cycle of the input. It is calculated using the cosine technique as described in [2]. The term instantaneous frequency measurement here is a misnomer, since the study actually measures the period of the dominant cycle, which is the inverse of the frequency. I have retained the original terminology use in John Ehlers article. The raw period measurement is smoothed by an exponential moving average of period smooth. Setting smooth equal to one eliminates the smoothing altogether. NOTE: It has been my experience that this study gives very different results than the the other two types of IFM, the basic IFM and IFMIQ algorithms. I will be investigating this in the near future, to determine if there is a problem with the algorithm or the implementation, or if this is just a property of the algorithm. In the meantime, I suggest that you treat the results of this study with caution, unless you see evidence that the results are valid for your particular application. User Value: CY_IFMIQ Summary: Calculates the dominant cycle period, using the IQ algorithm for Instantaneous Frequency Measurement. Remarks This study returns the period of the dominant cycle of the input. It is calculated using the IQ technique as described in [2]. The term instantaneous frequency measurement here is a misnomer, since the study actually measures the period of the dominant cycle, which is the inverse of the frequency. I have retained the original terminology use in John Ehlers article. The raw period measurement is smoothed by an exponential moving average of period Smooth. Setting Smooth equal to one eliminates the smoothing altogether. User Value: CY_ITLExp Summary: Calculates the instantaneous trendline, using an exponential moving average algorithm. 26