Noxa CSSA. <2007> <Noxa Analytics, Inc.> Causal Singular Spectrum Analysis

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1 Causal Singular Spectrum Analysis

2 Table of Contents Foreword 0 Part I Overview 1 Part II Disclaimer/ License Agreement 2 Part III CSSA in Action 5 1 Transaction Timing Built in Signals Crossover Signals Support/Resistance... Violation Signals 12 5 Trading Strategies Knowledge... Discovery 20 7 Trend Confirmation Setting the... Range 22 9 Inserting CSSA... Entry Indicators in a trading strategy 32 Part IV CSSA Singular Spectrum Embedding Decomposition Grouping Causality Part V CSSA indicators 54 1 CSSA-ShowRange CSSA-ShowEigenvectors CSSA-Cycles CSSA-Slope CSSA-Long... Entries # CSSA-Long... Entries # CSSA-Short... Entries # CSSA-Short... Entries # CSSA-Trendline CSSA-Instant... Trendline CSSA-QPhase CSSA-Oscillator CSSA-Percent... Variance 70

3 Contents 14 CSSA-Coupling... Index CSSA-Change... Point Score CSSA-Turning... Levels CSSA-Max Line CSSA-Min Line CSSA-Flatlines Index 0

4 1 1 Overview Category Nature and its parts fluctuate in cycles. Markets are no exceptions. A quick glance at any price chart will reveal cyclical behaviors; price bobs up and down with a good degree of regularity giving evidence of rhythm. Obviously, if cycles are genuine, the presumption is that they will continue. And mostly they do, so we cannot afford to ignore them. is a package that runs as an add-on to Neuroshell Trader v5.2 and above. It is packed with a set of non-lagging indicators that extract well-behaved cycles in financial data. Catch and trade cycles with unprecedented accuracy, Spot reversals faster in all time frames. What does CSSA offer that other tools don t? SSA (Singular Spectrum Analysis) is a powerful statistical technique that provides a complete multi-wave representation of the market. It breaks price into modes of variability that capture the variance at any time frame. Like other transformations, SSA is designed to enhance certain aspects of a data set; in Fourier decomposition it is the frequencies whereas in SSA it is the variance. Viewing cycles in terms of variance represents a radical departure from spectral analysis; it allows us to perform the transform from the data itself without making any assumption whatsoever on the way to proceed. Fourier methods assume that future data consist of a periodic repetition of past data in the form of pure sinusoids. Wavelets offer yet another way of analyzing price series. They operate with a fixed set of filters of predetermined shape. There is usually little physical evidence in markets for such assumptions. We find it most useful to extract cycles from the data itself, in which case the transform is ideally adapted to the kind of market that is being traded. Cycles are not forced to conform to some unsubstantiated mathematical representation therefore they retain a remarkable resemblance to the original series.

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8 5 3 CSSA in Action 3.1 Transaction Timing Quickly anticipate turning points The key to transaction timing is in knowing when we are at a low or a high. Let s first take a look at cycles in the Diamonds Trust (DIA). The next figure (top chart) is a daily high-low chart of the DIA from the most recent data (December 2006 to April 2007). Prices have certainly fluctuated during that period. GroupStart = 9, GroupDepth = 4

9 CSSA in Action 6 Turn your attention now to the bottom chart. A cycle composite from CSSA illustrates its timing capabilities. You ll notice that the peaks and troughs of this curve emphasize the swings quite well and would make good entry points. 3.2 Built in Signals Make the most of each market move. The previous chart made clear that trading the cycle peaks and valleys can be appropriate with CSSA. Here we show signals from CSSA-Long and Short entries #0 that actually tell when to buy bottoms and sell tops. Warning: Built in Signals do not show up in the Trading Strategy Wizard. They need to be created as new indicators prior to be added in a trading strategy. See Inserting CSSA Entry Indicators in a trading strategy 32 Long entry: -Long Entries #0(Close,50,9,4,1,0,1,1000) Short entry: -Short Entries #0(Close,50,9,4,1,0,1,1000)

10 7 These results are very pleasing; the entries occur at market turns as if they were predicted with perfect hindsight. Note on the predictive ability of CSSA indicators Compensate for inherent execution lags We saw that CSSA yields an effective response to the market. Lagless cycles tell us when to Buy low and sell high Or do they? The signals lag the cycle by one bar and another bar is needed to make the trade. In other words, our trade execution is two bars late! To remedy this lag we implemented a causal leading feature to CSSA indicators. Cycles are projected ahead so that the trade can be made at the exact turning points. This chart illustrates a cycle whose peaks and troughs lead by one bar (blue curve). Lead = 1

11 CSSA in Action 8 A word of caution Don t get whipsawed in and out All sounds pretty rosy so far. However CSSA-Long/Short entries #0 can lose its effectiveness when cycles fail to follow though. This is particularly true in trending markets. As you can see in the figure below, the DIA was in a trend free from cycles through October False signals were generated during that period. When strong trends are present, the anticipated reversals may simply never take place, leading to entries in the wrong direction.

12 9 Fortunately, the cycle composite usually rides below or above the zero line (hence no whipsaw effect) in the context of developing trends. It is therefore possible to discard those spurious signals by simply testing the levels at which CSSA-cycles sits. It is important to realize that despite its propensity to produce an excess of trades, this indicator, when used along with proper confirmation rules, can yield great profits. Take advantage of trends CSSA-Long/Short entries #2 is one method to actually disregard those signals that arise from riding waves. As you can see here, most signals concerned have been

13 CSSA in Action 10 filtered out. 3.3 Long entry: -Long Entries #2(Close,50,9,4,1,0,1,1000,0) Short entry: -Short Entries #2(Close,50,9,4,1,0,1,1000,0) Crossover Signals Naturally geared towards early entry signals CSSA-QPhase is the quadrature version of CSSA-Cycles. It has zero-crossings when

14 11 the cycle is at a peak or trough. Signals can then be triggered by simple crossovers as shown below: Long entry: CrossBelow(-QPhase(Close,50,9,4,1,0,1,1000,1),0) Short entry: CrossAbove(-QPhase(Close,50,9,4,1,0,1,1000,1),0) Crossover signals from CSSA-QPhase have the advantage over CSSA-Long/Short Entries that they mostly don t lag the cycle thus allowing a less extensive use of the Lead parameter. CSSA-Oscillator is an oscillator derived from CSSA-Cycles. Setting Mode to 2 in this indicator computes the oscillator derived from CSSA-QPhase. Similarly to CSSA-QPhase non-lagging entries can be set by crossovers: Long entry: CrossBelow(-Oscillator(Close,50,9,4,1,0,1,1000,2),0) Short entry: CrossAbove(-Oscillator(Close,50,9,4,1,0,1,1000,2),0)

15 CSSA in Action Support/Resistance Violation Signals CSSA-Turning Levels draws a line horizontally triggered by the base before an up move in CSSA (when Flag series = CSSA-Long Entries) or the peak before a down move (when Flag series = CSSA-Short Entries). The purpose of this indicator is to show where price is liable to find some local support and encounter some local resistance. The violation of these lines can generate great entry points. Long entries are triggered by CSSA-Trendline (top chart, red curve) crossing above the local support line (top chart, blue curve). Long entry: CrossAbove(-Trendline(Close,13,9,1,10000),-Turning Levels(Low,Noxa CSSA-Long Entries #2(Close,10,5,1,1,0.16,1,10000,0.71)))

16 13 Short entries are triggered by CSSA-Trendline (top chart, red curve) crossing below the local resistance level (top chart, blue curve). Short entry: CrossBelow(-Trendline(Close,5,9,1,10000),-Turning Levels(High,Noxa CSSA-Short Entries #2(Close,14,9,3,5,0.79,1,10000,-0.19)))

17 CSSA in Action 3.5 Trading Strategies 14

18 15 There are legitimate concerns that, with the recent proliferation of cycle analysis software, cycles become easily detectable; as a result, they might be distorted or traded away very quickly whenever they develop in the market. Well, let s go a step further and put CSSA to the test! The chart examples given here are not intended to form the basis of a specific trading system, but simply to illustrate the ability of CSSA to catch self sustained cycles. The models naturally lend themselves to countertrend trading style. Long entries are set when the cycle shows downward momentum. Similarly, short entries are set when upward momentum resumes. We used Optimization with early and frequent pausing to allow visual checks of the out-of-sample signals. CSSA indicators are optimal in that they pack as much information as possible in the smallest number of cyclic components. Cycles from CSSA are also optimally smooth; so trading strategies that use them maximize fitness very efficiently. We found it useful to stop the optimization early and frequently so that overtraining is avoided. If the out-of-sample results are not satisfying, we kept optimizing over the previous settings. Round-turn commissions were set to $20, results are given out-of-sample. Long/Short Entries This example illustrates the use of stop losses. A separate trading strategy dedicated to placing stop orders was built upon the signals from CSSA-Long/Short Entries. Long entry: -Long Entries #2(Close,25,8,7,5,0.77,1206,500,0.003) Long stop: PriceFloor%(Trading Strategy with stop losses,2.5) Short entry: -Short Entries #2(Close,25,10,10,9,0.05,284,500,-0.059) Short stop: PriceFloor%(Trading Strategy with stop losses,3)

19 CSSA in Action 16 As you can see above, tight stop losses straightened the equity cure. Because of the accuracy of the signals, the stop is never hit and the trade quickly turns profitable. In the case the signal fails, the stop is hit almost immediately resulting in only a small loss. QPhase Crossovers Even though securities develop trends, they can also fluctuate within those trends.

20 17 Long entry: CrossBelow(-QPhase(Close,12,3,8,0,0.91,175,300,1),-0.12) Short entry: CrossAbove(-QPhase(Close,20,3,5,2,0.63,1738,300,1),0.09) Oscillator Crossovers CSSA is particularly well suited to ranging markets. Long entry: CrossBelow(-Oscillator(Close,12,8,6,9,0.27,771,500,2),-0.071)

21 CSSA in Action Short entry: CrossAbove(-Oscillator(Close,45,9,5,5,0.82,2745,500,2),0.034) Turning Levels Violation Long entry: CrossAbove(Open,-Turning Levels(Low,-Long Entries #2(Close,48,9,8,5,0.11,1,10000,0.41))) Short entry: CrossBelow(Close,-Turning Levels(High,-Short Entries #2(Close,11,6,6,8,0.3,1,10000,-0.78))) 18

22 19

23 CSSA in Action Knowledge Discovery Until now, we showed how signals could be derived from CSSA. In generating entries, CSSA can also signal that something is amiss with trend. The following chart for the DIA shows early signs that the trend change (end of October 2005, end of March 2006 and more recently end 2007). addition to the current is about to of February CSSA-Percent Variance and CSSA-Coupling Index are variations of the same concept. They both use the variance accounted by individual cycles or group of cycles to compute the degree of coupling between them. Any sudden variation in this

24 21 coupling can be used as a proxy for change. CSSA-Change Point Score computes a degree of change between recent and past price action (the base). It can be interpreted as the probability that some change is likely to occur due to strong causal dependencies in the data. In other words this indicator reveals hidden dependencies that announce significant changes in trend. 3.7 Trend Confirmation In addition to generating signals, CSSA-Oscillator also provides useful trend confirmation with the following setting: GroupStart=2 GroupDepth=1 If the oscillator crosses the zero-line from below, a bullish trend is generally observed (and vice versa). It is recommended however to use CSSA-Instant Trendline in tandem with the oscillator to validate the trend; an up-trend is confirmed when the Instant Trendline sits above the zero line (and vice versa).

25 CSSA in Action Setting the Range Selecting the training range of CSSA indicators has causal repercussions! The training range of CSSA indicators allows you to set the most appropriate period in which to estimate the eigenvectors and eigenvalues but this has to be done with care

26 23 to avoid non causalities (read more 24 ) and future leaks (read more 26 ). You can use CSSA-ShowRange 55 to this effect as shown below. The horizontal time span of theindicator can be moved and stretched out with the mouse. Then read the values shown in the caption to set the training range accordingly; here we let the optimizer choose from the most appropriate 400 bar range:

27 CSSA in Action Read more on how to set the range. Setting the range to avoid spurious changes of past signals A system is non causal, thus not appropriate for use in a trading strategy when new data bars cause past values of an indicator to change on the fly. This in turn can cause the NeuroShell Trader signals to change in the past. So to avoid this problem, make sure to exclude the current bar from the training range. Let s take the example of a series with 48 bars: The training range that follows (20 bar wide starting at bar #8), is the period used to calculate the oscillation patterns or eigenvectors in the data. These patterns are then used to calculate the indicator.

28 25 TrainStart is the first bar of the range, TrainDepth is the number of bars in the range. In most cases, the range by default exceeds the total number of bars in the chart: Keeping the range by default can then be a problem when trading with the raw indicator. As new bars come in, the training range keeps growing causing the indicator to change some of its past values. The next figure shows a graph inflated by one bar; the effective training range is now one bar wider: In order to avoid this problem, the training range has to be set so that the current bar is not included:

29 CSSA in Action 26 Thus the training range does not inflate with new bars coming in. Then as expected, past values of the indicator do not change; only the last bar value is updated: To sum up, when trading with raw CSSA indicators, the training range can be set freely as long as the last bar is not included: Setting the range to avoid future leaks during optimization TrainStart and TrainBars are not seen as dates by Neuroshell; if you keep the range by default (1~10000) and assuming that your chart has less than bars, the GA will try values from the first bar in your chart to today independently of the dates you

30 27 have set to optimize and evaluate your trading strategy. But you need to set the training range before optimizing your system so that it does not overlap with the paper trading period as shown below: An overlap would mean using data from the evaluation period to calculate the indicator. This would constitute a future leak. Setting the range with ShowRange Step 1: How to get the total number of bars in the chart. - Insert a ShowRange indicator - Press shift and drag right to fully zoom out - Grab the green edges of the chooser to adjust the range When the range is fully expanded, the value in the caption indicates the number of bars in the chart. Step 2: adjust the training range making sure that it does not go past the paper trading range limit of bar #2130 (TrainStart + TrainDepth = = 2130, shown here by a vertical green line):

31 CSSA in Action 28 Step 3: use the values in the caption to manually set TrainStart and TrainDepth in the trading strategy wizard. Based on the values in the caption we set TrainDepth = 500 bars starting at bar #1600.

32 29 In this example, TrainDepth = 1000 but the range is free to slide; TrainStart = 1 ~ We verify again that the training range never goes past the paper trading limit of 2130; In the worst case, TrainDepth + TrainStart = = 2100 < 2130.

33 CSSA in Action 30

34 31 And finally we let the optimization choose TrainDepth in the range 500 ~ 1000 bars making sure again that TrainStart + TrainDepth never exceeds the paper trading range limit.

35 CSSA in Action Inserting CSSA Entry Indicators in a trading strategy NeuroShell uses entry and exit rules that are based either on true and false conditions. You can also use CSSA-Long/ Short entries but you ll need to insert them in your chart prior to building the trading strategy. Then, the indicators can be selected as entry and exit rules in the selection wizard as shown below:

36 33 Refer to the steps below for a detailed description on how to insert CSSA entry indicators. 1. Open the Indicator Wizard: Insert/ New Indicator

37 CSSA in Action 2. Choose the Noxa category 34

38 35 3. Select both CSSA-Long and Short Entries

39 CSSA in Action 4. Adjust the parameters as you like and click Finished 36

40 37 5. You are now set; the indicators appear in your chart.

41 CSSA in Action 38 The following steps describe how you can build a trading strategy using these entries. 6. Open the Trading Strategy Wizard: Insert/ New Trading Strategy

42 39 7. Choose (No Template)

43 CSSA in Action 8. Select the Long Entry tab and Click Add Condition(s) 40

44 41 9. Choose the CSSA-Long Entries indicator in the selection wizard and click OK

45 CSSA in Action 10. The CSSA-Long Entries rule is inserted as long entry: 42

46 You can proceed the same way with the Short entry rule:

47 CSSA in Action 44

48 45 4 CSSA 101 This section will take you through the steps needed to perform a Singular Spectrum Analysis. We will try to provide an explanation of what is happening at each point so that you can make informed decisions when you use this technique yourself. 4.1 Singular Spectrum Singular Spectrum Analysis (SSA) is a method that takes all the variability in a series and breaks it into a few oscillation patterns that we refer to as eigenvectors. It also gives a measure of significance of these patterns or eigenvalues. Eigen is a German word, which roughly translates to characteristic. Eigenvectors are structure functions that best represent the modes of behavior in price. The eigenvalues are a measure of the variance that these modes account for. The eigenvectors can be ordered by eigenvalue, highest to lowest, so that the first few patterns retain most of the variance in the data. The ordered eigenvalues are referred to collectively as the Singular Spectrum. The following figure gives an example of Singular Spectrum from CSSA-ShowEigenvectors. The top chart gives the spectrum of QUALCOMM INC (QCOM); the dots represent eigenvalues that can be selected with the green chooser. The bottom chart draws the corresponding eigenvector. The top left dot represents the component that accounts for most of the variability in the data; it is the lower frequency component (usually the trend) as shown below:

49 CSSA Eigenvector 1/30: The other dots represent cycles of smaller periods as we go further to the right. Each successive eigenvector explains progressively smaller portions of the variance. Eigenvector 3/30: Eigenvector 9/30: Most of the data is usually explained by the first few dominant eigenvectors only. And since no other eigenvectors contribute much (all eigenvalues are small) we can assume that everything else found in the series is structureless noise. Eigenvector 29/30:

50 Embedding The first step in SSA consists in embedding the series into a vector space. In short, SSA looks for linear relationships between lagged copies of market snapshots. The m-histories parameter is the number of lags of interest. Let s look at the example of m-histories=2, meaning that we consider only two consecutive market snapshots: This example is simple enough to give a two-dimensional graphic representation of the vector space. We can achieve this by plotting the price from market snapshot lag=0 versus the price from market snapshot lag=1:

51 CSSA SSA looks for the orthogonal directions in that plane that best fit the cloud of points: The first direction accounts for as much of the variance as possible (the longer axis). The second direction accounts for the remaining variance. The directions are chosen orthogonal meaning that the corresponding eigenvectors are uncorrelated from each other. Each one makes an independent contribution to accounting for the variance of the original series. Let s now consider a more practical case for which m-histories=50. The vector space has now 50 dimensions. Needless to say that such hyperspace is impossible to picture as a simple graph. Nevertheless, SSA extracts 50 eigenvectors, each of them representing a preferred direction in that hyperspace. What did we learn so far? m-histories corresponds to the number of components to decompose the series into, Embedding transforms a price series into a multi-dimensional space, Eigenvectors may be thought as elementary patterns of behavior that maximize the variance between lagged market snapshots. They provide a graphical representation of the structure in a price series. The eigenvalues are a measure of the importance of the eigenvectors. It is worth noting that SSA does not resolve periods longer than m-histories. m-histories is the maximum period (in bars) that can be detected.

52 Decomposition Adaptive filters are devised from the eigenvectors themselves to decompose the series into cyclic components. The following figure displays components 2 to 6 for QUALCOMM INC (QCOM).

53 CSSA TrainStart and TrainBars are parameters to set up the time span within which the eigenvectors are extracted. You can use CSSA-ShowRange 55 to this effect.

54 Grouping The last step in CSSA consists in choosing a selection of components (or group) to obtain the final cycle composite that best represents the price action. Here we have identified two groups which emphasize different time frames for EXXON MOBIL CP (NYSE:XOM): Blue curve (37 bar period cycle): GroupStart=3. GroupDepth=2 Brown curve (10 bar period cycle): GroupStart=9, GroupDepth=4 GroupStart sets the first component number in the group. Higher values lead to shorter cycles. GroupDepth is the number of components in the group. More components increase the level of detail of the cycle composite.

55 CSSA 101 Here are the corresponding CSSA-ShowEigenvectors: singular spectrums and eigenvectors 52 from GroupStart=3, GroupDepth=2 GroupStart=9 GroupDepth=4 4.5 Causality All indicators in this add-on are causal, hence the letter "C" in CSSA, meaning that they exclusively use historical data. One major caveat of the original SSA algorithm; the adaptive filters built from the eigenvectors are time symmetric filters that use past and future data. As a result, the last segment (m-histories wide) changes as the most recent price changes. In other words, SSA is non causal and cannot be used for generating signals. There are crude ways to make SSA cycles causal:

56 53 the easiest way would be to lag the cycle by m-histories, Another way would be to "re-run" the entire SSA calculation in a rolling window, adding one bar each time (end-point version). However we found both methods very limited in their predictive skills; they offered little guidance for trading so we devised a proprietary causal version for SSA that is particularly well-suited for use in trading strategies.

57 CSSA CSSA indicators Following is a brief overview of the indicators in the CSSA add-on: CSSA-ShowRange Select a range, and then use the values shown in the caption to set the training range of CSSA indicators. CSSA-ShowEigenvectors Visualize the elementary patterns of behavior in price and find propagating modes. Their inherent persistence over time makes these modes especially worthy of attention. CSSA-Cycles This indicator provides a full wave-composite picture of the market. The cycles are designed to be a direct reflection of the price action so that they don t lag. In other words, you will be able to quickly anticipate turning points independently of the time-frame. CSSA-Slope and Trendlines These indicators are derivatives from CSSA-Cycles; they are particularly useful in identifying and confirming the direction of momentum behind a move. CSSA-Long and Short Entries Signals are triggered by CSSA-Cycles from its bases and peaks. A causal lead and filtering features have been added to compensate for inherent execution lags so that you can make the most of each market move. CSSA-QPhase This indicator operates a 90 degree phase shift of CSSA-Cycles; the peaks and troughs of the cycle line become zero crossings. Signals are then triggered when the transform breaks through its center line. Because of the accuracy of the signals, tight stop losses can be kept for even better results. CSSA-Oscillator In addition to generating signals, this centered oscillator can also be used to confirm developing trends. CSSA-Percent Variance The ratio of the variance accounted by a group of cycles to the total variance in a rolling window is given. Any sudden change in this ratio can announce that something

58 55 is amiss with the current trend or that the current trend is about to change. CSSA-Coupling Index This indicator uses the variance accounted by individual cycles to return a degree of coupling between them. It computes the ratio of the variance accounted by two components in a rolling window. Any sudden change in this coupling can be used as a proxy for change. CSSA-Change Point Score The degree of change between recent and past price action (the base) is returned. It can be interpreted as the probability that some change is likely to occur due to strong causal dependencies in the data. In other words this indicator reveals hidden dependencies that may announce significant changes in trend. CSSA-Turning Levels Lines are drawn horizontally from the base before an up move in CSSA or a peak before a down move. The purpose of this indicator is to show where price is liable to find some local support and encounter some local resistance. The violation of these lines can generate reliable entry points. CSSA-Flatlines You might want to stay out when markets settle down and start to chop; a market moving sideways with very little upward and downward movement does not provide enough price range to overcome transaction costs. Sideways coils are also prone to fakeouts and we all know that escaping a position against a breakout can be expensive due to slippage. CSSA-Flatlines is a "flatline detector" in the form of upper and lower thresholds that can be used to identify those long flat areas of excessive chop so you can get out in time, or anticipate a breakout. 5.1 CSSA-ShowRange Category Input Parameters Name Setting Default Input series Time series Close

59 CSSA indicators 56 Description A window attaches itself to the bottom of Neuroshell. This is simply a visual tool to allow you to select a range, and then use the values shown in the caption to set the training range (TrainStart and TrainBars) of CSSA indicators. See the mouse action description given below to adjust the training range. Mouse action Shifting the range Grab the range (dark green) with the mouse and drag it. Sizing the range Grab the green edges with the mouse to adjust the range. To make the grabbing clearer, the mouse changes to left/right arrows Zooming Press shift and drag left to zoom in. Zooming does not vertically rescale until the mouse is let up. Use See Setting the Range CSSA-ShowEigenvectors Category Input Parameters

60 57 Name Setting Default Input series Time series Close m-histories Integer 5~ Definition m-histories Number of components Description A window attaches itself to the bottom of Neuroshell creating a visual representation of the patterns that SSA detects: The top graph is the spectrum of eigenvalues (log scale), of which any group can be selected, The bottom graph shows the sum of the corresponding eigenvectors. The bottom window of Eigenvectors has two modes. It starts with the normal sum of vectors, but if you click in the window it changes to Lissajous mode where it draws three curves: Black is the first eigenvector in the group, Grey is the last eigenvector in the group, Green is the Lissajous pattern of them. The Lissajous pattern is the graph of the first eigenvector plotted on the y axis combined with the last eigenvector plotted on the x axis.

61 CSSA indicators 58 Tips A plateau in the spectrum usually indicates significant structure in the series, Propagating modes are steady pairs of cycles whose eigenvectors are in quadrature (out of phase by 90 degrees) as shown above. The corresponding Lissajous pattern is a circle. Their inherent persistence over time makes them especially worthy of attention. Mouse action 5.3 Shifting Grab the (dark green) group of eigenvalues with the mouse to drag it. Rescaling Grab the edges to adjust the size of the group. To make the grabbing clearer, the mouse changes to left/right arrows. CSSA-Cycles Category Input Parameters

62 59 Name Setting Default Input series Time series Close m-histories Integer 5~ GroupStart Integer >=2 2 GroupDepth Integer >=1 1 Lead Integer >0 0 Smoothing Real 0~1 0 TrainStart Integer >=1 1 TrainBars Integer >=10 10,000 Mode Integer >=1 1 Definition m-histories Number of components GroupStart The first component# in group for reconstruction GroupDepth The number of components in group for reconstruction Lead The number of bars ahead to project the cycle Smoothing The amount of smoothing (lagless) to apply to cycles TrainStart The first bar# of training range TrainBars The number of bars in training range Mode Mode = 1: Amplitude not restored Mode = 2: Amplitude restored The lead and smoothing operations attenuate the amplitude of the cycles. Mode = 2 is a method to restore this amplitude. Restoring the amplitude might be useful in some crossover strategies. Description CSSA-Cycles is a causal version of the free SSA-Cycles indicator. It is appropriate for use in trading strategies, although it is different from the original implementation. This indicator provides a full wave-composite picture of the market. The cycles are designed to be a direct reflection of the price action so that they don t lag. In other words, you will be able to quickly anticipate turning points independently of the time-frame.

63 CSSA indicators Use See Transaction Timing CSSA-Slope Category Input Parameters Name Setting Default Input series Time series Close m-histories Integer 5~ GroupStart Integer >=2 2 GroupDepth Integer >=1 1 Lead Integer >0 0 Smoothing Real 0~1 0 TrainStart Integer >=1 1 TrainBars Integer >=10 10,000 Mode Integer >=1 1 Definition m-histories Number of components GroupStart The first component# in group for reconstruction GroupDepth The number of components in group for reconstruction Lead The number of bars ahead to project the cycle Smoothing The amount of smoothing (lagless) to apply to cycles TrainStart The first bar# of training range TrainBars The number of bars in training range Mode Mode = 1: Parabolic interpolation (smoother but lags 1 bar) Mode = 2: First order difference 60

64 61 Description CSSA-Slope computes the slope of CSSA-Cycles. It is good for identifying the direction of momentum behind a move. Momentum is bullish when the slope sits above its center line and bearish when the slope sits below its centerline. 5.5 CSSA-Long Entries #0 Category Input Parameters Name Setting Default Input series Time series Close m-histories Integer 5~ GroupStart Integer >=2 2 GroupDepth Integer >=1 1 Lead Integer >0 0 Smoothing Real 0~1 0 TrainStart Integer >=1 1 TrainBars Integer >=10 10,000 Definition m-histories Number of components GroupStart The first component# in group for reconstruction GroupDepth The number of components in group for reconstruction Lead The number of bars ahead to project the cycle Smoothing The amount of smoothing (lagless) to apply to cycles TrainStart The first bar# of training range TrainBars The number of bars in training range Description

65 CSSA indicators 62 CSSA-Long Entries #0 are entry points triggered by CSSA-Cycles from its bases. It is recommended to use the signals in tandem with other indicators for confirmation. A causal lead and filtering features have been added to compensate for inherent execution lags so that you can make the most of each market move. Use See Built in Signals CSSA-Long Entries #2 Category Input Parameters Name Setting Default Input series Time series Close m-histories Integer 5~ GroupStart Integer >=2 2 GroupDepth Integer >=1 1 Lead Integer >0 0 Smoothing Real 0~1 0 TrainStart Integer >=1 1 TrainBars Integer >=10 10,000 Threshold Real -1~+1 0 Definition m-histories Number of components GroupStart The first component# in group for reconstruction GroupDepth The number of components in group for reconstruction Lead The number of bars ahead to project the cycle

66 63 Smoothing The amount of smoothing (lagless) to apply to cycles TrainStart The first bar# of training range TrainBars The number of bars in training range Threshold Line above which signals from riding waves are filtered out Description CSSA-Long Entries #2 is a filtered version of CSSA-Long Entries #0. Signals generated by waves riding above and bellow the threshold line are filtered out. A causal lead and filtering features have been added to compensate for inherent execution lags so that you can make the most of each market move. Use See Built in Signals 5.7 9, Trading Strategies 15 CSSA-Short Entries #0 Category Input Parameters Name Setting Default Input series Time series Close m-histories Integer 5~ GroupStart Integer >=2 2 GroupDepth Integer >=1 1 Lead Integer >0 0 Smoothing Real 0~1 0 TrainStart Integer >=1 1 TrainBars Integer >=10 10,000 Definition

67 CSSA indicators m-histories Number of components GroupStart The first component# in group for reconstruction GroupDepth The number of components in group for reconstruction Lead The number of bars ahead to project the cycle Smoothing The amount of smoothing (lagless) to apply to cycles TrainStart The first bar# of training range TrainBars The number of bars in training range 64 Description CSSA-Short Entries #0 are entry points triggered by CSSA-Cycles from its peaks. It is recommended to use the signals in tandem with other indicators for confirmation. A causal lead and filtering features have been added to compensate for inherent execution lags so that you can make the most of each market move. Use See Built in Signals CSSA-Short Entries #2 Category Input Parameters

68 65 Name Setting Default Input series Time series Close m-histories Integer 5~ GroupStart Integer >=2 2 GroupDepth Integer >=1 1 Lead Integer >0 0 Smoothing Real 0~1 0 TrainStart Integer >=1 1 TrainBars Integer >=10 10,000 Threshold Real -1~+1 0 Definition m-histories Number of components GroupStart The first component# in group for reconstruction GroupDepth The number of components in group for reconstruction Lead The number of bars ahead to project the cycle Smoothing The amount of smoothing (lagless) to apply to cycles TrainStart The first bar# of training range TrainBars The number of bars in training range Threshold Line below which signals from riding waves are filtered out Description CSSA-Short Entries #2 is a filtered version of CSSA-Short Entries #0. Signals generated by waves riding above and below the threshold line are filtered out. A causal lead and filtering features have been added to compensate for inherent execution lags so that you can make the most of each market move. Use See Built in Signals 9, Trading Strategies 15

69 CSSA indicators CSSA-Trendline Category Input Parameters Name Setting Default Input series Time series Close m-histories Integer 5~ GroupDepth Integer >=1 10 TrainStart Integer >=1 1 TrainBars Integer >=10 10,000 Definition m-histories Number of components GroupDepth The number of components in group for reconstruction (component #1 included) TrainStart The first bar# of training range TrainBars The number of bars in training range Description CSSA-Trendline is a causal version of the free SSA-Trendline indicator. It is appropriate for use in trading strategies, although it is different from the original implementation. Use See Support/Resistance Violation Signals 12

70 CSSA-Instant Trendline Category Input Parameters Name Setting Default Input series Time series Close m-histories Integer 5~ GroupDepth Integer >=1 1 TrainStart Integer >=1 1 TrainBars Integer >=10 10,000 Mode Integer >=1 1 Definition m-histories Number of components GroupDepth The number of components in group for reconstruction (component #1 included) TrainStart The first bar# of training range TrainBars The number of bars in training range Mode Mode = 1: Parabolic interpolation (smoother but lags 1 bar) Mode = 2: First order difference Description CSSA-Instant Trendline computes the slope of CSSA-Trendline. Use See Trend Confirmation 21

71 CSSA indicators CSSA-QPhase Category Input Parameters Name Setting Default Input series Time series Close m-histories Integer 5~ GroupStart Integer >=2 2 GroupDepth Integer >=1 1 Lead Integer >0 0 Smoothing Real 0~1 0 TrainStart Integer >=1 1 TrainBars Integer >=10 10,000 Mode Integer >=1 1 Definition m-histories Number of components GroupStart The first component# in group for reconstruction GroupDepth The number of components in group for reconstruction Lead The number of bars ahead to project the cycle Smoothing The amount of smoothing (lagless) to apply to cycles TrainStart The first bar# of training range TrainBars The number of bars in training range Mode Mode = 1: +90 degree phase shift Mode = 2: -90 degree phase shift Description CSSA-QPhase operates a 90 degree phase shift of CSSA-Cycles so that the peaks and troughs of the cycle line become zero crossings. Signals can then be generated when the transform breaks through its center zero line. Because of the accuracy of the signals, tight stop losses can be kept for even better

72 69 results. Use See Crossover Signals , Trading Strategies 16 CSSA-Oscillator Category Input Parameters Name Setting Default Input series Time series Close m-histories Integer 5~ GroupStart Integer >=2 2 GroupDepth Integer >=1 1 TrainStart Integer >=1 1 TrainBars Integer >=10 10,000 Mode Integer >=1 1 Definition m-histories Number of components GroupStart The first component# in group for reconstruction GroupDepth The number of components in group for reconstruction TrainStart The first bar# of training range TrainBars The number of bars in training range Mode Mode = 1: Oscillator Mode = 2: QPhase transform applied Setting Mode to 2 allows for peaks and troughs to be measured through zero crossings. Extrema are reached when the QPhase transform of the oscillator breaks

73 CSSA indicators 70 through the zero line. Description CSSA-Oscillator is a centered oscillator. It oscillates above and below the zero line. It is particularly good for identifying the direction of price momentum behind a move. Readings above the center line indicate bullish momentum. Similarly, readings below the center line indicate bearish momentum. Setting Mode to 2 in this indicator computes the oscillator derived from CSSA-QPhase. Similarly to CSSA-QPhase non-lagging entries can be set by crossovers. In addition to generating signals, this centered oscillator can also be used to confirm developing trends Use See Crossover Signals , Trend Confirmation 21, Trading Strategies CSSA-Percent Variance Category Input Parameters Name Setting Default Input series Time series Close m-histories Integer 5~50 30 GroupStart Integer >=1 20 GroupDepth Integer >=1 10 Window Integer >=6 100 Definition m-histories Number of components GroupStart The first component# in group for reconstruction 17

74 71 GroupDepth The number of components in group for reconstruction Window Moving window Description CSSA-Percent Variance computes the ratio of the variance accounted by a group of cycles to the total variance in a rolling window. Any sudden change in this ratio can announce that something is amiss with the current trend or that the current trend is about to change. Use See Knowledge Discovery CSSA-Coupling Index Category Input Parameters Name Setting Default Input series Time series Close m-histories Integer 5~50 30 Component #1 Integer >=1 20 Component #2 Integer >=1 2 Window Integer >=6 100 Definition m-histories Number of components Component #1 Component #2 Window Moving window

75 CSSA indicators 72 Description CSSA-Coupling Index uses the variance accounted by individual cycles to return a degree of coupling between them. It computes the ratio of the variance accounted by component #1 to the variance accounted by component #2 in a rolling window. Any sudden change in this coupling can be used as a proxy for change. Use See Knowledge Discovery CSSA-Change Point Score Category Input Parameters Name Setting Default Input series Time series Close m-histories Integer 5~50 20 GroupDepth Integer >=1 2 BaseLag Integer >=1 5 Window Integer >=6 100 Definition m-histories Number of components GroupDepth The number of components in group for reconstruction BaseLag Lag in bars of the base matrix Window Moving window Description CSSA-Change Point Score computes a degree of change between recent and past price action (the base). It can be interpreted as the probability that some change is likely to occur due to strong causal dependencies in the data. In other words this indicator reveals hidden dependencies that may announce significant changes in trend.

76 73 Use See Knowledge Discovery 20 Reference Tsuyosji Ide, Koji Tsuda, Change-Point Detection using Krylov Subspace Learning 5.16 CSSA-Turning Levels Category Input Parameters Name Setting Default Input series Time series Close Flag series Time series Close Definition Flag series Can be either CSSA-Long or CSSA-Short entries Description CSSA-Turning Levels draws a line horizontally triggered by the base before an up move in CSSA (when Flag series = CSSA-Long Entries) or the peak before a down move (when Flag series = CSSA-Short Entries). The purpose of this indicator is to show where price is liable to find some local support and encounter some local resistance. The violation of these lines can generate reliable entry points. Long entries can be triggered by CSSA-Trendline crossing above the local support line. Short entries can be triggered by CSSA-Trendline crossing below the local support line.

77 CSSA indicators 74 Use See Support/Resistance Violation Signals , Trading Strategies 18 CSSA-Max Line Category Input Parameters Name Setting Default Input series Time series Close Threshold series Numeric value or time series 0 Mode Integer 1~2 2 Definition Threshold series Can be either a real value or a series Mode Mode=1: if (X > Y) then 1 otherwise 0 where X = trailing line, Y = Threshold series Mode=2: the trailing line Description Mode=2: Horizontal trailing lines are drawn from the local maxima of the Input series. Mode=1: Indicates the periods when the trailing line has just broken out above the Threshold series. Use CSSA-Min Line can be used with zeroed inputs. In the following chart example the input is a CSSA-Cycle. Mode = 2: Max line (Blue curve) Mode = 1: Boolean with threshold = 0.2 (green curve)

78 75 CSSA-Max Line can be also used with non zeroed inputs (CSSA-Trend line in this example): Red curve: Max-Line, Mode = 2

79 CSSA indicators 5.18 CSSA-Min Line Category Input Parameters Name Setting Default Input series Time series Close Threshold series Numeric value or time series 0 Mode Integer 1~2 2 Definition Threshold series Can be either a real value or a series 76

80 77 Mode Mode=1: if (X < Y) then -1 otherwise 0 where X = trailing line, Y = Threshold series Mode=2: the trailing line Description Mode=2: Horizontal trailing lines are drawn from the local minima of the Input series. Mode=1: Indicates the periods when the trailing line has just broken out below the Threshold series. Use CSSA-Min Line can be used with zeroed inputs. In the following chart example the input is a CSSA-Cycle. Mode = 2: Min line (Blue curve) Mode = 1: Boolean with threshold = -0.2 (green curve)

81 CSSA indicators 5.19 CSSA-Flatlines Category Input Parameters Name Setting Default Input series Time series Close Upper Threshold Numeric value or time series 0 Lower Threshold Numeric value or time series 0 Confirmation period Integer < Threshold flag mode Integer 1~3 1 Output flag mode Integer 1~7 3 Definition Upper Threshold Can be either a numeric value or a data series Lower Threshold Can be either a numeric value or a data series Confirmation period Numeric value in the 0~500 range (read more Threshold flag mode TF Mode = 1: Threshold = percentage of input series TF Mode = 2: Threshold = Price level TF Mode = 3: Threshold = Threshold series - Input series Output flag mode OF Mode = 1: Upper line OF Mode = 2: Lower line OF Mode = 3: Average line OF Mode = 4: Cross-below signals OF Mode = 5: Cross-above signals OF Mode = 6: Boolean indicating the periods when the input enters a range after crossing below the Upper line OF Mode = 7: Boolean indicating the periods when the input enters a range after crossing above the Lower line Output Flag Mode description 84 ) 78

82 79 OF Mode = 1: Upper line (see chart 80 ) Thresholds are added to the local maxima of the input series. Horizontal trailing lines are then drawn from these levels. OF Mode = 2: Lower line (see chart 81 ) Thresholds are added to the local minima of the input series. Horizontal trailing lines are then drawn from these levels. OF Mode = 3: Average line (see chart 81 ) (Upper line + Lower line) / 2 The average line is a piecewise approximation of the input series. OF Mode = 4: (see chart 82 ) Signals are triggered when the input has just crossed below the average line. OF Mode = 5: (see chart 82 ) Signals are triggered when the input has just crossed above the average line. OF Mode = 6: (see chart 83 ) Boolean = 1 indicates the periods when the input enters a range after crossing below the Upper line OF Mode = 7: (see chart 83 ) Boolean = 1 indicates the periods when the input enters a range after crossing above the Lower line Threshold Flag Mode description The thresholds are added to or subtracted from the peaks and valleys of the input series: TF Mode = 1: Thresholds = percentage of the input series TF Mode = 2: Thresholds = price value

83 CSSA indicators 80 The thresholds can also be an independent price series; in this case, the trailing lines are drawn from the threshold series itself: TF Mode = 3: Thresholds = Threshold series - Input series (see chart 85 ) Discussion You might want to stay out when markets settle down and start to chop; a market moving sideways with very little upward and downward movement does not provide enough price range to overcome transaction costs. CSSA-Flatlines and its upper and lower thresholds can help identifying these long flat areas of excessive chop so you can get out in time or anticipate a breakout. Breaking out or down out of a congestive range is one of the big unsolved problems in daytrading. Sideways coils are prone to fakeouts and we all know that escaping a position against a breakout can be expensive due to slippage. Use The examples given below use CSSA-Trendline as input series but any input that flattens out smoothly to the horizontal on the flat zones of the price can be used for that matter. OF Mode = 1: Upper line (blue curve) Upper threshold = 2

84 81 OF Mode = 2: Lower line (blue curve) Lower threshold = 2

85 CSSA indicators OF Mode = 3: Average line (red curve) Upper threshold = 2 Lower threshold = 2 Crossover signals are provided when Trendline crisscrosses the Average line. OF Mode = 4: Cross below signals (brown spikes) OF Mode = 5: Cross above signals (blue spikes) Upper threshold = 2 Lower threshold = 2 82

86 83 OF Mode = 6: the input enters a range after crossing below the Upper line (blue curve) OF Mode = 7: the input enters a range after crossing above the Lower line (red curve) Upper threshold = 2 Lower threshold = 2 Confirmation period = 0

87 CSSA indicators 84 You might want to wait some time after entering a range to either exit or wait for a definite change in direction. Here, the Confirmation period is set to 100 bars. OF Mode = 6: the input enters a range after crossing below the Upper line (blue curve) OF Mode = 7: the input enters a range after crossing above the Lower line (red curve) Upper threshold = 2 Lower threshold = 2 Confirmation period = 100

88 85 TF Mode = 3: the trailing lines are triggered by the input series and drawn from the threshold series itself. In this example the upper and lower thresholds series are Bollinger Bands High and Low.

89 CSSA indicators 86