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  • Auto-Hurst
  • SSA Decomposition
  • HP Decomposition
  • Henderson Filter
  • Statistical Analogs
  • Hull Moving Ave.
  • MESA spectrum
  • MESA dominant period
  • MEM linear prediction
  • SSA prediction
  • Mirror Image
  • comes with download enabled HLC Chart template
XLCycles gives you the time series analysis tools you need to decompose a market into easily forecasted cyclical components. You also get a powerful tool for finding statistical market analogs, the ability to mirror price action and tools for entropic methods.

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Solution Graphics

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Our goal is to make investing more of a science and less of a gamble. The scientific time-series analysis tools contained in XLCycles and XLCycle.xll make that possible.
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XLCycles had been reorganized and has new added features. The XLTrader group has two sections: Filters and Prediction. Filters has tools to decompose the time series and prediction has tools to forecast the time series. Usually filters and forecasts are done simultaneously. There is also a "light switch" and arrows in the group which are used to adjust the curve by tweaking the appropriate variables in the first few rows of the data sheet.

Most market observers agree that there are regular oscillations between periods of optimism and pessimism. These mood swings correlate well with rising and falling markets. To take advantage of these cycles we extract the regular oscillations. XLCycles has the state-of-the-art tools that investors of yesterday could only dream about, that we need to apply time-series analysis to the study of cycles.

First there was Claud Cleeton who used Trigonometric regression as explained in his 1976 book: The Art of Independent Investing. XLCycles can do Trigonometric regression. Then there was Herb Brooks who wrote: Investing with a Computer--A Time-Series Analysis approach, who pioneered the use of digital filters. And of course there is John Ehlers, today's foremost cycle analyst. But the best known cycle technician is J.M. Hurst. In 1970 Hurst penned what's become a classic: The Profit Magic of Stock Transaction Timing, in which he argues persuasively in favor of short term trading using cycles.

Trained as an electrical engineer, Hurst's innovation was to use Fourier analysis to detect sinusoids in stock market returns. That had never been done before and proved scientifically the existence of regular oscillations in the DJIA. However, as John Ehlers says on his website, Fourier analysis is not a good choice for stock market time series. Burg's method, also known as Maxiumum Entropy Spectral Analysis (MESA) is much better and is included in XLCycles. But what's even more exciting than MESA is a relative newcomer to the time-series analyst's tool box: Singular Spectrum Analysis (SSA).

Imagine if you will a rock quarry where heavy machinery operators carve out hillsides and dump huge buckets of earth onto a belt which streams it into a sieve. The sieve's job is to sift through the rocks and debris separating the gravel from the stones from the boulders. In essence the job of the sieve is to make "order out of chaos". What we need is a "cycle sieve" to extract order out of the chaos streaming out of the markets.

Necessity being the mother of invention, pioneering chaos theoreticians (first by Lorenz in 1956 then later, Takens, Broomhead & King, Famer & Packard and others) came up with a way to separate the cyclical "wheat from the chafe".

When there is an attractor, the data will reside in a small subspace of the time delay embedding space.... We can define a new set of vectors to eliminate the redundant information that are orthogonal, thus independent

The mathematics behind SSA is known by many names: PCA, Principal Value Decomposition, Singular Value Decomposition, Singular System Analysis, bi-orthoganal decomposition, Karmen Loeve decomposition and the Caterpillar method. But all you need to know is that SSA separates the time series into empirical orthogonal function EOF's or statistical "modes". Usually the majority of the variance in the time-series is contained in the first few EOF's. The patterns of those first few EOF's may be linked to dynamic mechanisms such as the trend and the cycles.

Its a "model-free" statistical approach to "feature detection" in a time-series. Like the sieve at the rock quarry, the SSA algorithm takes data and separates it into statistically independent "streams". These independent data streams are, unlike Mesa or Fourier methods, are not forced to conform to a Trigonometric function (or any other function for that matter). As if by magic, SSA extracts order from chaos… and by chaos I mean: the non-linear dynamic system (NLDS) that is presumed to be largely unknowable yet responsible for causing the regular oscillations with which we are all so familiar.

Take a moment to watch a demonstration of XLCycles

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In XLCycles you also get the eigen function plot from an SSA decomposition to help you decide which eigenvectors to use in the smoothed reconstruction. You get an algorithm for performing Trigonometric regression as described in Hurst appendix 6 (and in Cleeton). You get the MESA frequency spectrum. You get a search algorithm that finds market analogies based on Spearman's correlation, a statistical funcltion. You get a mirror image foldback function and you get some entropy functions which have been discussed recently in TASC magazine and elsewhere. Last but not least, all of the functions on the XLL can be called by your own custom formulas and VBA macros.


Singular Spectrum Analysis aka Caterpillar

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We use SSA to separate the trend from the cycles. The cycles are further separated from smallest to largest. We toss out the smallest cycles (the noise) and we reconstruct a smoothed replica of the original. We forecast the trend and the cycles we've retained into the future using either SSA or MEM (maximum entropy method). What we end up with is a scientifically based time-series prediction of where the market is likely headed. While, this all may sound complex and confusing, the XLCycles addin makes it easy.

Because of the intensive matrix calculations involved, all algorithms are in a complied XLL. The XLCycles addin access' the functions in the XLL for you and is designed to work with the event-enabled templates. The functions are accessible from either the Trading day or Calender day charts When you click on the SSA button, a form pops up asking you to select and confirm a data series.

Clicking on the "YES" button automatically takes you to the data sheet where where the "time pattern filter and forecast" form pops up. This is where you specify the details of the analysis and (optional) forecast. You are also asked to specify a column where the results will be put. The figures below show SSA results from both individual component and and smoothed reconstruction.

Automatic Hurst using SSA

cyclesautohurstOne of the new feature is called Automatic Hurst. It uses a combination of SSA analysis to extract and project the cycles. The parameters used in the analysis are a starting point. You can change them as you see fit.


SSA Eigenvectors

When we perform an SSA analysis, we specify the time delay embedding dimension. This value specifies the number of EOF's or statistically independent data streams the time series will be separated into. As mentioned above, most of the time series variance is contained in the first few EOF's. The trend component is almost always the first one. When a cycle is present, it will appear as a pair of EOF's which have nearly identical variance. The eigenvector plot lets us visually inspect how the variance is distributed amongs EOF's


Trigonometric Regression

The Trigonometric regression algorithm will calculate from the time-series the two dominant sinusoids and a linear trend component. It also lets you forecast the resulting equation into the future.


Hodrick-Prescott Decomposition

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Another new feature is the Hodrick-Prescott filter. Its like the SSA but has fewer adjustable parameters and extracts either the Trend or the Cyclical components from the time series.cycles_hpma


Hull Moving Average

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The Hull moving average was discussed in the January 2011 issue of TASC. Its quite responsive and smooth.


Mesa Dominant Period

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Use the Mesa dominant period to as a variable input to other indicators. In a trend it will saturate at a value of 50 (bars).


Henderson Filter

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The 13 point Henderson filter is ideal for smoothing out a noisy time series. You should be aware that it has a future leak. Do not try to use it as a tracking filter.


Mesa Spectrum

cyclesmemspec The MESA power spectrum plot will calculate for you the dominant periods in the series. Shown below is a MESA power spectrum on the midpoint which gets plotted on the secondary axis and shows cyclical peaks at 10 and 24 bars.


Mirror Image Foldback

Its amazing how many times the market mirrors what happened prior to a major CIT. This module lets you click on and data point as see what would happen if the market reflects what came before.


Entropy

If you are a subscriber to Technical Analysis of Stocks and Commodities magazine then you may have read about "ENTROPY". This module lets you easily calculate those functions (both entropy and probablity). (BTW… The place to learn more about entropic methods is John Conover's NTROPIX website).


Prediction Methods

cycleslpcyclespatterncyclesssaextrap XLCycles provides two ways to forecast something. The first is linear prediction using MEM (maxium entropy). This is the same thing as an AR model. The second method is using SSA.cycles_mem_lp


Market Analogs

The other new feature added is the Market Analog. This method looks for times in the past when the market had a pattern similar to the current one. The critereon is base on Spearman's correlation. It then projects what happened. The seven closest matching occurrences are plotted along with an average. cycles_market_analogs