# Inside the Currency Market: Currency Cycles--f(x) a X Cos (bx + c) + d

Currency Cycles--- Currency cycles are trading periods where certain currency pairs trade at their highs and lows within a given year. Its the measurement that is always questioned that dates this debate beginning with Charles Dow at the turn of the century when he found the 1/3 market correction. Market genius, Gann came next in the 1920's and built on Dow's 1/3 correction by factoring Time in relation to Price. In the early 1930's, Elliott, not my favorite, added more corrective lines, 5, and measured those lines in relation to Fibonnaci numbers to build on Gann. 1935, Harold Gartley found what we call today Gartley Patterns which are short term Fibonnaci patterns. In the 1950's Edson Gould, found Speed Resistance Lines, better known as 1/3, 2/3 market corrections. A currency cycle?

Now the modern day free float currency pair came along and a debate was held as to the length of a currency cycle. 12-16 weeks was the prevailing view set by the world's currency masters FX Concepts. They factored early 1980's models based on 16 weeks then further built on their models over years and shortened the length of their cycles. Today their mathematical models account for currerncy cycles of 13.3 weeks to be exact.Yet I use 13 weeks because it factors as 13 X 4=52 weeks. Its of vital importance in a mathematical model because of a chosen length and time frame for a moving average, calculating time in relation to price in whatever chosen manner. I don't exclude the Japanese who long calculated time in relation to price by Goichi Hosada's brilliant 1940's Ichimoku invention. I personally find none better than Chris Capre at 2nd Skies in his understanding of Ichimoku. The Japanese were long ahead of my United States examples that I present here. So now we want to measure cycles.

f (x)= a X cos (bx + c) + d. Market cycles here are measured by the Cosine wave and employed due because of James Hurst's 1970 classic book "Profit Magic of Stock Transaction Tiiming." Hurst is considered the father of modern day cycles but all Time and price models derived from market genius Gann who can be further seen in the latest edition of FX Trader magazine. I address much of what I speak here in my own book Inside the Currency Market but a further and detailed discussion can be found in "Technical Analysis, The Complete Resource for Financial Market Technicians", 2nd edition by Charles Kirkpatrick and Julie Dahlquist.

The formula: a=amplitude, bx= period ( constant b times X time in radians), c=phase in radians and d= error factor. This trigonometry formula is a complete trading method and if used correctly can be highly profitable. Why? because Time and Price can be measured accurately for perfect entry and exits and it serves as a complete signal system by some form as -1 to + 1 for example. + 1 would be the sell signal and -1 would be the buy signal. It almost eliminates candle chart reading because the Cosine wave would almost eliminate the need to view the charts. I'm in the process of relearning this trading method again after a 3 year hiatus in favor of my moving average system.

Explanation. f (x) is a function denoted by f but x is the input, an input that = x squared for example. F takes x and squares it, simple. F of X relates an input to an output as in height to age, weight to height, price to time. A= amplitude is the measure of the power, strength of the price move and calculates as Max minus Minimum/ 2 to determine the vertical stretch of the graph.

Bx = period (time) ( constant b times X time in radians). Period is the horizontal distance along the X axis between 2 points. One point starts the cycle the other point ends the cycle. b relates to 2 PI /b. We want to know the stretch or shrink on the X axis to determine compression or expansion. When will price get to its destination is the question here.

c= phase in radians. This is the signal aspect to this trading system denoted by the shift of the phase and measured by c/b. Is the shift moving left to right, right to left. One side will be positive the other negative and allows for the -1, +1 signals to generate. We can only know which way by the inputs entered into our time dimension denoted by Bx as well as the inputs entered into the phase.

Radians. A radian is a center circle projected forward by measure of lines B and A. Between A + B= amplitude, the a line. So a radian measures angles in degrees. 360 degrees in a circle, 90 degrees in a right angle and equilateral triangle =60 degrees. Radians=2 Pi radians in a circle. So 2 PI radians=360 degrees. Therefore, 1 radian=180/ PI and 1 degree=PI/180 radians. The next A and B line measures would be 195, 13 PI/ 112, 165, 11 PI/ 12.

Final Analysis. What we are doing here is drawing a complete circle that accounts for every A and B line with a measure of amplitude and time inside those A and B lines. A and B lines expand and contract and represent the signal aspect. A smaller amplitude signals compression while the wider amplitude signals expansion, sell and buy.  Radians are simply the measure of every degree of every A and B line accounted for within the full circle. The original formula above represents only a small portion of the calculation of only one set of A and B lines within the full circle. What the formula does is allow the A and B lines to be viewed from a sideways perspective with a top A line and bottom B. Both are measured by a centerline so we can plot the wave form within the A and B lines to allow a trading signal within the confines of the cycle as it hovers above or below the centerline. The time and price dimension would then factor for the 13 week currency cycle. This methodology is just another form of trading Time Series much as a moving average system but this aspect delves deeper by incorporating a factor of time. Its a small insight into the overall genius of Gann and his earlier time series methodologies.

Stay tuned as Brian Twomey again goes Inside the Currency Market. My Inside the Currency Market book is found at btwomey.com and a training syllabus is in the works and near completion for the select few.

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