Time must be divided into quarters for a proper interpretation of market cycles. Blending the Quarterly Theory (not to be confused with the Quarters Theory) and basic ICT concepts leads to enhanced precision. Understanding Quarterly Theory allows to be flexible. It fits in with any style of trading, as it is universal to all time-frames. The Quarterly Theory removes ambiguity, as it gives specific time-based reference points to look for when entering trades. Before being able to apply this theory to trading, one must first understand that time is fractal:

Yearly Quarters = 4 quarters, three months each.
Monthly Quarters = 4 quarters, one week each.
Weekly Quarters = 4 quarters, one day each (Monday - Thursday). Friday has its own specific function.
Daily Quarters = 4 quarters, 6 hours each = 4 trading sessions of a trading day.
Sessions Quarters =  4 quarters, 90 minutes each.
90 Minutes Quarters =  4 quarters, 22.5 minutes each.

Yearly Quarters
Q1 - January, February, March
Q2 - April, May, June (True Open)
Q3 - July, August, September
Q4 - October, November, December

Monthly Quarters (starts with the first month’s Monday regardless of the date)
Q1 - Week 1, first Monday of the month
Q2 - Week 2, second Monday of the month (True Open)
Q3 - Week 3, third Monday of the month
Q4 - Week 4, fourth Monday of the month

Weekly Quarters (ignore Friday's and Sunday’s price action)
Q1 - Monday
Q2 - Tueday (True Open)
Q3 - Wednesday
Q4 - Thursday

Daily Quarters (EST/New York)
Q1 - 18:00 - 00:00 Asia
Q2 - 00:00 - 06:00 London (True Open)
Q3 - 06:00 - 12:00 NY AM
Q4 - 12:00 - 18:00 NY PM

90 Minute Quarters (EST/New York)
Q1 - 18:00 - 19:30
Q2 - 19:30 - 21:00 (True Open)
Q3 - 21:00 - 22:30
Q4 - 22:30 - 00:00

Micro Quarters (22.5 minute quarters; EST/New York)
Q1 - 18:00 - 18:22:30
Q2 - 18:22:30 - 18:45 (True Open)
Q3 - 18:45 - 19:07:30
Q4 - 19:07:30 - 19:30

The Monthly Cycle is comprised of four quarters, one week each. Start counting the quarters from the first full week, meaning if the first week relating to the traditional month is a partial week, it is omitted and viewed as distortion. The first full week of the month is the first quarter, the second week is the second quarter, the third week is the third quarter and the fourth week is the fourth quarter.

The Weekly Cycle is comprised of four quarters, one day each. Monday is the first quarter, Tuesday is the second quarter, Wednesday is the third quarter and Thursday is the fourth quarter. Friday is not included into the weekly cycle due to the fact that it has its own specific function.

The Daily Cycle is comprised of four quarters, six hours each, which perfectly aligns with the four trading sessions of a trading day. The first quarter is the Asian session, the second quarter is the London session, the third quarter is the New York session and the fourth quarter is the afternoon session. 
Each Session is comprised of four quarters, 90 minutes each. During the Asian session, the 90 minute cycles are as follows: 6pm to 7.30pm is the first quarter, 7.30pm to 9pm is the second quarter, 9pm to 10.30pm is the third quarter and 10.30pm to 12.00pm midnight is the fourth quarter. During the London session, the first quarter is 12.00am midnight to 1.30am. The second quarter is 1.30am to 3.00am. The third quarter is 3.00am to 4.30am. The fourth quarter is 4.30am to 6.00am. During the New York session, the first quarter is 6.00am to 7.30am. The second quarter is 7.30am to 9.00am. The third quarter is 9.00am to 10.30am. And the fourth quarter is 10.30am to 12.00pm. During the Afternoon session the first quarter is 12.00pm to 1.30pm. The second quarter is 1.30pm to 3.00pm. The third quarter is 3.00pm to 4.30pm. And the fourth quarter is 4.30pm to 6.00pm.

Now that we understand that time is fractal, we can begin to look into the functions of some of the quarters. Price is delivered by an algorithm. So there must be some initial input which is used to make decisions throughout each cycle. This is the function of Q1. Q1 dictates the quarters which follow, meaning Q1 is used as a barometer for forecasting market conditions in the subsequent quarters of each cycle. If the first quarter is overextended, expect the second quarter to consolidate, and if the first quarter is in a tight range, expect the second quarter to expand. 
True Opens are the main components of quarterly theory. There are specific openings of price which serve as a time-based filter for gauging manipulation swings or stop-hunts. True opens are the beginning of Q2 of every cycle.  True Opens are defined by these times:
  • Yearly True Open = 1st Monday of April.
  • Monthly True Open = 2nd Monday of the month.
  • Weekly True Open = 6:00 PM EST every Monday.
  • Daily True Open = 12:00 P.M (Midnight) EST time.
  • NY Session True Open = 7:30 A.M EST time.
  • Asian Session True Open = 7:30 P.M EST time.
  • London Session True Open = 1:30 A.M EST time. 
Buy below True Open. Sell above True Open.
It is a simple concept to understand. If you are bullish within a specific cycle, you want to buy below its true open, and if you are bearish within a specific cycle, you want to sell above its true open. This will increase your accuracy tremendously, as key levels usually rest above or below true opens. Every cycle has its own true open. The true year open is the opening price of the first Monday of April. The true month open is the opening price of the second Monday of the month. The true week open is Monday at 6 p.m. The true day open is 12 o'clock midnight. The true open of the age on session is 7 30 p.m. The true open of the London session is 1 30 a.m. The true open of the New York session is 7 30 a.m. And the true open of the afternoon session is 1 30 p.m. The image to the right depicts how true opens function during bullish market environments.

There are two sets of instructions that the algorithm follows:  

A = Accumulation (required for a cycle to occur)
M = Manipulation
D = Distribution
X = Reversal or Continuation

After a tight Q1 range the Q2 Manipulation Phase begins. ICT calls this the 'Judas Swing'. According to his algorithmic theory, the purpose of this fake move is to get traders offside. After Q2 the real move takes place: the Q3 distribution phase and is usually the easiest to trade as the previous quarter has already established a trend of the cycle. The fourth phase is which can either continue to establish range of the cycle or reverse. In regards to this example, the fourth quarter is reversal. As you can see, price reverses at Higher Time Frame Premium-Discount Arrays (PDAs) or key levels. 
 The AMD-Principle is represented in every bar of every time-frame (monthly, weekly, daily, 4 Hour, etc.) 
with a price value at which it starts trading (opening price), the highest price value (high), the lowest (low), 
and  a value of the time it ends trading (close).

Liquidity is induced when price breaches old highs and old lows while trading into key levels. If you usually trade with the one minute chart, you need a 15 minute PDA. If you usually trade with the five minute chart, you need a one hour PDA. If you usually trade with the 15 minute chart, you need a four hour PDA. If you usually trade with the one hour chart, you need a daily PDA. And if you usually trade with the four hour chart, you need a weekly PDA. 
Regarding X-AMD, the first quarter is the continuation or reversal of the previous Q. Of the previous cycle, using what we understand from the function of Q1, Q2 should then accumulate, resulting in high range price action. Q3 would then be the manipulation phase. However, the rules for the true opens are static. They don't change. The opening price of Q2 will always be its true open. So if the profile that you're looking at is X-AMD, even though accumulation takes place during Q2, you will use the opening price of Q2, which is its true open to gauge, the Judah swing, which will present itself more times or not in Q3. The last phase will be the distribution phase, which will be the easiest phase to trade in regards to X-AMD. 
Dividing a 90 Minute Cycle into 22.5 Minute Quarters (Micro Sessions).
Quarterly Theory - the Hack of the Algorithm?
Is this proof of the algorithm existing or not? I do think so;-) 
And it's mind blowing how this fractal quarterly theory happens over and over again.  

 S&P 500 (15 minute bars)
Week January 08 (Monday) to January 11 (Thu) =
X-AMD Weekly Quarters Template  +   
AMD-X Monthly Quarters Template  +   
X-AMD Yearly Quarters Template

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