Averages, MACD, AO and EWO: reproducible wave checks
Teaching tables and diagrams with explicit inputs, formulas, seeds, local conditions and limits when checking Elliott wave hypotheses.
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This lab connects indicators to a wave hypothesis through explicit calculations. Every example price, volume and parameter is invented. A positive indicator condition describes a local state; it does not establish an entire Elliott count or measure a probability of profit.
Invented inputs and calculation rules
The table contains completed bars. t is an ordinal index; O/H/L/C mean open/high/low/close and V is invented volume from one source, not an entire-market total. Dataset A has a preceding bar t=−1 with C=99, H=100, L=98. Windows include the current bar unless explicitly stated otherwise.
SMA_n is the mean of the latest n values. EMA_n uses α=2/(n+1) and RMA_n uses α=1/n; both recursions y_t=αx_t+(1−α)y_(t−1) start with the mean of the first n available values. Intermediate values are not rounded; tables display up to six decimals. “—” means insufficient history or an undefined value, not zero. Missing inputs are not replaced with zero. Short teaching periods are not recommended settings; the seeds and zero policies are declared here, without a claim of parity with every platform.
| Dataset | t | O | H | L | C | V |
|---|---|---|---|---|---|---|
| A | 0 | 99.5 | 101 | 99 | 100 | 10 |
| A | 1 | 101.5 | 103 | 101 | 102 | 12 |
| A | 2 | 100.5 | 102 | 100 | 101 | 8 |
| A | 3 | 103.5 | 105 | 103 | 104 | 15 |
| A | 4 | 102.5 | 104 | 102 | 103 | 9 |
| A | 5 | 105.5 | 107 | 105 | 106 | 20 |
| A | 6 | 103.5 | 105 | 103 | 104 | 11 |
| A | 7 | 106.5 | 108 | 106 | 107 | 18 |
| A | 8 | 104.5 | 106 | 104 | 105 | 14 |
| A | 9 | 107.5 | 109 | 107 | 108 | 22 |
| A | 10 | 103.5 | 105 | 103 | 104 | 16 |
| B | 0 | 99.5 | 101 | 99 | 100 | 10 |
| B | 1 | 101.9 | 103.4 | 101.4 | 102.4 | 11 |
| B | 2 | 99.3 | 100.8 | 98.8 | 99.8 | 12 |
| B | 3 | 101.7 | 103.2 | 101.2 | 102.2 | 13 |
| B | 4 | 99.1 | 100.6 | 98.6 | 99.6 | 14 |
| B | 5 | 101.5 | 103 | 101 | 102 | 15 |
| B | 6 | 103.9 | 105.4 | 103.4 | 104.4 | 16 |
| B | 7 | 101.3 | 102.8 | 100.8 | 101.8 | 10 |
| B | 8 | 103.7 | 105.2 | 103.2 | 104.2 | 11 |
| B | 9 | 101.1 | 102.6 | 100.6 | 101.6 | 12 |
| B | 10 | 103.5 | 105 | 103 | 104 | 13 |
| B | 11 | 105.9 | 107.4 | 105.4 | 106.4 | 14 |
| B | 12 | 103.3 | 104.8 | 102.8 | 103.8 | 15 |
| B | 13 | 105.7 | 107.2 | 105.2 | 106.2 | 16 |
| B | 14 | 103.1 | 104.6 | 102.6 | 103.6 | 10 |
| B | 15 | 105.5 | 107 | 105 | 106 | 11 |
| B | 16 | 107.9 | 109.4 | 107.4 | 108.4 | 12 |
| B | 17 | 105.3 | 106.8 | 104.8 | 105.8 | 13 |
| B | 18 | 107.7 | 109.2 | 107.2 | 108.2 | 14 |
| B | 19 | 105.1 | 106.6 | 104.6 | 105.6 | 15 |
| B | 20 | 107.5 | 109 | 107 | 108 | 16 |
| B | 21 | 109.9 | 111.4 | 109.4 | 110.4 | 10 |
| B | 22 | 107.3 | 108.8 | 106.8 | 107.8 | 11 |
| B | 23 | 109.7 | 111.2 | 109.2 | 110.2 | 12 |
| B | 24 | 107.1 | 108.6 | 106.6 | 107.6 | 13 |
| B | 25 | 109.5 | 111 | 109 | 110 | 14 |
| B | 26 | 111.9 | 113.4 | 111.4 | 112.4 | 15 |
| B | 27 | 109.3 | 110.8 | 108.8 | 109.8 | 16 |
| B | 28 | 111.7 | 113.2 | 111.2 | 112.2 | 10 |
| B | 29 | 109.1 | 110.6 | 108.6 | 109.6 | 11 |
| B | 30 | 111.5 | 113 | 111 | 112 | 12 |
| B | 31 | 113.9 | 115.4 | 113.4 | 114.4 | 13 |
| B | 32 | 111.3 | 112.8 | 110.8 | 111.8 | 14 |
| B | 33 | 113.7 | 115.2 | 113.2 | 114.2 | 15 |
| B | 34 | 111.1 | 112.6 | 110.6 | 111.6 | 16 |
| B | 35 | 113.5 | 115 | 113 | 114 | 10 |
| B | 36 | 115.9 | 117.4 | 115.4 | 116.4 | 11 |
| B | 37 | 113.3 | 114.8 | 112.8 | 113.8 | 12 |
| B | 38 | 115.7 | 117.2 | 115.2 | 116.2 | 13 |
| B | 39 | 113.1 | 114.6 | 112.6 | 113.6 | 14 |
Can an early undefined indicator value be replaced by zero and counted as a negative signal?
No. A missing full window and a calculated zero are different states; freeze the warm-up policy in advance.
SMA: the mean of a declared window
Three closes have equal weights; the oldest leaves as the window advances. Formula and worked calculation: SMA3_t=(C_t+C_(t−1)+C_(t−2))/3. t2: (100+102+101)/3=101. t7: (106+104+107)/3=105.666667.
The first full window is t2; earlier values are undefined. SMA3_seed in the EMA table is a rolling three-bar reference, not a new EMA seed on every bar.
Local research predicate: t7: C>SMA3. C>SMA3 holds at t7, but the line reacts to prices that have already occurred. Comparison with a lagging mean cannot choose between two otherwise valid wave counts.
| t | C | SMA3 |
|---|---|---|
| 0 | 100 | — |
| 1 | 102 | — |
| 2 | 101 | 101 |
| 3 | 104 | 102.333333 |
| 4 | 103 | 102.666667 |
| 5 | 106 | 104.333333 |
| 6 | 104 | 104.333333 |
| 7 | 107 | 105.666667 |
| 8 | 105 | 105.333333 |
| 9 | 108 | 106.666667 |
| 10 | 104 | 105.666667 |
Reproduce the highlighted calculation and evaluate the local predicate. Does the result establish the entire wave count?
107>105.666667. No. It is the result of the stated calculation on invented data, not proof of a wave structure or profit.
EMA: a recursion with a declared seed
EMA3 uses α=1/2; its first value is SMA3 at t2, followed by recursive EMA updates. Formula and worked calculation: EMA3_t=0.5C_t+0.5EMA3_(t−1). EMA3_2=101; EMA3_6=104.1875; EMA3_7=0.5×107+0.5×104.1875=105.59375.
Seeding with the first close would produce a different short history. Freeze C as source, α and the SMA seed before comparing platforms; do not backfill warm-up values.
Local research predicate: t7: C>EMA3. C>EMA3 at t7 describes price position, not proof of a third wave. Faster response than an SMA does not make EMA an independent source of evidence.
| t | C | SMA3(C) | EMA3 |
|---|---|---|---|
| 0 | 100 | — | — |
| 1 | 102 | — | — |
| 2 | 101 | 101 | 101 |
| 3 | 104 | 102.333333 | 102.5 |
| 4 | 103 | 102.666667 | 102.75 |
| 5 | 106 | 104.333333 | 104.375 |
| 6 | 104 | 104.333333 | 104.1875 |
| 7 | 107 | 105.666667 | 105.59375 |
| 8 | 105 | 105.333333 | 105.296875 |
| 9 | 108 | 106.666667 | 106.648438 |
| 10 | 104 | 105.666667 | 105.324219 |
Reproduce the highlighted calculation and evaluate the local predicate. Does the result establish the entire wave count?
107>105.59375. No. It is the result of the stated calculation on invented data, not proof of a wave structure or profit.
MACD: line, signal and histogram
The teaching version is EMA3−EMA5 with an EMA2 signal; the histogram is line minus signal. Formula and worked calculation: M=EMA3(C)−EMA5(C); S=EMA2(M); h=M−S. t7: M=105.59375−104.7037037037=0.890046; S=0.833333; h=0.056713.
EMA3 starts at t2; EMA5 and M at t4. The signal is seeded with the mean of M4 and M5 at t5. No histogram exists before t5. Other average types or seeds change values.
Local research predicate: t7: h>0. h>0 means M>S, not necessarily M>0 or a crossing on that particular bar. Both inequalities hold at t7; they cannot be counted as two independent confirmations.
| t | C | EMA3 | EMA5 | MACD | S_EMA2 | h=M−S |
|---|---|---|---|---|---|---|
| 0 | 100 | — | — | — | — | — |
| 1 | 102 | — | — | — | — | — |
| 2 | 101 | 101 | — | — | — | — |
| 3 | 104 | 102.5 | — | — | — | — |
| 4 | 103 | 102.75 | 102 | 0.75 | — | — |
| 5 | 106 | 104.375 | 103.333333 | 1.041667 | 0.895833 | 0.145833 |
| 6 | 104 | 104.1875 | 103.555556 | 0.631944 | 0.719907 | -0.087963 |
| 7 | 107 | 105.59375 | 104.703704 | 0.890046 | 0.833333 | 0.056713 |
| 8 | 105 | 105.296875 | 104.802469 | 0.494406 | 0.607382 | -0.112976 |
| 9 | 108 | 106.648438 | 105.868313 | 0.780125 | 0.722544 | 0.057581 |
| 10 | 104 | 105.324219 | 105.245542 | 0.078677 | 0.293299 | -0.214622 |
Reproduce the highlighted calculation and evaluate the local predicate. Does the result establish the entire wave count?
0.8900462962962963−0.8333333333333334=0.056712962962963>0. No. It is the result of the stated calculation on invented data, not proof of a wave structure or profit.
Awesome Oscillator: complete windows of 5 and 34
This uses separate dataset B with 40 bars; HL2 is the midpoint of H and L. Formula and worked calculation: HL2=(H+L)/2; AO=SMA5(HL2)−SMA34(HL2). t39: 114.8−109=5.8.
SMA34 first exists at t33. Earlier rows remain “—” rather than using a shortened mean. No signal line has been added to this definition.
Local research predicate: t39: AO5_34>0. AO>0 at t39 means the short average exceeds the long average, not an automatic wave-three label. Our symmetric artificial bars make HL2=C, so AO and EWO are especially dependent here.
| t | C | HL2 | SMA5(HL2) | SMA34(HL2) | AO5/34 |
|---|---|---|---|---|---|
| 0 | 100 | 100 | — | — | — |
| 1 | 102.4 | 102.4 | — | — | — |
| 2 | 99.8 | 99.8 | — | — | — |
| 3 | 102.2 | 102.2 | — | — | — |
| 4 | 99.6 | 99.6 | 100.8 | — | — |
| 5 | 102 | 102 | 101.2 | — | — |
| 6 | 104.4 | 104.4 | 101.6 | — | — |
| 7 | 101.8 | 101.8 | 102 | — | — |
| 8 | 104.2 | 104.2 | 102.4 | — | — |
| 9 | 101.6 | 101.6 | 102.8 | — | — |
| 10 | 104 | 104 | 103.2 | — | — |
| 11 | 106.4 | 106.4 | 103.6 | — | — |
| 12 | 103.8 | 103.8 | 104 | — | — |
| 13 | 106.2 | 106.2 | 104.4 | — | — |
| 14 | 103.6 | 103.6 | 104.8 | — | — |
| 15 | 106 | 106 | 105.2 | — | — |
| 16 | 108.4 | 108.4 | 105.6 | — | — |
| 17 | 105.8 | 105.8 | 106 | — | — |
| 18 | 108.2 | 108.2 | 106.4 | — | — |
| 19 | 105.6 | 105.6 | 106.8 | — | — |
| 20 | 108 | 108 | 107.2 | — | — |
| 21 | 110.4 | 110.4 | 107.6 | — | — |
| 22 | 107.8 | 107.8 | 108 | — | — |
| 23 | 110.2 | 110.2 | 108.4 | — | — |
| 24 | 107.6 | 107.6 | 108.8 | — | — |
| 25 | 110 | 110 | 109.2 | — | — |
| 26 | 112.4 | 112.4 | 109.6 | — | — |
| 27 | 109.8 | 109.8 | 110 | — | — |
| 28 | 112.2 | 112.2 | 110.4 | — | — |
| 29 | 109.6 | 109.6 | 110.8 | — | — |
| 30 | 112 | 112 | 111.2 | — | — |
| 31 | 114.4 | 114.4 | 111.6 | — | — |
| 32 | 111.8 | 111.8 | 112 | — | — |
| 33 | 114.2 | 114.2 | 112.4 | 106.658824 | 5.741176 |
| 34 | 111.6 | 111.6 | 112.8 | 107 | 5.8 |
| 35 | 114 | 114 | 113.2 | 107.341176 | 5.858824 |
| 36 | 116.4 | 116.4 | 113.6 | 107.829412 | 5.770588 |
| 37 | 113.8 | 113.8 | 114 | 108.170588 | 5.829412 |
| 38 | 116.2 | 116.2 | 114.4 | 108.658824 | 5.741176 |
| 39 | 113.6 | 113.6 | 114.8 | 109 | 5.8 |
Reproduce the highlighted calculation and evaluate the local predicate. Does the result establish the entire wave count?
114.8−109=5.8>0. No. It is the result of the stated calculation on invented data, not proof of a wave structure or profit.
EWO: the selected 5/35 version
For reproducibility, EWO is defined as SMA5(C)−SMA35(C), with no normalization or extra signal. The name does not specify a unique implementation. Formula and worked calculation: EWO5_35=SMA5(C)−SMA35(C). B, t39: 114.8−108.8=6.
All 35 closes are required: the first value is at dataset B’s t34. An EMA, another source or a normalized version requires a separate calculation.
Local research predicate: t39: EWO5_35>0. A positive EWO neither numbers waves nor checks overlap rules. EWO=6 versus AO=5.8 here comes from windows 35 and 34, not two independent assessments of the market.
| t | C | SMA5(C) | SMA35(C) | EWO5/35 |
|---|---|---|---|---|
| 0 | 100 | — | — | — |
| 1 | 102.4 | — | — | — |
| 2 | 99.8 | — | — | — |
| 3 | 102.2 | — | — | — |
| 4 | 99.6 | 100.8 | — | — |
| 5 | 102 | 101.2 | — | — |
| 6 | 104.4 | 101.6 | — | — |
| 7 | 101.8 | 102 | — | — |
| 8 | 104.2 | 102.4 | — | — |
| 9 | 101.6 | 102.8 | — | — |
| 10 | 104 | 103.2 | — | — |
| 11 | 106.4 | 103.6 | — | — |
| 12 | 103.8 | 104 | — | — |
| 13 | 106.2 | 104.4 | — | — |
| 14 | 103.6 | 104.8 | — | — |
| 15 | 106 | 105.2 | — | — |
| 16 | 108.4 | 105.6 | — | — |
| 17 | 105.8 | 106 | — | — |
| 18 | 108.2 | 106.4 | — | — |
| 19 | 105.6 | 106.8 | — | — |
| 20 | 108 | 107.2 | — | — |
| 21 | 110.4 | 107.6 | — | — |
| 22 | 107.8 | 108 | — | — |
| 23 | 110.2 | 108.4 | — | — |
| 24 | 107.6 | 108.8 | — | — |
| 25 | 110 | 109.2 | — | — |
| 26 | 112.4 | 109.6 | — | — |
| 27 | 109.8 | 110 | — | — |
| 28 | 112.2 | 110.4 | — | — |
| 29 | 109.6 | 110.8 | — | — |
| 30 | 112 | 111.2 | — | — |
| 31 | 114.4 | 111.6 | — | — |
| 32 | 111.8 | 112 | — | — |
| 33 | 114.2 | 112.4 | — | — |
| 34 | 111.6 | 112.8 | 106.8 | 6 |
| 35 | 114 | 113.2 | 107.2 | 6 |
| 36 | 116.4 | 113.6 | 107.6 | 6 |
| 37 | 113.8 | 114 | 108 | 6 |
| 38 | 116.2 | 114.4 | 108.4 | 6 |
| 39 | 113.6 | 114.8 | 108.8 | 6 |
Reproduce the highlighted calculation and evaluate the local predicate. Does the result establish the entire wave count?
114.8−108.8=6>0. No. It is the result of the stated calculation on invented data, not proof of a wave structure or profit.
MACD divergence: compare the line, not the histogram
Compare H at t5 and t7 with MACD3/5 at those same bars. Do not select indicator extremes from different timestamps. Formula and worked calculation: H5=107 < H7=108; MACD3/5_5=1.041667 > MACD3/5_7=0.890046; τ_avail=8.
The price-pivot rule requires one completed bar on each side, with pivot H strictly above both neighbors. Thus t5 is confirmed at t6, t7 at t8, and the pair is available only at t8. MACD3/5 uses the formula and seeds declared above.
Local research predicate: t8: H7>H5 ∧ MACD3/5_7<MACD3/5_5 ∧ τ_avail(p7)≤8. Price makes a higher high while MACD3/5 is lower: that is the declared bearish divergence. Yet later H9=109 and C9=108 move higher again. The observation promises no lasting reversal, proves no wave-five completion and permits no backdated entry at t7.
| t | C | H | MACD |
|---|---|---|---|
| 0 | 100 | 101 | — |
| 1 | 102 | 103 | — |
| 2 | 101 | 102 | — |
| 3 | 104 | 105 | — |
| 4 | 103 | 104 | 0.75 |
| 5 | 106 | 107 | 1.041667 |
| 6 | 104 | 105 | 0.631944 |
| 7 | 107 | 108 | 0.890046 |
| 8 | 105 | 106 | 0.494406 |
| 9 | 108 | 109 | 0.780125 |
| 10 | 104 | 105 | 0.078677 |
Reproduce the highlighted calculation and evaluate the local predicate. Does the result establish the entire wave count?
108>107; 1.041667>0.890046; τ_avail=8≠7; H9=109. No. It is the result of the stated calculation on invented data, not proof of a wave structure or profit.
A testable condition and a wave strategy
For a study, freeze the source, timeframe, parameters, formula, availability time and alternative wave count first. Each section gives a local predicate with a threshold chosen for arithmetic practice. Record both positive and negative outcomes at bar close without selecting settings after seeing the result. Check a structural wave-rule violation from price separately.
RSI, averages, MACD and other price transforms share overlapping inputs. Several agreeing lines are not independent votes and do not supply probabilities that can be multiplied. A strategy test needs a separate sample and a predeclared outcome; simulated trades also need execution and cost assumptions. This lab supplies no trading performance, accuracy rate or product features.
| Value | Local research predicate |
|---|---|
| SMA: the mean of a declared window | t7: C>SMA3 |
| EMA: a recursion with a declared seed | t7: C>EMA3 |
| MACD: line, signal and histogram | t7: h>0 |
| Awesome Oscillator: complete windows of 5 and 34 | t39: AO5_34>0 |
| EWO: the selected 5/35 version | t39: EWO5_35>0 |
| MACD divergence: compare the line, not the histogram | t8: H7>H5 ∧ MACD3/5_7<MACD3/5_5 ∧ τ_avail(p7)≤8 |
Three price transforms agree. Does that provide three independent confirmations and establish the count?
No. Shared inputs create dependence; local filters are checked separately from price rules, and usefulness needs another sample.
EWO: regular divergence and confirmation time
New invented dataset R contains 50 completed bars. The table supplies C; H=C+1 and L=C−1. EWO is specifically SMA5(C)−SMA35(C), using a full 35-bar history, not a universal oscillator definition. At price highs t 36/t 46, H rises 147→149 while EWO falls 17.571429→15.4. Compare oscillator readings at the price pivots, not independently chosen oscillator peaks.
Our high pivot needs one lower H on each side. Thus t 36 is known at close 37, t 46 at 47; divergence is available at 47. A conditional bearish scenario needs a new close below L47=144 by the end of 49. At 49 a new H=151 exceeds H46=149: the divergence did not guarantee reversal. Neither its presence nor absence establishes a wave number.
| t | C | H | L | RSI3 | MACD3/5 | EWO5/35 |
|---|---|---|---|---|---|---|
| 0 | 100 | 101 | 99 | — | — | — |
| 1 | 101 | 102 | 100 | — | — | — |
| 2 | 102 | 103 | 101 | 100 | — | — |
| 3 | 103 | 104 | 102 | 100 | — | — |
| 4 | 104 | 105 | 103 | 100 | 1 | — |
| 5 | 105 | 106 | 104 | 100 | 1 | — |
| 6 | 106 | 107 | 105 | 100 | 1 | — |
| 7 | 107 | 108 | 106 | 100 | 1 | — |
| 8 | 108 | 109 | 107 | 100 | 1 | — |
| 9 | 109 | 110 | 108 | 100 | 1 | — |
| 10 | 110 | 111 | 109 | 100 | 1 | — |
| 11 | 111 | 112 | 110 | 100 | 1 | — |
| 12 | 112 | 113 | 111 | 100 | 1 | — |
| 13 | 113 | 114 | 112 | 100 | 1 | — |
| 14 | 114 | 115 | 113 | 100 | 1 | — |
| 15 | 115 | 116 | 114 | 100 | 1 | — |
| 16 | 116 | 117 | 115 | 100 | 1 | — |
| 17 | 117 | 118 | 116 | 100 | 1 | — |
| 18 | 118 | 119 | 117 | 100 | 1 | — |
| 19 | 119 | 120 | 118 | 100 | 1 | — |
| 20 | 120 | 121 | 119 | 100 | 1 | — |
| 21 | 121 | 122 | 120 | 100 | 1 | — |
| 22 | 122 | 123 | 121 | 100 | 1 | — |
| 23 | 123 | 124 | 122 | 100 | 1 | — |
| 24 | 124 | 125 | 123 | 100 | 1 | — |
| 25 | 125 | 126 | 124 | 100 | 1 | — |
| 26 | 126 | 127 | 125 | 100 | 1 | — |
| 27 | 127 | 128 | 126 | 100 | 1 | — |
| 28 | 128 | 129 | 127 | 100 | 1 | — |
| 29 | 129 | 130 | 128 | 100 | 1 | — |
| 30 | 130 | 131 | 129 | 100 | 1 | — |
| 31 | 131 | 132 | 130 | 100 | 1 | — |
| 32 | 132 | 133 | 131 | 100 | 1 | — |
| 33 | 133 | 134 | 132 | 100 | 1 | — |
| 34 | 134 | 135 | 133 | 100 | 1 | 15 |
| 35 | 140 | 141 | 139 | 100 | 1.833333 | 15.857143 |
| 36 | 146 | 147 | 145 | 100 | 2.805556 | 17.571429 |
| 37 | 140 | 141 | 139 | 55.737705 | 1.662037 | 18.085714 |
| 38 | 139 | 140 | 138 | 50.184502 | 0.837191 | 18.257143 |
| 39 | 140 | 141 | 139 | 56.661316 | 0.589378 | 18.428571 |
| 40 | 141 | 142 | 140 | 63.73405 | 0.57521 | 17.6 |
| 41 | 142 | 143 | 141 | 70.865929 | 0.641286 | 15.771429 |
| 42 | 143 | 144 | 142 | 77.502344 | 0.723097 | 15.342857 |
| 43 | 144 | 145 | 143 | 83.231766 | 0.796518 | 15.314286 |
| 44 | 145 | 146 | 144 | 87.866702 | 0.854905 | 15.285714 |
| 45 | 146 | 147 | 145 | 91.422913 | 0.89855 | 15.257143 |
| 46 | 148 | 149 | 147 | 95.435985 | 1.096673 | 15.4 |
| 47 | 145 | 146 | 144 | 46.492079 | 0.479936 | 14.857143 |
| 48 | 144 | 145 | 143 | 37.003533 | 0.0277 | 13.971429 |
| 49 | 150 | 151 | 149 | 77.793168 | 0.872339 | 13.942857 |
Check availability
The second pivot becomes available only after the completed right-hand bar; structural validation is separate.