QuanTAlib/lib/oscillators/dem/Dem.md

DEM: DeMarker Oscillator

The trend is your friend — right up until DeMark starts counting against it.

Property	Value
Category	Oscillator
Inputs	OHLCV bar (TBar)
Parameters	period (default 14)
Outputs	Single series (Dem)
Output range	Varies (see docs)
Warmup	period + 1 bars
PineScript	dem.pine

• DEM (DeMarker Oscillator) is a bounded [0, 1] momentum oscillator that measures sequential demand pressure by comparing each bar's high and low aga...
• Similar: MACD, AO | Complementary: Volume | Trading note: DeMarker; compares current high/low to previous. Overbought >0.7, oversold <0.3.
• Validated against TA-Lib, Skender, and Tulip reference implementations where available.

DEM (DeMarker Oscillator) is a bounded [0, 1] momentum oscillator that measures sequential demand pressure by comparing each bar's high and low against the previous bar's high and low. It isolates bullish demand momentum in the numerator and bearish supply pressure in the denominator, then normalizes their ratio with SMA smoothing over a configurable period. Values near 0.7 signal overbought exhaustion; values near 0.3 signal oversold exhaustion. Neither external library in common use (TA-Lib, Skender, Tulip, Ooples) implements DeMarker, so self-consistency tests against batch/streaming/span modes serve as the primary validation.

Historical Context

Tom DeMark introduced the indicator in his 1994 book The New Science of Technical Analysis, published by John Wiley & Sons. DeMark's central thesis was that standard momentum indicators like RSI conflate bar-level price structure with inter-bar price continuation, producing a muddied signal. His fix was surgical: extract only the directional component of each bar by asking specifically whether the current bar's extreme extended beyond the prior bar's corresponding extreme.

The comparison is asymmetric by design. DeMax measures whether buyers pushed today's high above yesterday's high — pure buying initiative. DeMin measures whether sellers pushed today's low below yesterday's low — pure selling initiative. Bars where today's range falls entirely inside yesterday's range contribute zero to both, leaving the rolling SMA unchanged. This innards-of-the-range filtering is what distinguishes DEM from RSI, which responds to close-to-close changes and therefore blurs intrabar range dynamics with inter-session momentum.

DeMark's original publication discussed the oscillator in the context of his broader market timing research, which emphasized exhaustion patterns, sequential countdown structures (TD Sequential), and supply/demand imbalances. The 14-bar default period mirrors RSI's universal default, making side-by-side comparison natural. DEM tends to lead RSI at local turning points because it responds to bar-level range extensions rather than net close-to-close displacement.

The oscillator's bounded [0, 1] output — rather than RSI's [0, 100] — is a matter of convention. Some platforms scale DEM to [0, 100] by multiplying by 100. This implementation uses [0, 1] throughout, consistent with the normalized ratio form from DeMark's original derivation.

Architecture and Physics

1. Per-Bar Demand Extraction

On each bar, two non-negative scalars are computed:

\text{DeMax}_i = \max(H_i - H_{i-1},\; 0)

\text{DeMin}_i = \max(L_{i-1} - L_i,\; 0)

DeMax is positive when today's high exceeded yesterday's high — buyers extended the range. DeMin is positive when today's low undercut yesterday's low — sellers extended the range. If neither condition holds (inside bar), both contributions are zero.

The max(0, ...) clamp is load-bearing: it prevents inside bars from creating phantom negative pressure in the running sums. Inside bars carry no directional information in DeMark's framework.

2. SMA Smoothing via Circular Buffers

Both DeMax and DeMin are smoothed over N bars by simple moving average. The implementation maintains two circular buffers of size N with O(1) running sums:

Buffer	Contents	Running Sum
deMaxBuf	\text{DeMax}_i per bar	SMA numerator sum
deMinBuf	\text{DeMin}_i per bar	SMA denominator sum

On each new bar: subtract the outgoing slot value from the running sum, write the new value to the slot, add the new value to the running sum, advance the index modulo N. Cost: 2 subtractions + 2 additions + 2 array writes per bar regardless of period.

\overline{\text{DeMax}}_t = \frac{1}{N} \sum_{i=t-N+1}^{t} \text{DeMax}_i

\overline{\text{DeMin}}_t = \frac{1}{N} \sum_{i=t-N+1}^{t} \text{DeMin}_i

3. DEM Ratio and Division Guard

\text{DEM}_t = \frac{\overline{\text{DeMax}}_t}{\overline{\text{DeMax}}_t + \overline{\text{DeMin}}_t}

When the denominator is zero (flat market or inside-bar sequence contributing nothing to either SMA), the output falls back to 0.5 — the neutral midpoint. This is the mathematically correct neutral state: zero demand pressure and zero supply pressure are indistinguishable from equilibrium.

4. Warmup Semantics

DEM requires period + 1 bars before the first valid output. The first bar establishes prevHigh and prevLow with no DeMax/DeMin contribution (bootstrap). The following period bars fill the circular buffer. IsHot flips to true after period + 1 bars have been processed.

Mathematical Foundation

Parameter Mapping

Parameter	Symbol	Default	Range	Description
Period	N	14	[1, 5000]	SMA smoothing window

Range Proof

Claim: \text{DEM}_t \in [0, 1] always (excluding the zero-denominator guard, which returns exactly 0.5).

Proof: Both running sums are non-negative by construction (max(0, ...) clamps). The numerator \overline{\text{DeMax}}_t \geq 0 and the denominator \overline{\text{DeMax}}_t + \overline{\text{DeMin}}_t \geq \overline{\text{DeMax}}_t. Therefore the ratio is at most 1. Since the numerator is non-negative and the denominator is at least as large, the ratio is at least 0. QED.

Relationship to RSI

RSI computes a ratio of average gains to average gains plus average losses over close-to-close differences:

\text{RSI}_t = \frac{\overline{U}_t}{\overline{U}_t + \overline{D}_t}

where U_i = \max(C_i - C_{i-1}, 0) and D_i = \max(C_{i-1} - C_i, 0).

DEM substitutes bar-level range extensions for close-to-close differences:

\text{DEM}_t = \frac{\overline{\text{DeMax}}_t}{\overline{\text{DeMax}}_t + \overline{\text{DeMin}}_t}

Both are normalized ratios with the same algebraic structure. DEM's advantage at turning points is that inside bars — which RSI treats as momentum continuation if the close is unchanged — contribute zero to DEM, reducing response to consolidation noise.

Z-Domain Transfer Function

The SMA stage has transfer function:

H(z) = \frac{1}{N} \cdot \frac{1 - z^{-N}}{1 - z^{-1}}

This produces N-1 zeros on the unit circle at angles 2\pi k/N for k = 1, \ldots, N-1, suppressing all harmonics of the fundamental 1/N cycle. The DEM ratio is then a nonlinear combination of two FIR-filtered series.

Performance Profile

Operation Count (Streaming Mode)

DeMarker compares high/low extremes vs prior bar to build smoothed directional sums.

Operation	Count	Cost (cycles)	Subtotal
SUB × 2 (DeMax, DeMin raw)	2	1	2
MAX × 2 (clip to 0)	2	1	2
FMA × 2 (SMA/EMA smooth DeMax, DeMin)	2	4	8
DIV (DeMax / (DeMax + DeMin))	1	15	15
CMP (div-by-zero guard)	1	1	1
Total	8	—	~28 cycles

~28 cycles per bar. O(1) EMA smoothing on two running values.

Batch Mode (SIMD Analysis)

Operation	Vectorizable?	Notes
DeMax / DeMin computation	Yes	VSUBPD + VMAXPD (clip to 0)
EMA smoothing × 2	No	Recursive IIR — sequential
Division	Yes	VDIVPD after EMA passes

Operation	Cost	Notes
Per-bar Update	O(1)	2 buffer reads + 2 subtractions + 2 additions + 2 writes
Batch(Span)	O(n)	Stackalloc for period ≤ 256, ArrayPool otherwise
Memory	O(period)	Two double[] buffers + two snapshot arrays
Snapshot/restore	O(period)	Array.Copy for both buffers on isNew=true

Quality Metrics

Metric	Score	Notes
Smoothness	6/10	SMA introduces lag proportional to period
Responsiveness	7/10	Range extensions visible before close confirms
Noise rejection	6/10	Inside bars contribute zero — selective filtering
SMA lag	7 bars	At period=14, approximate half-period lag

Validation

No external library in the QuanTAlib test suite implements the DeMarker Oscillator:

Library	DEM Support	Notes
TA-Lib (TALib.NETCore)	No	Has DEMA (Double EMA) — different indicator
Skender.Stock.Indicators	No	Not implemented
Tulip (Tulip.NETCore)	No	Not implemented
OoplesFinance	No	Not implemented

Validation relies on self-consistency checks:

Test	Method	Result
Streaming == Batch	Compare Update loop vs Batch(Span)	Match to 1e-12
Constant price → 0.5	Flat market, zero DeMax + DeMin	0.5 exact
All rising → 1.0	Strictly rising highs, flat lows	1.0 exact
All falling → 0.0	Flat highs, strictly falling lows	0.0 exact
Math identity	Manual SMA recompute matches batch	Match to 1e-9
Range bound	500 GBM bars, all periods	All output in [0, 1]

Common Pitfalls

1. Period sensitivity at extremes. Period=1 produces binary output (0, 0.5, or 1.0 only), since a single bar's DeMax and DeMin directly determine the ratio. This is technically correct but produces a step function useless for trend identification. Periods below 5 are noisy in practice.

2. Misidentifying DEMA as DEM. TA-Lib contains a function named DEMA — this is the Double Exponential Moving Average, not the DeMarker Oscillator. The abbreviation collision has caused real confusion in the wild. Searching "DEMA" in financial code almost always returns the wrong indicator.

3. Inside-bar sequences produce 0.5. When the market consolidates inside a narrow range for an extended period, DeMax and DeMin both accumulate to zero. The output locks at 0.5 indefinitely. This is correct behavior, not a bug. It means "no directional information available," not "equilibrium between bulls and bears."

4. Divergence signal timing differs from RSI. DEM divergences tend to form 1–3 bars earlier than RSI divergences on the same data because DeMax/DeMin capture intrabar range extensions before those extensions appear in the closing price. Traders accustomed to RSI divergence timing need to adjust lookback windows.

5. The 0.3/0.7 thresholds are not universal. DeMark's original publication cited these levels, but they were calibrated for daily data on equity indices. Intraday futures data with frequent gap-opens will have different statistical distributions. Empirical threshold calibration per instrument is generally necessary.

6. Warmup period is period+1, not period. The first bar cannot contribute a DeMax or DeMin because there is no prior bar to compare against. Consumers who assume warmup equals period will have an off-by-one error in IsHot checks. The WarmupPeriod property returns period + 1.

7. Flat open without a gap. When High[i] == High[i-1] and Low[i] == Low[i-1] (exact repeat bar), the indicator produces zero for both components. This is not a degenerate case — it is a correctly priced inside bar contributing zero directional information.

References

• DeMark, Tom (1994). The New Science of Technical Analysis. John Wiley & Sons. ISBN 0-471-03548-3.
• DeMark, Tom (1997). New Market Timing Techniques. John Wiley & Sons. ISBN 0-471-14970-5.
• Colby, Robert W. (2003). The Encyclopedia of Technical Market Indicators (2nd ed.). McGraw-Hill. Entry: "DeMark Indicators."
• Pring, Martin J. (2002). Technical Analysis Explained (4th ed.). McGraw-Hill. Chapter on oscillator construction methodology.