QuanTAlib/lib/oscillators/td_seq/Td_seq.md

TD_SEQ: TD Sequential

Property	Value
Category	Oscillator
Inputs	OHLCV bar (TBar)
Parameters	None
Outputs	Single series (TdSeq)
Output range	Varies (see docs)
Warmup	comparePeriod + 1 bars

TL;DR

• TD Sequential is Tom DeMark's exhaustion counting system that identifies potential trend reversals through two phases: a 9-count Setup phase that d...
• No configurable parameters; computation is stateless per bar.
• Output range: Varies (see docs).
• Requires comparePeriod + 1 bars of warmup before first valid output (IsHot = true).
• Validated against TA-Lib, Skender, and Tulip reference implementations where available.

TD Sequential is Tom DeMark's exhaustion counting system that identifies potential trend reversals through two phases: a 9-count Setup phase that detects overextended trends, and a 13-count Countdown phase that pinpoints probable reversal timing. Unlike oscillators that measure momentum magnitude, TD Sequential counts consecutive qualifying bars, producing integer outputs (Setup: \pm 1 to \pm 9; Countdown: \pm 1 to \pm 13) that represent the progression toward exhaustion. A completed 9-count Setup followed by a completed 13-count Countdown signals high-probability trend exhaustion. All state is maintained in O(1) scalar variables with no buffers required.

Historical Context

Thomas DeMark developed TD Sequential during the 1970s-1990s as part of his comprehensive market timing framework, published in The New Science of Technical Analysis (1994) and New Market Timing Techniques (1997). The indicator was conceived as a structural alternative to momentum oscillators: rather than measuring how overbought or oversold a market is, it counts how long a directional condition has persisted and identifies specific exhaustion points. DeMark's key insight was that trends exhaust at predictable counting thresholds (9 for Setup, 13 for Countdown), a pattern he validated across equity, fixed-income, commodity, and currency markets. The indicator found significant institutional adoption, with Bloomberg terminals providing native DeMark indicators and firms like Tudor Investment Corporation licensing the methodology. The compare period (typically 4 bars) determines the lookback for the close comparison: each Setup bar requires close above/below close[4], creating a structural requirement that the trend has been sustained for at least 4 additional bars beyond the count itself. The Countdown phase adds a higher bar: the close must exceed the high or low of 2 bars ago, a condition that doesn't occur on every bar, making the Countdown non-consecutive.

Architecture & Physics

Two-Phase State Machine

Phase 1: Setup (\pm 1 to \pm 9)

The Setup counter compares the current close to the close comparePeriod bars ago. If close > close[comparePeriod], the sell setup count increments (positive); if close < close[comparePeriod], the buy setup count decrements (negative). The count resets to zero when the condition breaks or reverses direction. Counts are clamped to \pm 9.

When the count reaches exactly \pm 9 for the first time (without having been reset), the setup is "complete" and Phase 2 begins. The setupComplete flag prevents re-triggering until a reset occurs.

Phase 2: Countdown (\pm 1 to \pm 13)

After a completed 9-count Setup, the Countdown phase begins. Unlike Setup, Countdown is non-consecutive: a sell countdown bar requires close > high[2]; a buy countdown bar requires close < low[2]. Only qualifying bars increment the countdown. The count progresses toward \pm 13, at which point the countdown completes and the directional signal resets.

An opposite 9-count Setup during an active Countdown resets and restarts the Countdown in the new direction.

Zero-Buffer Design

The entire indicator state consists of four scalar variables: setupCount, countdownCount, countdownDir, and setupComplete. No circular buffers, arrays, or sliding windows are needed. The only historical lookback dependency is PineScript's close[comparePeriod], low[2], and high[2].

Mathematical Foundation

Setup counting (comparePeriod = p):

S_t = \begin{cases} S_{t-1} - 1 & \text{if } C_t < C_{t-p} \text{ and } S_{t-1} \leq 0 \\ -1 & \text{if } C_t < C_{t-p} \text{ and } S_{t-1} > 0 \\ S_{t-1} + 1 & \text{if } C_t > C_{t-p} \text{ and } S_{t-1} \geq 0 \\ +1 & \text{if } C_t > C_{t-p} \text{ and } S_{t-1} < 0 \\ 0 & \text{if } C_t = C_{t-p} \end{cases} S_t = \text{clamp}(S_t, -9, +9)

Setup completion trigger:

\text{if } |S_t| = 9 \text{ and not previously complete} \Rightarrow \text{begin Countdown, dir} = \text{sign}(S_t)

Countdown (non-consecutive):

CD_t = \begin{cases} CD_{t-1} - 1 & \text{if dir} = -1 \text{ and } C_t < L_{t-2} \\ CD_{t-1} + 1 & \text{if dir} = +1 \text{ and } C_t > H_{t-2} \\ CD_{t-1} & \text{otherwise (no qualifying bar)} \end{cases}

Countdown completion:

\text{if } |CD_t| \geq 13 \Rightarrow CD_t = \text{sign}(dir) \times 13, \text{ reset dir}

Countdown reset on opposite Setup:

\text{if dir} = +1 \text{ and } S_t = -9, \text{ or dir} = -1 \text{ and } S_t = +9 \Rightarrow \text{reset CD, new dir}

Default parameters: comparePeriod = 4.

Performance Profile

Operation Count (Streaming Mode)

TD Sequential counts sequential close comparisons (Setup: 9 bars; Countdown: 13 bars). Pure comparison arithmetic, no floating-point math.

Operation	Count	Cost (cycles)	Subtotal
CMP (close[0] > close[4]) setup count	1	1	1
CMP (close[2] ≤ close[0]) countdown	1	1	1
Counter increment/reset	2	1	2
RingBuffer reads × 2 (lag 2 and lag 4)	2	1	2
State encode (setup bar, countdown bar)	2	1	2
Total	8	—	~8 cycles

The cheapest oscillator in the library: purely integer comparisons and counters. ~8 cycles per bar.

Batch Mode (SIMD Analysis)

Operation	Vectorizable?	Notes
Lag-4 comparison (Setup)	Yes	VCMPPD on offset arrays
Lag-2 comparison (Countdown)	Yes	VCMPPD on offset arrays
Sequential counter	No	State-dependent — each bar depends on prior count

The counter state is inherently sequential. The individual comparisons are vectorizable in a pre-pass, but the sequential counting dependency prevents full SIMD acceleration.

Quality Metrics

Metric	Score	Notes
Accuracy	10/10	Exact binary comparisons; no floating-point
Timeliness	9/10	9-bar setup window is short; immediate signal
Smoothness	3/10	Discrete count output jumps at signal events
Noise Rejection	5/10	Sequential counting requires exact pattern; no noise tolerance

Resources

• DeMark, T.R. (1994). The New Science of Technical Analysis. Wiley
• DeMark, T.R. (1997). New Market Timing Techniques. Wiley
• Bloomberg Terminal: DeMark Indicators (DMRK) implementation reference
• PineScript reference: td_seq.pine