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Miha Kralj
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- LTMA (Linear Trend Moving Average): Introduces a predictive moving average using dual cascaded EMAs for trend estimation. - MCNMA (McNicholl EMA): Implements a zero-lag TEMA using a cascaded EMA structure for enhanced responsiveness. - NLMA (Non-Lag Moving Average): Utilizes a damped cosine kernel to achieve reduced lag in moving averages. - NMA (Natural Moving Average): Adapts smoothing based on volatility profiles using a square-root kernel. - NYQMA (Nyquist Moving Average): Applies the Nyquist-Shannon theorem to prevent aliasing in cascaded moving averages. - RAIN (Rainbow Moving Average): Combines multiple SMA layers with weighted averages for multi-scale smoothing. - TRAMA (Trend Regularity Adaptive Moving Average): Adapts smoothing based on the frequency of new highs and lows in price data.
61 lines
4.8 KiB
Markdown
61 lines
4.8 KiB
Markdown
# TD_SEQ: TD Sequential
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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.
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## Historical Context
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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.
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## Architecture & Physics
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### Two-Phase State Machine
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**Phase 1: Setup ($\pm 1$ to $\pm 9$)**
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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 $\pm 9$.
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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.
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**Phase 2: Countdown ($\pm 1$ to $\pm 13$)**
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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.
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An opposite 9-count Setup during an active Countdown resets and restarts the Countdown in the new direction.
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### Zero-Buffer Design
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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]`.
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## Mathematical Foundation
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**Setup counting** (comparePeriod = $p$):
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$$S_t = \begin{cases} S_{t-1} - 1 & \text{if } C_t < C_{t-p} \text{ and } S_{t-1} \leq 0 \\ -1 & \text{if } C_t < C_{t-p} \text{ and } S_{t-1} > 0 \\ S_{t-1} + 1 & \text{if } C_t > C_{t-p} \text{ and } S_{t-1} \geq 0 \\ +1 & \text{if } C_t > C_{t-p} \text{ and } S_{t-1} < 0 \\ 0 & \text{if } C_t = C_{t-p} \end{cases}$$
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$$S_t = \text{clamp}(S_t, -9, +9)$$
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**Setup completion trigger:**
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$$\text{if } |S_t| = 9 \text{ and not previously complete} \Rightarrow \text{begin Countdown, dir} = \text{sign}(S_t)$$
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**Countdown** (non-consecutive):
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$$CD_t = \begin{cases} CD_{t-1} - 1 & \text{if dir} = -1 \text{ and } C_t < L_{t-2} \\ CD_{t-1} + 1 & \text{if dir} = +1 \text{ and } C_t > H_{t-2} \\ CD_{t-1} & \text{otherwise (no qualifying bar)} \end{cases}$$
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**Countdown completion:**
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$$\text{if } |CD_t| \geq 13 \Rightarrow CD_t = \text{sign}(dir) \times 13, \text{ reset dir}$$
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**Countdown reset on opposite Setup:**
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$$\text{if dir} = +1 \text{ and } S_t = -9, \text{ or dir} = -1 \text{ and } S_t = +9 \Rightarrow \text{reset CD, new dir}$$
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**Default parameters:** comparePeriod = 4.
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## Resources
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- DeMark, T.R. (1994). *The New Science of Technical Analysis*. Wiley
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- DeMark, T.R. (1997). *New Market Timing Techniques*. Wiley
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- Bloomberg Terminal: DeMark Indicators (DMRK) implementation reference
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- PineScript reference: [`td_seq.pine`](td_seq.pine)
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