Miha Kralj
90d5638008
- 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.
4.9 KiB
VWAPSD: VWAP with Standard Deviation Bands
VWAP with Standard Deviation Bands combines the Volume Weighted Average Price with a single configurable standard deviation band pair, providing a simpler alternative to VWAPBANDS (which uses dual \pm 1\sigma and \pm 2\sigma levels). Three running sums enable O(1) streaming updates. A session reset mechanism clears accumulations at configurable intervals, keeping the indicator anchored to current market structure. The configurable deviation parameter allows traders to select their desired confidence level (1\sigma ≈ 68%, 2\sigma ≈ 95%, 3\sigma ≈ 99.7%).
Historical Context
VWAP emerged in the 1980s as institutional traders needed a benchmark reflecting actual market participation. Berkowitz, Logue, and Noser (1988) established VWAP as the standard for measuring execution quality. The concept is straightforward: weight each price by the volume traded at that price, producing an average that reflects where the most conviction-backed trading occurred.
The standard deviation extension follows the same reasoning as Bollinger Bands but applied to volume-weighted statistics. By adding bands at n standard deviations from VWAP, the indicator creates a statistically grounded channel that adapts to actual volume-weighted volatility.
VWAPSD differs from VWAPBANDS only in output structure: VWAPSD emits one band pair at a configurable distance, while VWAPBANDS always emits two band pairs (\pm 1\sigma and \pm 2\sigma). The underlying VWAP and variance calculations are identical.
Architecture & Physics
1. Running Sum Accumulation
Three cumulative sums, reset at session boundaries:
\Sigma_{pv} = \sum_{i=1}^{n} P_i \cdot V_i, \quad \Sigma_v = \sum_{i=1}^{n} V_i, \quad \Sigma_{p^2v} = \sum_{i=1}^{n} P_i^2 \cdot V_i
where P_i is the source price (typically HLC3) and V_i is volume. Zero-volume bars are skipped to prevent distortion.
2. VWAP (Center Line)
\text{VWAP}_t = \frac{\Sigma_{pv}}{\Sigma_v}
3. Volume-Weighted Standard Deviation
Using the computational identity \text{Var}(X) = E[X^2] - (E[X])^2:
\sigma^2 = \frac{\Sigma_{p^2v}}{\Sigma_v} - \text{VWAP}^2
\sigma = \sqrt{\max(0,\;\sigma^2)}
4. Band Construction
U_t = \text{VWAP}_t + k \cdot \sigma_t
L_t = \text{VWAP}_t - k \cdot \sigma_t
where k is the number of standard deviations (default 2.0).
5. Session Reset
On a reset condition, all running sums restart from zero. Configurable reset intervals include intraday (1m through 4H), daily, weekly, monthly, quarterly, semi-annual, annual, or never.
6. Complexity
Streaming: O(1) per bar. Three additions to running sums, one division, one square root. Memory: three doubles for running sums plus scalar state (~64 bytes per instance).
Mathematical Foundation
Parameters
| Symbol | Name | Default | Constraint | Description |
|---|---|---|---|---|
k |
numDevs | 2.0 | 0.1 – 5.0 |
Number of standard deviations for bands |
Pseudo-code
function vwapsd(source[], volume[], reset[], numDevs):
sum_pv = 0, sum_vol = 0, sum_pv2 = 0
for each bar t:
price = source[t]
vol = volume[t]
if reset[t]:
if vol > 0:
sum_pv = price * vol
sum_vol = vol
sum_pv2 = price * price * vol
else:
sum_pv = 0, sum_vol = 0, sum_pv2 = 0
else:
if vol > 0:
sum_pv += price * vol
sum_vol += vol
sum_pv2 += price * price * vol
vwap = sum_vol > 0 ? sum_pv / sum_vol : price
variance = sum_vol > 0 ? sum_pv2 / sum_vol - vwap * vwap : 0
stddev = sqrt(max(0, variance))
upper = vwap + numDevs * stddev
lower = vwap - numDevs * stddev
emit (vwap, upper, lower)
VWAPSD vs VWAPBANDS
| Aspect | VWAPSD | VWAPBANDS |
|---|---|---|
| Band pairs | 1 (configurable k\sigma) |
2 (\pm 1\sigma and \pm 2\sigma) |
| Default deviation | 2.0 | 1.0 (inner); 2.0 (outer) |
| VWAP calculation | Identical | Identical |
| Variance calculation | Identical | Identical |
Output Interpretation
| Output | Interpretation |
|---|---|
| Price above VWAP | Buyers paying above fair value; bullish intraday bias |
| Price below VWAP | Sellers accepting below fair value; bearish intraday bias |
| Price at upper band | Overextended above volume-weighted mean by k\sigma |
| Price at lower band | Overextended below volume-weighted mean by k\sigma |
| Band width expanding | Intraday volume-weighted dispersion increasing |
| Band width near zero | Very tight price clustering around VWAP |
Resources
- Berkowitz, S., Logue, D. & Noser, E. (1988). "The Total Cost of Transactions on the NYSE." The Journal of Finance, 43(1), 97–112.
- Kissell, R. (2013). The Science of Algorithmic Trading and Portfolio Management. Academic Press.