Normalized Momentum Z
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# Normalized Momentum Z - Momentum in standard scores
*Category: Momentum | Difficulty: intermediate | Window: separate window below the chart | Markets: Universal (Forex, indices, commodities, crypto, stocks) | Suggested timeframes: M15, M30, H1, H4, D1*
## Short description
> Standardises momentum against its own recent historical distribution and returns a z score. A value of +2 marks a thrust stronger than roughly 97 per cent of the instrument recent moves.
### Overview
Raw momentum has a flaw that severely limits its usefulness: it has no scale. Saying that ten bar momentum equals thirty means nothing until you know whether thirty is a lot or a little for that instrument, on that timeframe, in that volatility regime. Normalized Momentum Z fixes this at the root by standardising momentum against its own recent distribution. It computes the mean and standard deviation of momentum over the last InpStatPeriod bars and converts the current value into a z score, that is a number of standard deviations from the mean. The result carries an immediate and identical meaning everywhere: two means unusually strong, zero means perfectly ordinary, minus two unusually weak.
### How the calculation works
1. Raw momentum is the difference between the current applied price and the price InpMomPeriod bars earlier.
2. Over the InpStatPeriod window the mean and variance of that same momentum series, not of price, are computed.
3. Variance is obtained as the mean of squares minus the square of the mean, with a guard against negative values caused by rounding.
4. The z score is the distance of the current momentum from the mean, divided by the standard deviation.
5. The result is clamped at six sigma, beyond which the extra information is nil and the vertical scale would become unreadable.
6. A signal average over InpSignalPeriod bars accompanies the histogram to read its tendency.
### How to use it
- Use the two sigma thresholds as an exceptionality filter: only beyond that level does the thrust deserve operational attention.
- Compare the value across several instruments at the same moment to see where market thrust is concentrating.
- In an established trend the score drifts back to zero even while price rises: it means that advance has become the new normal.
- The histogram crossing the signal average marks the start or the end of an acceleration phase.
- On instruments with highly variable volatility raise InpStatPeriod to obtain a more stable reference distribution.
### Who it is for and on which timeframes
It is the natural tool for traders working on a basket of instruments who need to compare them, and for system builders whose logic must work without recalibration across different markets. It works from M15 to D1. On very low timeframes the momentum distribution is dominated by microstructure and extreme scores lose meaning. No advanced statistical background is required, but understanding what a standard deviation is helps avoid over-reading values around one.
### Practical example of reading a signal
A trader monitors eight currency pairs on H1. On seven of them the score oscillates between minus one and plus one: ordinary movement, nothing to do. On AUDNZD the score jumps to +2.6 and the histogram turns green. In absolute terms the move is only twenty five pips, far less than what EURUSD did in the same hour, but for the recent distribution of AUDNZD it is a rare event. That is where attention concentrates: the pair is doing something anomalous relative to itself, which is more informative than the absolute size of the move.
## Input parameters
| Parameter | Default | Description |
|---|---|---|
| `InpMomPeriod` | 10 | Horizon of the observed momentum, in bars. It defines which scale of move is being standardised. |
| `InpStatPeriod` | 120 | Window over which the reference distribution is estimated. Below 60 the estimate is noisy; above 200 the reference becomes slow to react to regime changes. |
| `InpSignalPeriod` | 5 | Period of the signal average overlaid on the histogram. |
| `InpExtremeZ` | 2.00 | Threshold in standard deviations beyond which the thrust is considered exceptional and the histogram is coloured. |
| `InpAppliedPrice` | PRICE_CLOSE | Price momentum is computed on. |
## Advantages / strengths
- A universal, interpretable scale: a score of two means the same thing on any instrument and timeframe.
- It adapts automatically to volatility changes, because the reference is the recent distribution rather than a fixed value.
- Ideal for selecting between markets, a use where classic momentum is completely unusable.
- No repaint, and an implementation using a single pass over the statistical window.
## Limitations and warnings
- In a very prolonged trend the score normalises towards zero: strong becomes the new average and the indicator stops flagging it.
- Standardisation implicitly assumes a reasonably symmetric distribution: on markets with strongly asymmetric tails the scores must be read with care.
- Right after a volatility regime change the statistical window still holds the old regime and produces exaggerated values.
- It is not a standalone directional signal: a high score says the thrust is unusual, not that it will continue.
**No repaint:** values printed on a closed bar are never modified afterwards.
**Disclaimer.** This product is a technical analysis tool, not an automated trading system, and it offers no profit guarantee whatsoever. Financial markets carry the risk of total loss of the invested capital. Past performance is not indicative of future results. Every signal must be confirmed with your own analysis, a money management plan and prior testing on a demo account. The author is not responsible for trading decisions taken on the basis of this indicator.
## Suggested tags / keywords for MQL5
`momentum`, `z score`, `normalization`, `statistics`, `oscillator`, `market scan`, `no repaint`, `standard deviation`
