Price Z-Score Calculator
Calculate how many sample standard deviations the latest entered value sits above or below its selected historical window mean.
Enter an ordered price or spread series
Use one measurement, one source and equally spaced completed observations from oldest to newest.
Whole number from 3 through 500, no longer than the entered series.
Separate finite decimal values with line breaks, spaces, commas or semicolons. Use one consistent unit.
Latest entered-window z-score
Entered Mean-Reversion Diagnostics 1.0.0.
| Audit item | Range or location | Value | Method |
|---|
How the price z-score is calculated
Sample SD = √[Σ(x − mean)² ÷ (n − 1)]
Latest z-score = (latest value − sample mean) ÷ sample SD
Version 1.0.0 selects the final lookback observations from the ordered series. The latest observation is therefore included in both the window mean and its sample standard deviation. This convention makes the calculation reproducible and avoids silently mixing an in-sample score with a forecast-style score.
The denominator is the sample standard deviation with n minus one, not the population standard deviation with n. Both are legitimate in different contexts, but they produce different magnitudes on a short window. The result panel exposes the mean, variance basis and window range so another spreadsheet or statistics package can reproduce the answer.
A positive value means the latest observation is above the entered-window mean; a negative value means it is below. The number is unitless, so a price, spread, return or indicator series can be standardized only when every observation uses the same definition and unit.
A careful interpretation workflow
Start with the estimator and visible audit fields, then check whether the data and assumptions support the question you want to ask. A clean number is not a substitute for a valid series.
- Read the sign as direction relative to the entered-window mean, not as trade direction.
- Read the magnitude as standardized sample distance, not as a guaranteed tail probability.
- Compare scores only when their series definition, sampling and denominator convention match.
- Inspect the displayed sample standard deviation; a small denominator can amplify the score.
- Use completed, equally spaced observations when a time-series interpretation matters.
- Pair the statistic with separate stationarity, data-quality and trading-cost analysis.
Worked example from the audited fixture
How to interpret the result
A result of +1.264911 describes the latest value only relative to this five-observation sample. It does not say there is a fixed probability of reversal and it is not labelled overbought. Changing the window, sampling interval, series definition or volatility regime can materially change the score.
Which mean-reversion diagnostic answers which question?
These three pages are complementary rather than interchangeable. They describe different properties of the same entered numbers, and none establishes a complete trading strategy by itself.
| Diagnostic | Question answered | Main dependency | What it does not prove |
|---|---|---|---|
| Latest z-score | How far is the latest value from its selected sample mean? | Window and sample standard deviation | Normality or future reversal |
| Classical Hurst R/S | What log-log rescaled-range slope appears across selected scales? | Estimator, scale set and sample path | A stable persistent or mean-reverting regime |
| AR(1) half-life | What positive geometric decay time follows from the fitted φ? | Sampling interval and AR(1) specification | Stationarity, cointegration or forecast accuracy |
Assumptions and limits
- At least three observations are required and the selected lookback cannot exceed 500 or the entered sample length.
- A constant window is rejected because division by a zero standard deviation is undefined.
- The calculator does not test normality, so standard-normal tail probabilities must not be inferred automatically.
- The calculator does not establish stationarity, cointegration, mean reversion or structural stability.
- Missing observations, uneven timing, stale prices and mixed data sources are not detected from numeric values alone.
- The latest observation is included in the estimated mean and standard deviation; this is not an out-of-sample forecast score.
- No threshold is converted into overbought, oversold, entry, exit, stop or position-size advice.
Prepare the entered series before calculating
Choose the economic object first: a price level, log price, return, spread, residual or indicator value is not interchangeable with the others. Export completed observations in chronological order, keep one feed and one transformation, and remove headers before pasting.
Check timestamps outside this calculator. A numeric list cannot reveal a missing weekend rule, duplicated bar, daylight-saving shift or gap in broker history. If observations are unevenly spaced, a bar-labelled decay or time-series interpretation can be false even though the arithmetic runs.
Record the symbol, timeframe, time zone, sample dates, preprocessing, window and model version with any saved result. That audit trail makes later comparisons meaningful and reduces the risk of selecting only the most attractive statistic.
Frequently asked questions
- It measures the latest entered value minus its selected-window mean, divided by that window’s sample standard deviation.
- It uses the sample standard deviation with the n minus one denominator and displays that convention.
- Yes. Version 1.0.0 includes the latest observation in the selected window mean and sample standard deviation.
- No. The result is descriptive sample distance and does not establish a reversal probability, normal distribution or trade signal.
- Yes, if every observation has the same definition, source, unit and ordering; the calculator does not validate those properties.
- Its standard deviation is zero, so dividing the latest distance by that denominator is undefined.
- No. Use separate unit-root, stationarity or cointegration diagnostics for those questions.
- No. It calculates only the finite decimal observations entered in the browser.
Sources and methodology
- NIST/SEMATECH e-Handbook — Z-scores — Defines standardization as value minus mean divided by standard deviation.
- NIST/SEMATECH e-Handbook — Measures of scale — Documents the sample standard-deviation convention and its denominator.
- NIST/SEMATECH e-Handbook — Normal probability plot — Useful context for why normality should be assessed rather than assumed.
The operational contract is version 1.0.0. Its formulas, fixture outputs, maximum sample and withheld-output rules are tested locally before staging release.
Continue the statistical diagnostic workflow
Compare the chart feed and trading terms
Before transferring an entered-series result to execution, confirm the broker’s symbol specification, chart history, time zone, spreads, commissions and financing. Calculations based on one feed need not reproduce on another.
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