🚀 ROC — Rate of Change
ROC is the most direct momentum measurement possible: the percentage change of price over the last \(N\) periods, with nothing else layered on top.
💡 Financial Meaning
If ROC is positive and rising, price is not just going up — it is going up faster than \(N\) periods ago. Traders watch for zero-line crosses (a shift from momentum loss to momentum gain, or vice versa) and for divergences: price makes a new high while ROC makes a lower high, warning that the advance is losing steam even though the price chart still looks strong.
🔢 Mathematical Formula
This is simply a percentage \(N\)-period return, re-expressed as a running indicator rather than a one-off calculation.
⚙️ Parameters
| Parameter | Key | Default | Description |
|---|---|---|---|
| Period (\(N\)) | period |
12 | Number of sessions back used as the reference price. |
🎛️ Signal Processing Equivalent — Normalised Finite-Difference Derivative
ROC is a discrete derivative of \(\log\)-free price, taken over a fixed lag of \(N\) samples rather than a single sample, and normalised by the base value:
Unlike MACD (which subtracts two low-pass outputs to approximate a smoothed derivative), ROC is a raw, unsmoothed finite difference — it inherits all the high-frequency noise of the price series, amplified rather than filtered.
flowchart LR
C0["💹 C(t−N)"] --> DIFF["➖ C(t) − C(t−N)"]
C1["💹 C(t)"] --> DIFF
DIFF --> NORM["➗ ÷ C(t−N)"]
NORM --> SCALE["✖️ ×100"]
SCALE --> ROC["🚀 ROC(t)"]Noise amplification
Because ROC applies no smoothing, short periods (\(N \le 5\)) produce a very jagged series. It is often used with a longer \(N\), or fed through an additional moving average, when a cleaner momentum reading is needed.