Rate of Change — Technical Indicators

10 — Oscillators

Rate of Change#

Debated1 min read

◆ The PatternSpeed rather than level: the percentage change over N bars, the first derivative of price

Rate of Change — a pure momentum oscillator measuring percentage price change.

ROC = ((Close − Close_N) / Close_N) × 100

Oscillates around zero. Positive = upward momentum; negative = downward.

Uses:
• ROC crossing above zero → bullish shift
• Divergences between ROC and price signal weakening trends
• Common period: 12 or 14

Worked example

Five-day ROC on day 13: the close of 99 against 108 five days earlier (day 8) gives 100 × (99 / 108 − 1) = −8.3%. On day 15 it is +0.97% (104 against 103 on day 10): the fall has stopped, not reversed.

The example data: 15 days, used in every indicator here

Day	High	Low	Close	Volume
1	101	99	100	50,000
2	103	100	102	62,000
3	103	100	101	48,000
4	105	101	104	70,000
5	108	104	107	85,000
6	108	105	106	60,000
7	110	106	109	90,000
8	110	107	108	72,000
9	108	104	105	80,000
10	105	102	103	66,000
11	105	102	104	55,000
12	104	101	102	75,000
13	102	98	99	95,000
14	102	99	101	64,000
15	105	101	104	71,000

Where it misleads

It rests on a single price N bars back, so one unusual day enters the reading and later drops out of it.
Zero-line crossings come late in a reversal and often in a range.
Percent changes are not comparable across volatility: −8% means something different for a utility than for a crypto asset.

In code

df['roc5'] = 100 * (df['close'] / df['close'].shift(5) - 1)

Python, in your browser — edit the code and run it again

Assumes import numpy as np, import pandas as pd, and a DataFrame df with columns high, low, close and volume — the 15 days above.

Sources

N. Jegadeesh & S. Titman, “Returns to Buying Winners and Selling Losers”, Journal of Finance 48(1), 1993 — momentum measured as past returns
Technical Analysis of the Financial Markets, J. J. Murphy, New York Institute of Finance, 1999

Last reviewed October 2026 · How this site checks its content · Report a mistake

Pattern bridge: Rate of change is the discrete gradient of price — the slope at each point. In statistics, it’s the first difference used to make time series stationary.

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