Two Common Definitions of an N-Day Low
Summary
The document compares two ways to define an n-day low. One treats it as the lowest price in a rolling window of the previous n data points, ending at the last close; as the calendar advances, the observations in the window roll forward. The other defines today as an n-comparison low when today’s close is below the closes of each of the n preceding days. Under this second convention, an n-day low compares today with n earlier observations, so the total number of closes involved differs from the rolling-window convention.
A worked three-day example illustrates how the rolling window shifts across a weekend, while the comparison-based definition is expressed through close-to-close inequalities. The document highlights that both conventions are used, creating a potential one-observation difference in terminology. It also cautions that market data sources may use different price fields, such as closes rather than intraday lows, especially for longer windows. Verify the chosen convention before interpreting signals or comparing results.
Key ideas
- A rolling-window n-day low is the minimum price among the prior n observations as the window advances.
- A comparison-based n-day low requires today’s close to be below each of the previous n closes.
- The two conventions differ in whether the current observation is included in the stated window length.
- Data providers may use different price fields, so the definition should be checked before use.
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Full text
# What is the definition of a 10-day low?
# What is the definition of a 10-day low?
Or for that matter a [n]-day low? (As it relates to market data/trading).
When does a [n]-day low get disrupted and you have to begin tallying again?
## Answer by Jan Sila (score 1, accepted)
https://quant.stackexchange.com/a/28396
It is the lowest price recorded in previous n days, as of last (yesterday's) close. So it in fact does not get disrupted, it is rolling with the dates.
Say 3 day low (over weekend and Monday) would be the lowest recorded price between Wednesday, Thursday and Friday. On Tuesday it would be Thursday, Friday and Monday 1 Aug.
But I would make sure to check how my source computed it in the documentation or FAQ section. They might consider only close prices for longer windows - say 52 weeks high/low etc.
## Answer by Alex C (score 2)
https://quant.stackexchange.com/a/28400
How should an n-day low be defined?
Let's start with the simplest case: a 1 day low. We say that today is a 1 day low if the close of today is lower than the close of yesterday: $c_t<c_{t-1}$. This is the same as a Down Day.
Generalizing, today is a 2-day low if $c_t<c_{t-1} \wedge c_t<c_{t-2} $. In words: today's close is below both yesterday's close and the day before close.
An n-day low is defined by n comparison operations: today's close is below n previous days: $c_t<c_{t-1} \wedge c_t<c_{t-2} \wedge \cdots \wedge c_t<c_{t-n}$
Note that this definition differs from the definition given by Jan Sila: what he calls a 3 day low I consider a 2 day low. Both definitions are used, so it is best to check how an author defines it. To distinguish the two definitions we could refer to the definition given here as a "n comparison low" (since it makes n "less than" comparisons), while the definition Jan Sila gave is a "n datapoint low" (since it uses the data of the last n datapoints).Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.