Time-series frequency is the cadence at which observations in a time series are recorded: for example, hourly, daily or monthly. In financial modelling, it gives a lag or return window its time meaning. A one-step forecast on five-minute data has a different horizon from a one-step forecast on daily data.
This is the observation-clock meaning of sampling frequency. It describes when measurements are taken, without asserting how often the measured variable rises and falls.
Read the spaces, not just the rows
Suppose a synthetic price feed records observations at 09:00, 09:05 and 09:10 UTC on the same day, following a fixed five-minute schedule. Each adjacent pair is separated by five minutes, or 300 seconds. The schedule therefore has:
There are three timestamps but only two elapsed intervals between the first and last: ten minutes in total. Counting all three rows and dividing by that elapsed span would overstate the cadence because both endpoints are included. With consecutive, equally spaced observations, the endpoint span is .
Filled dots mark observations; brackets mark elapsed intervals. This synthetic clock shows the schedule only, without prices or a presumed market cycle.
On a complete five-minute grid, a lag of 12 observations means 60 minutes. If observations are missing and rows are simply dropped, the same row lag can cover more elapsed time. Keep the scheduled frequency separate from the timestamps actually present.
State which clock you mean
A frequency label is useful only with its conventions:
- Calendar and session: “daily” may mean each calendar day or each trading session. Adjacent session closes can be separated by a weekend or holiday, so their elapsed-hour gaps vary.
- Timestamp and time zone: specify the zone and whether a timestamp marks an interval's start, its end or an individual event. Local clock labels can repeat or skip during daylight-saving changes.
- Regular or event time: transaction-by-transaction data follow market activity. One transaction later need not be a fixed number of seconds later.
- Measurement rule: a five-minute closing price, average price and traded-volume total describe different quantities even when their timestamps match.
Time-Series Data develops timestamp alignment, time zones and resampling rules, including the danger of treating an incomplete bin as completed (public preview; full lesson requires membership).
The other meanings of “frequency”
Spectral frequency measures oscillation: cycles per unit of time, or cycles per observation. Sampling every five minutes does not mean prices complete a cycle every five minutes. A stipulated cycle that repeats once per hour would span 12 observation intervals on this grid, giving cycle per observation. The three timestamps above establish no such cycle. NIST's spectral-plot guide explains the frequency-domain interpretation.
Software conventions also need units. R's
ts documentation defines its frequency argument as observations per unit of time. A seasonal period, by contrast, counts observations before a seasonal pattern repeats. Choosing an observation grid does not demonstrate that a seasonal pattern exists.Finally, frequency does not count independent information. Nearby observations can exhibit autocorrelation; recording more frequently does not guarantee more independent observations. Specify the cadence first, then assess dependence for the series and estimator being used.
Sources
- Chris Brooks, Introductory Econometrics for Finance, second edition, Cambridge University Press, 2008, §1.3.1, pp. 3–4: observation frequency and irregularly spaced financial records.
- R Core Team, Time-Series Objects: equally spaced observations and the units of
frequency. - NIST/SEMATECH, e-Handbook of Statistical Methods, §1.3.3.27, “Spectral Plot”: cyclic frequency and cycles per observation.
- Rob J. Hyndman and George Athanasopoulos, Forecasting: Principles and Practice, third edition, §§2.1 and 2.8: time indices, seasonal periods and autocorrelation.