Sampling frequency is how often observations of a time series are recorded or selected. It determines which price moves a quant can see, the horizon attached to each return, and what information enters an estimate of risk. A daily close and a transaction-by-transaction price series describe the same market through different observation clocks.
For observations separated by a constant interval , frequency is , expressed in the chosen time unit. Daily sampling has a shorter interval and a higher frequency than sampling every two days. State whether “day” means a calendar day or a trading session: adjacent trading-day closes need not be equally spaced in elapsed hours. Transaction data can be irregularly spaced, so “one row later” need not mean a fixed amount of time later.
A round trip that coarse sampling hides
Consider synthetic closing prices at equally spaced trading-day observations. Prices are USD per share. There are no dividends, fees or corporate actions, and the investor holds one share throughout.
| Observation | Price | Simple price return since the previous day |
|---|---|---|
| Day 0 | 100 | — |
| Day 1 | 110 | |
| Day 2 | 100 |
Sampling every day retains the rise and fall. Sampling only on days 0 and 2 retains equal endpoint prices and produces a two-day price return of zero. It cannot reveal the intermediate excursion from those endpoints alone. Zero holding-period return does not mean the price stayed constant.
The same synthetic path on two observation grids. Filled dots identify retained observations. Connectors guide the eye; the coarse dashed connector does not establish a flat intervening path.
The corresponding daily simple returns compound:
Adding them gives , which is not the two-day simple return. The percentage loss is smaller than the percentage gain because it is measured against the higher starting price. For positive prices, log returns do add across adjacent intervals: here .
Resampling requires an economic rule
Changing frequency is more than changing date labels. The rule depends on what the field measures:
| Field | A possible lower-frequency construction | Meaning |
|---|---|---|
| Closing price | Last observed price in each completed bin | Endpoint mark, subject to a stated stale-price policy |
| Traded volume | Sum across non-overlapping constituent intervals | Activity during the larger interval |
| Simple return | Compound gross returns, then subtract one | Holding-period performance over the combined interval |
| Log return | Sum across adjacent intervals | Log of the endpoint price ratio |
A mean price answers a different question from an endpoint close. An incomplete weekly bin can also carry a Friday label even if its latest observation is from an earlier day. Missing observations and market closures need explicit treatment; neither interpolation nor forward-filling creates new market information.
For a practical Python treatment, Time-Series Data develops time zones, alignment and resampling, including incomplete bins (public preview; full lesson requires membership).
More frequent does not automatically mean more reliable
Finer observations can reveal variation that coarse endpoints miss. But very short-interval transaction prices also reflect bid–ask bounce, discrete price ticks and other market microstructure effects. Aït-Sahalia, Mykland and Zhang show that ignoring noise can make a finite sampling frequency preferable for their volatility-estimation problem, while modelling noise allows fuller use of the available observations. This is an estimator-and-model result, not a universal best interval for every asset or task. Their paper explains the distinction.
More rows over the same calendar span also do not establish independence, remove dependence, or supply a longer history of market regimes. Overlapping return windows share part of the same price path. Choose the clock and aggregation to match the question, then check the assumptions of the estimator at that frequency.
Sources
- Chris Brooks, Introductory Econometrics for Finance, second edition, Cambridge University Press, 2008, §1.3.1, p. 4; §1.4 and Box 1.3, pp. 7–8; pp. 424–425: observation frequency, irregular transaction times, return construction and information lost by coarse volatility proxies.
- Rob J. Hyndman and George Athanasopoulos, Forecasting: Principles and Practice, third edition, §2.1: observations, time indices and data frequencies.
- Yacine Aït-Sahalia, Per A. Mykland and Lan Zhang, “How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise”, Review of Financial Studies 18(2), 2005, pp. 351–416, especially pp. 351–353: sampling-frequency choice and noise-aware estimation.