Missing data and market calendars in cross-asset studies

Classify absence before deciding how to fill it

Separate scheduled closure, temporary source failure, stale quotation, instrument nonexistence, and economic data not yet released. A holiday explains why an exchange did not produce a new settlement; it does not establish that the asset's economic value was unchanged. A security that did not yet exist is different again. Keep a reason code and the last genuine observation time alongside every missing cell.

Use the originating source's metadata to identify missing-value markers. A blank, a dot, a zero, and a carried value can represent different states. Converting all of them into numeric zero can create extraordinary returns or apparent price collapses. Validate the conversion process on known closures and known source interruptions before applying it across a long history.

Build a time model, not just a date join

Record local session dates, observation times, publication times, timezones, and any processing cutoff. Normalize timestamps with daylight-saving rules where relevant. Two daily observations stamped Wednesday may have been measured many hours apart. An overnight futures session can also cross a calendar boundary while belonging to a single exchange trading day. Do not assume a midnight timestamp supplied by a file is an actual observation time.

ECB reference-rate documentation identifies its publication convention and nonpublication on specified closing days. Such metadata make an informational series interpretable; they do not synchronize it automatically with every equity close or futures settlement. If exact intraday matching is unavailable, describe the timing limitation and select a defensible interval rather than present a convenient daily merge as simultaneous evidence.

Worked hypothetical example: a holiday creates false opposition

Suppose two invented markets close Monday at 100. Market A trades Tuesday and rises to 110, then remains at 110 Wednesday. Market B is closed Tuesday and first updates to 110 Wednesday. Forward-filling B at 100 on Tuesday creates paired daily returns of plus 10% and zero for A, against zero and plus 10% for B. The two-pair sample correlation is minus one.

That statistic reflects the imposed timing pattern, not established economic opposition. Over the common Monday-to-Wednesday interval both markets rise 10%. There is only one aligned return pair, which is insufficient to calculate a meaningful sample correlation. The appropriate conclusion is that the daily comparison lacks synchronized observations, not that either correlation estimate reveals the assets' structural relationship.

Choose aggregation according to the variable

An average is appropriate for some rate questions; a period-end observation answers a valuation question; a sum can describe an accumulated flow. FRED's documentation explains that these aggregation methods can treat internal missing observations differently from period boundaries. Reproduce the documented behavior rather than assume a weekly result always represents a Friday observation or exactly five underlying data points.

For investment returns, aggregate valid subperiod returns by the appropriate compounding method or use matching endpoint values. Averaging daily prices and then computing a monthly percentage change produces a different statistic. For physical flows, account for the days represented by each observation. A partial month's total should not be compared with a complete month without an explicit coverage adjustment.

Keep economic releases on an availability timeline

A macro observation labeled January may not have been released until February. Attaching it to January market returns can be valid for an ex post descriptive question but invalid for a claim about what a researcher knew in January. Retain the reference period separately from publication and receipt times. When only a release date is available, do not manufacture an intraday timestamp that favors the study.

ALFRED provides historical vintages and explains how release dates are determined. Vintage availability is useful but does not automatically establish that a particular office received the value before its decision cutoff. Model the delivery lag conservatively when verified timing is unavailable, or narrow the claim. A carried macro value can describe the latest known state without pretending to be a newly released measurement.

Measure the consequences of deletion and imputation

Dropping incomplete rows changes the sample, potentially removing the very stress periods under study. Pairwise deletion can leave each asset pair with different dates; combining those estimates into one correlation matrix can create inconsistencies for portfolio calculations. Report common coverage, pair counts, and excluded intervals. Consider a joint-sample or explicitly modeled approach when the downstream analysis requires a coherent covariance estimate.

Interpolation is an estimate, not a recovered observation. It can be appropriate for selected descriptive applications but can leak future values into historical decision tests. Never linearly interpolate across a gap in a causal study using an endpoint that was not yet available. Compare reasonable handling policies and show whether the economic conclusion changes, while keeping the primary policy fixed and justified.

Publish a coverage report with the result

Summarize expected observations, genuine observations, closures, unexplained gaps, carried values, and exclusions by series. Add a maximum staleness measure and identify periods with mismatched endpoints. Test both routine holiday cases and a hypothetical source outage. A reproducible calendar rule should tell another analyst exactly which interval each reported return spans without requiring personal explanations from the original author.

Common warning signs are a volatility decline after blanket forward-filling, a lead-lag pattern that disappears with synchronized closes, and a monthly endpoint silently drawn from several days earlier. Investigate those patterns before giving them a macro interpretation. A slightly shorter but clearly aligned sample can be more informative than a visually complete panel whose apparent observations are mostly assumptions.

What to retain

• Distinguish market closures, source failures, stale values, and unreleased data.
• Align actual return intervals rather than rely on matching date labels.
• Report coverage and imputation effects instead of hiding them behind a complete chart.

Source notes

1. FRED Help: Missing values in aggregation methods
2. FRED Help: What is Frequency Aggregation?
3. ECB: Euro foreign exchange reference rates, timing and closing days
4. Federal Reserve Bank of St. Louis: ALFRED vintage-data help

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