Definition and the core idea
Positive correlation means that two variables tend to move in the same direction over the period being studied. In finance, the variables are often returns (how much an exchange rate changes) rather than the raw price level. A positive correlation does not mean one variable causes the other; it only describes co-movement under the chosen data preparation and time window.
To “assess” positive correlation, you need enough information to (1) reproduce the data transformation and (2) compute the correlation statistic you choose. You also need to document the assumptions that affect the result.
Data you need: what to collect
1) The two time series (or more)
You need historical values for the two variables you plan to compare. In currency contexts, that typically means two exchange-rate series or, more commonly, two return series derived from them.
Material choice: decide whether you compare:
- Returns computed from each exchange rate (common), or
- Levels directly (less stable, often more misleading).
If your goal is “positive correlation” as commonly used in risk discussion, returns are usually the more interpretable input because exchange-rate levels can drift even when co-movement is weak.
2) Consistent sampling frequency and timestamps
You need the exact frequency (for example, hourly, daily, or another interval) and a consistent timestamp convention. Mismatched sampling can create artificial correlation or destroy real co-movement.
Record assumptions such as:
- Time zone handling (how timestamps are interpreted)
- Whether you align by clock time or by bar close time
- How weekends/holidays or non-trading gaps are treated
3) The calculation window
Correlation depends on the time interval. You need:
- Start and end dates
- The size of the rolling or fixed window (if you repeat the calculation)
Document whether you use a single window for one estimate, or multiple windows for stability checks.
4) The return definition (assumptions for every calculation)
Choose a return formula and state it. Common options include:
- Simple returns (percentage change)
- Log returns (natural log of the ratio)
Also specify whether you use raw or adjusted series (for example, any corporate actions are usually not relevant to exchange rates, but data vendors may apply processing).
Provenance and timeliness: where the data should come from
5) Data source and method
Use a single, documented source for each time series. Provenance means you can answer:
- Who produced the data?
- How was it measured or aggregated?
- What series identifiers were used?
If the series come from different providers, confirm that their definitions (pricing time, conventions, and transformations) match; otherwise, correlation can reflect inconsistent data handling.
6) Timeliness and reproducibility
Because historical analysis is retrospective, “timeliness” mostly means reproducibility: you should keep the dataset snapshot (or at least the extraction date and the exact retrieval method). For independent verification, others should be able to re-run the same steps.
Quality checks: verifying the data before computing correlation
7) Missing values and data cleaning choices
Correlation is sensitive to gaps and outlier handling. You should record:
- How missing observations are treated (dropped, filled, or interpolated)
- Outlier treatment (whether you winsorize, remove points, or keep everything)
Be careful: some cleaning can artificially increase correlation by removing periods where co-movement breaks down.
8) Stationarity and regime changes (material limitation)
Correlation is not guaranteed to be stable. Currency relationships can change across volatility regimes, macro events, or market structure shifts. A result that looks “positive” in one period can weaken or reverse in another.
This is a key failure mode: a single correlation number can be a snapshot, not a durable property.
9) Non-synchronous data (another limitation)
If one series effectively “responds” earlier or later than the other, simple correlation on aligned timestamps may understate or mischaracterize co-movement. Assess whether synchronization assumptions are reasonable for your chosen sampling frequency.
Evidence and example: how to compute the correlation from the needed data
A reproducible procedure needs these inputs and decisions:
- Two exchange-rate series for the same dates and the same sampling frequency.
- A return definition (simple or log) applied identically to both.
- A window (start/end dates) and a missing-data rule.
- A correlation method.
Correlation methods commonly include Pearson correlation (linear co-movement) or rank-based alternatives (co-movement in order).