Testing Crypto Futures Price Series for Stationarity Before Pair Trading

Summary

This research note introduces time-series stationarity as preparation for studying pairs trading in cryptocurrency futures. It explains weak stationarity through stable mean and variance and covariance that depends on the time gap rather than the observation date. White noise is offered as a stationary example, while a random walk illustrates nonstationarity; first differencing is presented as a way to make a random walk stationary.

The note applies the Augmented Dickey-Fuller test to minute ETHUSDT futures prices. It reports that the original price series fails to reject the unit-root null, while the first-differenced series rejects it at the stated significance levels. This illustrates how to interpret the ADF statistic, p-value, and critical values. The material tests one contract over a short sample and examines a single series, not a relationship between two assets. It therefore explains a statistical prerequisite rather than specifying or validating a complete pairs-trading strategy; the reported finding should not be generalized to other periods or instruments.

Key ideas

• Weak stationarity requires stable mean and variance, with covariance determined by the time lag.
• The note contrasts stationary white noise with a nonstationary random walk.
• First differencing can remove the random-walk trend and produce a series suitable for further analysis.
• The ADF test evaluates a unit-root null hypothesis using its statistic, p-value, and critical values.
• The example concerns one contract and does not test a pair or establish a trading strategy.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.