Stationarity in Financial Time Series

Stationarity refers to a time series whose statistical properties, such as mean, variance, and autocorrelation, remain constant over time. Most standard statistical models, including many used in options pricing and volatility forecasting, rely on the assumption that financial data is stationary.

However, cryptocurrency and derivative price series are often non-stationary, exhibiting trends, changing volatility, and structural breaks that evolve as the market matures. If a model assumes stationarity when the underlying data is not, the resulting forecasts and risk estimates will be inherently flawed.

Practitioners must often transform data through techniques like differencing or log returns to achieve a level of stationarity that allows for meaningful analysis. Understanding the limitations of this assumption is key to building models that do not break down when market dynamics shift unexpectedly.