Stationarity — The Mathematical Backbone

A stationary time series shows constant statistical properties over time. Its mean, variance, and autocorrelation remain stable. This stability assists mean reversion strategies. Non-stationary series

Strict stationarity describes a time series where the joint probability distribution of any set of observations remains constant over time. Shifting the entire time series by any amount does not chang

Stationarity forms the basis of mean reversion strategies. A stationary time series shows consistent statistical properties. Its mean, variance, and autocorrelation remain stable. Non-stationary serie

Visual inspection offers a first check for stationarity. Plot the time series. Look for a constant mean. Observe the variance. Assess the autocorrelation structure.

The Augmented Dickey-Fuller (ADF) test evaluates a time series for stationarity. A stationary series shows consistent statistical properties. Its mean, variance, and autocorrelation remain stable. Non

The Phillips-Perron (PP) test assesses time series stationarity. It improves upon the Augmented Dickey-Fuller (ADF) test. The PP test handles autocorrelation and heteroscedasticity. Autocorrelation me

The Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test directly assesses a time series for stationarity. The Augmented Dickey-Fuller (ADF) test differs. KPSS considers the null hypothesis that a time serie

The Hurst Exponent quantifies long-range dependence. It measures the persistence or anti-persistence of a time series. A value of 0.5 indicates a random walk, like a fair coin toss. Values above 0.5 s

Variance ratio tests determine if a time series shows mean reversion. They compare the variance of multi-period returns to the variance of single-period returns. If a series is a random walk, its vari

Individual stationarity tests have limits. Each test relies on specific assumptions. Violating these assumptions produces misleading results. For example, the Augmented Dickey-Fuller (ADF) test assume