enhetrot

Enhetrot, or unit root, is a concept in time series econometrics describing a non-stationary property of a stochastic process. A series with a unit root experiences shocks that have permanent effects, causing its statistical properties to evolve over time. A common representation is an autoregressive process of order one with a coefficient equal to one, such as x_t = μ + x_{t-1} + ε_t, where ε_t is white noise. In this case, the first difference Δx_t = x_t − x_{t-1} = μ + ε_t is stationary, so the series is integrated of order one, I(1).

Implications for analysis and modeling are significant. Non-stationary series in levels can lead to spurious regressions if ordinary least squares is applied without differencing. Therefore, researchers often difference the data to achieve stationarity or model long-run relationships using cointegration when multiple I(1) series share a stationary linear combination. If cointegration exists, error-correction models can describe short-run dynamics while preserving the long-run equilibrium.

Common tools for detecting unit roots include the Augmented Dickey-Fuller (ADF) test, the Phillips-Perron test, and the DF-GLS test, which test for the presence of a unit root in a time series. The KPSS test, by contrast, assesses stationarity around a deterministic trend, helping distinguish between a unit root and trend-stationary behavior. Power and size of these tests can be sensitive to structural breaks and model specification.

Examples of unit-root phenomena include many macroeconomic level series such as GDP and price levels. Financial returns, in contrast, are typically stationary. Understanding whether a series has a unit root guides appropriate differencing, model specification, and interpretation of long-run relationships.