epästationaaristen

epästationaariset (non‑stationary series) are sequences of observations whose statistical properties change over time. In a non‑stationary series, at least one of the following characteristics varies: the mean, the variance, or the autocovariance structure. This contrasts with stationary series, where these properties remain constant, allowing reliable extrapolation and inference. Non‑stationarity is common in economic, financial, environmental and engineering applications where underlying forces evolve.

The most widely recognized form of non‑stationarity is the presence of a unit root. A unit root process, formally expressed as (1−L)Yt = εt with εt white noise, exhibits a random walk. Such series display persistence and long memory: shocks have permanent effects on the level of the series. If an additional polynomial trend is present, the process is trend‑stationary, implying a deterministic trend but stochastic fluctuations around it.

Detecting non‑stationarity typically involves unit root tests such as the Augmented Dickey‑Fuller, Phillips‑Perron, or KPSS test. A significant test result leads analysts to transform the data, most often through first differencing, to achieve stationarity. Differencing removes unit roots, stabilizing the mean and variance while preserving the underlying temporal dynamics.

Maintaining awareness of non‑stationarity is crucial for time‑series modelling. Forecasting methods like ARIMA require stationary input; failure to transform or account for unit roots can result in biased parameters and unreliable predictions. Conversely, some models, such as cointegration frameworks, exploit non‑stationary relationships to uncover long‑run equilibrium structures among multiple series.