NichtStationarität

NichtStationarität refers to a property of a time series where its statistical characteristics, such as mean, variance, or autocorrelation, change over time. In contrast, a stationary time series has statistical properties that remain constant throughout its entire duration. The presence of nichtStationarität can significantly complicate the analysis and modeling of time series data. Many standard time series forecasting techniques assume stationarity, and their application to nicht-stationary data can lead to inaccurate predictions and unreliable conclusions.

Several factors can cause nichtStationarität. Trends, where the mean of the series systematically increases or decreases over time, are a common source. Seasonality, which involves cyclical patterns that repeat at fixed intervals (e.g., daily, weekly, or yearly), also introduces nichtStationarität. Furthermore, changes in the variance of the series, known as heteroskedasticity, can also render a time series nicht-stationary.

Identifying nichtStationarität is a crucial first step in time series analysis. Various statistical tests, such as the Augmented Dickey-Fuller test or the Kwiatkowski-Phillips-Schmidt-Shin test, are employed to formally detect its presence. Once detected, common methods to address nichtStationarität include differencing the series, transforming the data (e.g., using logarithms), or modeling the time-varying components separately. Understanding and appropriately handling nichtStationarität is fundamental for building robust and meaningful time series models.