nonstationnarité

Nonstationnarité refers to a property of a time series where its statistical properties, such as mean, variance, or autocorrelation, change over time. In contrast, a stationary time series has statistical properties that remain constant throughout the observed period. Understanding nonstationnarité is crucial in time series analysis and forecasting because many standard statistical models assume stationarity.

The presence of nonstationnarité can lead to misleading results if not properly addressed. For example, if a time series has a trend, its mean will increase over time, violating the stationarity assumption. Similarly, if the variability of the series fluctuates, its variance is not constant. Autocorrelation, which measures the correlation of a series with its past values, can also change over time in a non-stationary series.

Common sources of nonstationnarité include trends, seasonality, and structural breaks, which are sudden changes in the underlying data-generating process. Techniques to handle nonstationnarité include differencing, where the difference between consecutive observations is taken to remove trends or seasonality, and transformations, such as logarithmic transformations, to stabilize variance. Alternatively, models specifically designed for non-stationary data, like ARIMA models (which incorporate differencing), can be employed. Detecting nonstationnarité is often done through visual inspection of plots, statistical tests like the Augmented Dickey-Fuller (ADF) test or the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test, and by examining the autocorrelation and partial autocorrelation functions.