Northern Hemisphere stratospheric variability is investigated with respect to chaotic behavior using time series from three different variables extracted from four different reanalysis products and two numerical model runs with different forcing. The time series show red spectra at all frequencies and the probability distribution functions show persistent deviations from a Gaussian distribution. An exception is given by the numerical model forced with perpetual winter conditions—a case that shows more variability and follows a Gaussian distribution, suggesting that the deviation from Gaussianity found in the observations is due to the transition between summer and winter variability. To search for the presence of a chaotic attractor the correlation dimension and entropy, the Lyapunov spectrum, and the associated Kaplan–Yorke dimension are estimated. A finite value of the dimensions can be computed for each variable and data product, with the correlation dimension ranging between 3.0 and 4.0 and the Kaplan–Yorke dimension between 3.3 and 5.5. The correlation entropy varies between 0.6 and 1.1. The model runs show similar values for the correlation and Lyapunov dimensions for both the seasonally forced run and the perpetual-winter run, suggesting that the structure of a possible chaotic attractor is not determined by the seasonality in the forcing, but must be given by other mechanisms.