Periodic Correlation in Stratospheric Ozone Data

A fifty-year time series of monthly stratospheric ozone readings from Arosa, Switzerland is analyzed. The time series exhibits the properties of a periodically correlated (PC) random sequence with annual periodicities. Spectral properties of PC random sequences are reviewed and a test to detect periodic correlation is presented. An ARMA model with periodically varying coefficients (PARMA) is fit to the data in two stages. First, a periodic autoregressive model (PAR) is fit to the data. This fit yields residuals that are stationary, but non-white. Next, a stationary ARMA model is fit to the residuals and the two models are combined to produce a larger model for the data. The combined model is shown to be a PARMA model and yields residuals that have the correlation properties of white noise.