Stochastic Models for Radon Daily Time Series: Seasonality, Stationarity, and Long-Range Dependence Detection

Abstract

This study detects the presence of seasonality, stationarity, and long-range memory structures in daily radon measurements from a permanent monitoring station in central Italy. The transient dynamics and the seasonality structure are identified by power spectral analysis based on the continuous wavelet transformation and a clear 1-year periodicity emerges. The stationarity in the data is assessed with the Dickey–Fuller test; the decay of the estimated autocorrelation function and the estimated Hurst exponent indicate the presence of long-range dependence. All the main characteristics of the data have been properly included in a modeling structure. In particular, an autoregressive fractionally integrated moving average (ARFIMA) model is estimated and compared with the classical ARMA and ARIMA models in terms of goodness of fit and, secondarily, of forecast evaluation. An autoregressive model with a noninteger value of the differencing parameter ((Formula presented.)) resulted to be the most appropriate on the basis of the Akaike Information Criterion, the diagnostic on the residuals, and the root mean squared error. The results suggest that there is statistically significant evidence for not rejecting the presence of long memory in the radon concentration. The radon measurements are better characterized as being stationary, but with long memory and so, the statistical dependence decays more slowly than an exponential decay.