Autoregression as a means of assessing the strength of seasonality in a time series

The study of the seasonal variation of disease is receiving increasing attention from health researchers. Available statistical tests for seasonality typically indicate the presence or absence of statistically significant seasonality but do not provide a meaningful measure of its strength. We propose the coefficient of determination of the autoregressive regression model fitted to the data ( ) as a measure for quantifying the strength of the seasonality. The performance of the proposed statistic is assessed through a simulation study and using two data sets known to demonstrate statistically significant seasonality: atrial fibrillation and asthma hospitalizations in Ontario, Canada. The simulation results showed the power of the in adequately quantifying the strength of the seasonality of the simulated observations for all models. In the atrial fibrillation and asthma datasets, while the statistical tests such as Bartlett's Kolmogorov-Smirnov (BKS) and Fisher's Kappa support statistical evidence of seasonality for both, the quantifies the strength of that seasonality. Corroborating the visual evidence that asthma is more conspicuously seasonal than atrial fibrillation, the calculated for atrial fibrillation indicates a weak to moderate seasonality ( = 0.44, 0.28 and 0.45 for both genders, males and females respectively), whereas for asthma, it indicates a strong seasonality ( = 0.82, 0.78 and 0.82 for both genders, male and female respectively). For the purposes of health services research, evidence of the statistical presence of seasonality is insufficient to determine the etiologic, clinical and policy relevance of findings. Measurement of the strength of the seasonal effect, as can be determined using the technique, is also important in order to provide a robust sense of seasonality.