Modelling seasonal patterns in longitudinal profiles with correlated circular random walks

Seasonal patterns, as they occur in time series of infectious disease surveillance counts, are frequently modelled using a superposition of sine and cosine functions. However, in some cases this might be too simple. We propose the use of circular second order random walks instead and extend this approach to multivariate time series of counts. A correlated Gaussian Markov random field approach combines a uniform correlation matrix with a circular random walk to allow the seasonal pattern to be similar across regions, say, but not identical. Thus, spatially-varying disease onsets may be accounted for. The methodology is applied to weekly number of deaths from in uenza and pneumonia in nine major regions of the USA. Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-52612 Accepted Version Originally published at: Riebler, A; Held, L; Rue, H (2011). Modelling seasonal patterns in longitudinal profiles with correlated circular random walks. In: 26th International Workshop on Statistical Modelling, Valencia, 11 July 2011 15 July 2011, 503-508. Modelling seasonal patterns in longitudinal profiles with correlated circular random walks Andrea Riebler, Leonhard Held and H̊avard Rue 1 Division of Biostatistics, Institute of Social and Preventive Medicine, University of Zurich, Hirschengraben 84, 8001 Zurich, Switzerland; Email: [email protected], [email protected] 2 Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway; Email: [email protected] Abstract: Seasonal patterns, as they occur in time series of infectious disease surveillance counts, are frequently modelled using a superposition of sine and cosine functions. However, in some cases this might be too simple. We propose the use of circular second order random walks instead and extend this approach to multivariate time series of counts. A correlated Gaussian Markov random field approach combines a uniform correlation matrix with a circular random walk to allow the seasonal pattern to be similar across regions, say, but not identical. Thus, spatially-varying disease onsets may be accounted for. The methodology is applied to weekly number of deaths from influenza and pneumonia in nine major regions of the USA.