# ESA 2012: Analysis of Time-Series Data Using State-Space Models

Time-series data are commonly collected as part of ecological studies, and increasingly ecologists want to analyze multivariate time-series data, for example data from multiple sites or multiple environmental covariates. Variability enters such data through process error (stochasticity in the underlying ecological dynamics) and through observation error. In many ecological studies, the variability due to observation error cannot be independently estimated because it arises from changes in detectability due to some complex (often unknown) function of abiotic or biotic covariates. State-space modeling provides an statistical framework for analyzing time-series data with process and observation error. Additionally, state-space models provide a framework for including multiple observation time series, covariate data, and missing observations and a framework for modeling parameters with a hierarchical structure. This workshop will overview of state-space time-series modeling and give students hands-on practice analyzing time-series data. The morning lectures will introduce autoregressive and state-space modeling. The afternoon will consist of computer labs using R: estimation of trends from spotty multi-site count data, inference about environmental drivers from covariate data, analysis of spatial structure within multi-location data, and dynamic factor analysis. The material will be presented at an introductory level, but students need to have a basic understanding of likelihood inference (e.g. familiarity with the terms likelihood function, likelihood surface, and probability density function). The computer labs will be done in R, but knowledge of R is not necessary. Students must provide laptops. Note, lab material changes year-to-year so that there is only 50% overlap with previous yearsâ€™ workshops.

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