Research in ecology and environmental sciences often involves measuring responses over time–whether data is generated by field observations, lab experiments, or computer simulations. Yet, analyzing time-series data is challenging because conventional statistical methods assume that observations are independent of each other. Time-series modeling tools leverage such dependencies, and provide strong inference where other methods would fail. They also allow us to ask sophisticated questions: Can we identify the trend and periodic patterns in a time series–and thus disentangle signals from unpredictable ‘noise’? Can we tell if two time series are more strongly associated than would be expected by chance? Based on past observations can we say anything about the future–such as the probability of temperature surpassing a critical threshold, or of a species going functionally extinct?
In this course we will learn how to analyze time-series data using real-world examples from ecology and environmental sciences. We will study how to mathematically describe a time series, and test hypotheses about the underlying processes generating the observed patterns. We will cover univariate and multivariate state-space models, with an incursion into statistical forecasting and analyses in the frequency domain (e.g., Discrete Fast Fourier Transform). We will draw examples from data generated by high-frequency sensors and long-term monitoring programs. The course is hands-on, will deal with practical problems (e.g., missing data, observation error), and will encourage students to develop a project analyzing their own data sets. We will use a range of statistical packages in the R environment.