5 - Introduction to Stochastic Processes

Summary

Climate data are correlated over short spatial and temporal scales. For instance, today’s weather tends to be correlated with tomorrow’s weather, and weather in one city tends to be correlated with weather in a neighboring city. Such correlations imply that weather events are not independent. This chapter discusses an approach to accounting for spatial and temporal dependencies based on stochastic processes. A stochastic process is a collection of random variables indexed by a parameter, such as time or space. A stochastic process is described by the moments at a single time (e.g., mean and variance), and also by the degree of dependence between two times, often measured by the autocorrelation function. This chapter presents these concepts and discusses common mathematical models for generating stochastic processes, especially autoregressive models. The focus of this chapter is on developing the language for describing stochastic processes. Challenges in estimating parameters and testing hypotheses about stochastic processes are discussed.