3 - Time varying signals

Abstract

This chapter illustrates how data vary with time and how their order is crucial. Such data is considered as a time series defined as a collection of observations made sequentially in time. Random processes are considered with relationships between the variables at different times. There is one time series, which can be thought of as a sample of one from the underlying multivariate distribution that represents the random process. Time series can be classified into the same four categories as models for random processes. It is useful to split a time series into constituent parts, which may include a trend, oscillations about the trend such as seasonal effects, and a random component. ARIMA models for discrete random processes include discrete white noise (DWN), random walk, moving average processes, autoregressive processes, and ARIMA (p, d, q) processes. Models of random processes can be used as part of simulation studies. The basic tool in any simulation is the generation of realizations of DWN.