Basic Data Analysis for Time Series with R

3 THE MODELING APPROACH TAKEN IN THIS BOOK AND SOME EXAMPLES OF TYPICAL SERIALLY CORRELATED DATA

3.1 SIGNAL AND NOISE

In general, most data can be understood as observations of the form: . This model envisions the observations as produced by a deterministic “signal” contaminated with random “noise.” In data analysis, a model is fitted to the data, producing an “estimated signal” (), and the resulting residuals become the “estimated noise” . The residuals, aka the estimated noise, are the basis for modeling the uncertainty in the model.

In most courses in data analysis, the focus is on white noise (independent, normal errors, with zero mean and constant variance). In the context of serial correlation, the noise itself has a complex structure based on the temporal or spatial order of the observations. The time series analysis undertaken in this book will differ from regression in that the noise has a complex structure that must be identified. Once the structure is (approximately) identified, it will be possible to perform the usual regression tasks (model selection, prediction, confidence intervals, etc.) in a routine manner, after making some relatively routine adjustments to the ...