Chapter 5 Time Series Data

We will start with univariate time series, which is defined as a sequence of measurements of the same characteristic collected over time at regular intervals. We’ll notate this time series as

\[y_t\text{, for } t = 1,2,...,n\]

where \(t\) indexes time in a chosen unit.

For example, if data are collected yearly, \(t=1\) indicates the first year, etc. If data are collected every day, then \(t=1\) indicates the first day of data collection. In other settings, we may have monthly or hourly measurements such that \(t\) indices months or hours from the beginning of the study period.

There are two main approaches to analyzing time series data: time-domain and frequency-domain analysis. In this class, we’ll focus on time-domain analysis. For frequency domain approaches, check out the Other Time Series References.