Chapter 13 Introduction to Time-Series Data

In this chapter we look at time-series data, which is also another fairly common type of data. Time-series data is data for one or more variables that vary across time, which we can denote as \(Y_t\) to indicate the \(Y\) variable at time \(t\).

In principle, we can use many different predictors in a time-series model:

\[ Y_t = b_0 + b_1 Y_{t-1} \\ + b_2 X_2 + ... \] where we can use the outcome variables at previous time-steps (\(Y_{t-1}, ...\)), or we can also use regressors at the current (or previous) time-steps (\(X_t, ...\)). We’ll be covering smoothing-based time-series models (the former), as well as modelling time-series data using regression models (the latter).

The learning objectives for this chapter are:

• Readers should be able to understand and be able to use simple time-series models, such as the Moving Average, Exponential Smoothing, and Holt-Winters models.

• Readers should be able to understand concepts important to time-series modelling, such as trends and seasonality, lagged analyses.

• Readers should be able to apply time-series variables in regression analyses.