## 4.5 Analysis of De-seasonalised Data

### Linear Regression of Ordinary Time Series Data

• As with any other type of bivariate data, it is often useful to apply linear regression to time series data in order to predict values for which we have no data.
• For time series data, time is always the explanatory variable.
• Unprocessed data with seasonality is generally poorly modelled by a linear fit.

Note: if you cannot remember how to construct and interpret a linear fit, revise notes for 3.1 Least Squares Linear Regression and 3.2 Modelling Linear Associations.

### Re-seasonalising Data

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## 4.4 Introduction to Seasonal Indices

### Seasonal Indices

• Seasonal indices provide a method to de-seasonalise data.
• The seasonal index of a season/month/period/etc. compares the average value of a particular season to the average of all seasons in a cycle.
• A seasonal index of 1 indicates the average value of the season is exactly equal to the average value of the entire cycle.
• A seasonal index greater than 1 indicates the average value of the season is greater than that of the entire cycle (e.g. a seasonal index of 1.2 indicates the season’s average is 20% higher than the cycle’s average).
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