86  Equi-distant Time Series

Within the context of this handbook a time series is defined as a series of chronologically ordered values about some variable of interest that have been observed at regular time intervals. The term “equi-distant” does not imply that the time intervals between observations is exactly equal. Rather it is assumed that we can treat the time intervals as if they were equal because this allows us to employ easier types of analysis.

Here are two examples of non-equi-distant time series:

Here are a few examples of equi-distant time series:

Non-equi-distant time series can be converted to equi-distant time series by means of:

In any case it is important to understand that the so-called “sampling frequency” causes artifacts in time series that should be treated appropriately. For instance, some business cycles or seasonal effects may be artificially caused by the process that converts a non-equi-distant into an equi-distant time series. In addition, the diagnostic tools that are used to investigate the dynamical properties of time series are (to some extent) artifacts of the sampling frequency. The statistical methods that employ non-equal time intervals are beyond the scope of this document.

86.1 Example

Suppose a website records each transaction with an irregular timestamp. If we aggregate all transactions by month (sum of sales or average price per month), we obtain an equi-distant monthly time series. This allows us to use the diagnostics in Section 87.5, Section 88.6, and Section 92.6.