Time Series

What is a Time Series?

A time series is a sequence of data points ordered by time. Each data point represents an observation at a specific point or time period. A time series has a constant granularity, such as month, week, or day.

A time series has a start point (the first observation) and an end point (the last observation).

Time series can consist of various types of data, such as sensor measurements or monthly sales of a product. They serve as the basis for analysis in areas where patterns are sought and meaningful information is derived from historical data. Examples include fields like statistics, signal processing, financial mathematics, and weather forecasting.

A time series analysis often aims to make predictions about future developments based on given data. The methods used in such analysis are diverse and can differ significantly in approach. However, most methods share the assumption that data points closer in time are more strongly related to one another than those that are further apart.

Time series can also differ greatly in their structure, and as a result, they are classified into certain types. Not every method should or can be applied to all time series types. To ensure the highest prediction quality, the correct classification of the time series and the appropriate selection of the forecasting method are essential.

Example of a time series on a monthly basis with a stable seasonal pattern

Different Types of Time Series

Time series can vary greatly in their qualities, and therefore, different techniques are required to model them. A simple classification is as follows:

Smooth Time Series:

Few to no values equal to 0, small coefficient of variation.

Erratic Time Series:

Few to no values equal to 0, higher coefficient of variation.

Sporadic/Intermittent Time Series:

Sporadic time series with many zero values

Many values equal to 0, no clustering.

Lumpy Time Series:

If non-zero values appear, they are clustered.

Trivial Types of Time Series

In addition, there are other "trivial" types where no patterns can typically be detected:

few observations: extremely few non-zero values.
(almost) constant: a value that remains (almost) constant over time.
very short: very few values or an extremely short data history.

Properties

Granularity

The granularity of a time series determines the temporal frequency at which observations are measured over time. Monthly granularity occurs when one observation is recorded per month. Daily granularity refers to when observations are recorded daily.

Seasonality

Seasonal time series on a monthly basis with a season length of 12 months. It can be observed that the first half of the year (Jan-Jun) is generally stronger than the second half (Jul-Dec), with a pronounced dip in December.

Seasonality refers to a typical structural component in time series: seasonality occurs when cyclical, repeating patterns are found in the time series. The length of the period after which these seasonal patterns repeat is referred to as the season length. Monthly data, for example, often exhibit seasonality with a season length of 12 months.

Trend

In addition to seasonality, the trend of a time series is another important structural characteristic: a trend exists when there is a clear directional development within the time series, either upward (positive growth) or downward (negative growth). Different types of trends can be modeled: linear trend, parabolic trend, exponential trend, etc. In practice, the focus is often on linear trends and dampened linear trends. While a linear trend extrapolates a recognized trend linearly into the future, a dampened trend models trend saturation, where the trend weakens over time.

Outliers

Monthly time series with an outlier in the seasonal pattern — The usual weak December value of the time series in 2008 is significantly higher than in other years — an outlier in the seasonal pattern.

Outliers are extraordinary values in the time series history that disrupt the usual structure of the series. Outliers may arise from exceptional situations or data errors. Such exceptional values can distort the model estimation and therefore the forecasts. It is important to identify outliers based on the data and, if necessary, replace them with an appropriate substitute value.