Understanding time series seasonality

Analyzing and coping with seasonality is a key exercise in time series evaluation.

In this text, we’ll describe three varieties of seasonality and methods to detect them.

Seasonality is one among the important thing components that make up a time series. Seasonality refers to systematic movements that repeat over a given period with an analogous intensity.

Seasonal differences might be attributable to various aspects, akin to weather, calendar, or economic conditions. Examples abound in various applications. Flights are dearer in the summertime due to vacations and tourism. One other example is consumer spending which increases in December attributable to holidays.

Seasonality means the common value in some periods will probably be different than the common value at other times. This issue causes the series to be non-stationary. Because of this it is crucial to investigate seasonality when constructing a model.

There are three varieties of seasonal patterns that may emerge in time series. Seasonality might be deterministic or stochastic. On the stochastic side, seasonal patterns might be either stationary or not.

A majority of these seasonality will not be mutually exclusive. A time series can have each a deterministic and stochastic seasonal component.

Let’s describe each pattern in turn.

Deterministic seasonality

Time series with a deterministic seasonality have a continuing seasonal pattern. It at all times recurs in a predictable way, each in intensity and periodicity:

• : the extent of the seasonal pattern stays the identical over the identical seasonal period;
• : the situation of the peaks and troughs doesn’t change. In other words, the time between each repetition of the seasonal pattern is constant.

Here’s an artificial monthly time series with a deterministic seasonality:

import numpy as np
period = 12
size = 120
beta1 = 0.3
beta2 = 0.6
sin1 =…