Trend, seasonality and noise

A time series is a sequence of measurements in time order. Most can be understood as three parts added together:

Trend: the long-term direction.
Seasonality: patterns that repeat on a fixed cycle — daily, weekly, yearly.
Noise: what's left, which no model can predict.

import pandas as pd

temps = pd.read_csv("https://data.giss.nasa.gov/gistemp/tabledata_v4/GLB.Ts+dSST.csv",
                    skiprows=1, na_values="***")
annual = temps.set_index("Year")["J-D"].dropna()   # annual mean anomaly, °C

annual.rolling(10).mean().plot()                    # a 10-year moving average shows the trend

The GISTEMP series is mostly trend: global temperature anomalies have risen markedly since the late 1970s. It has little seasonality at the annual level, and a lot of year-to-year noise.

Bike sharing rentals are the opposite: strong seasonality (more rides in summer, at rush hour, on working days), plus growth between 2011 and 2012.

Always plot the series first. It tells you which of these parts matter, and reveals gaps, outliers and changes in how the data was recorded.

Check your understanding

Further reading