Autocorrelation

Goal

Identify dominant periodicities in a time series using autocorrelation. Peaks in the autocorrelation function (ACF) reveal repeating cycles — daily, weekly, or seasonal — which are fundamental to understanding building energy and climate data.

Data Basis

Dataset: flatTempHum.csv — Hourly indoor temperature and humidity measurements from four residential flats (A–D).
Column used: FlatA_Temp
Time range: October 2018 – September 2020

Data Preparation

import pandas as pd

url = "https://raw.githubusercontent.com/retomarek/edap/main/edap/sampleData/flatTempHum.csv"
df = pd.read_csv(url, sep=";")
df["time"] = pd.to_datetime(df["time"])
df = df.set_index("time", drop=True)
df.head()

	FlatA_Hum	FlatA_Temp	FlatB_Hum	FlatB_Temp	FlatC_Hum	FlatC_Temp	FlatD_Hum	FlatD_Temp
time
2018-10-03 00:00:00	53.0	24.43	38.8	22.40	44.0	24.5	49.0	24.43
2018-10-03 01:00:00	53.0	24.40	38.8	22.40	44.0	24.5	49.0	24.40
2018-10-03 02:00:00	53.0	24.40	39.3	22.40	44.7	24.5	48.3	24.38
2018-10-03 03:00:00	53.0	24.40	40.3	22.40	45.0	24.5	48.0	24.33
2018-10-03 04:00:00	53.3	24.40	41.0	22.37	45.2	24.5	47.7	24.30

Visualization

The autocorrelation plot shows how a signal correlates with itself at increasing time lags. The blue shaded area marks the 95% confidence interval — values inside the band are not statistically significant.

from pyedautils.plots import plot_autocorrelation

fig = plot_autocorrelation(
    df,
    column="FlatA_Temp",
    lags=168,
    title="Autocorrelation — FlatA Temperature (1 week)",
)
fig.show()

Reading the autocorrelation plot

• Peak at lag 24 → daily cycle (temperature now resembles temperature 24 hours ago)

• Peak at lag 168 → weekly cycle (same day last week)

• Slow overall decay → strong trend in the data (non-stationary)

• Residential buildings typically show a clear daily cycle but a weak weekly cycle (no weekday/weekend occupancy difference)

Longer Lag Window

Increase the number of lags to look for longer-period cycles.

fig = plot_autocorrelation(
    df,
    column="FlatA_Temp",
    lags=720,
    title="Autocorrelation — FlatA Temperature (30 days)",
    height=350,
)
fig.show()

Customization

• Lags count steps of the regular time grid that plot_autocorrelation builds itself; gaps of up to max_gap steps (default 6) are interpolated, longer gaps are left out of the calculation.

• Set lags=24 for a single-day view.

• Set lags=8760 to check for annual cycles (requires at least 2 years of hourly data).

• The confidence band widens at higher lags because it adds up the autocorrelations at all shorter lags (Bartlett’s formula): in a strongly autocorrelated series, a single peak at a long lag is harder to tell from chance.