Seasonal Decomposition
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from pandas.plotting import register_matplotlib_converters
register_matplotlib_converters() # datetime converter for a matplotlib
import seaborn as sns
sns.set(style="ticks", font_scale=1.5)
from statsmodels.tsa.seasonal import seasonal_decompose
import matplotlib.dates as mdates
from matplotlib.dates import DateFormatter
Trends in Atmospheric Carbon Dioxide
Mauna Loa CO2 concentration.
data from NOAA
url = "https://gml.noaa.gov/webdata/ccgg/trends/co2/co2_weekly_mlo.csv"
df = pd.read_csv(url, header=47, na_values=[-999.99])
# you can first download, and then read the csv
# filename = "co2_weekly_mlo.csv"
# df = pd.read_csv(filename, header=47, na_values=[-999.99])
df
df['date'] = pd.to_datetime(df[['year', 'month', 'day']])
df = df.set_index('date')
df
fig, ax = plt.subplots(1, figsize=(8,6))
ax.plot(df['average'])
ax.set(xlabel="date",
ylabel="CO2 concentration (ppm)",
# ylim=[0, 430],
title="Mauna Loa CO2 concentration");
fill missing data. interpolate method: 'time'
interpolation methods visualized
df['co2'] = (df['average'].resample("D") #resample daily
.interpolate(method='time') #interpolate by time
)
df
letters = ['a', 'b', 'c', 'd', 'e']
numbers = [1, 2, 3, 4, 5]
# zip let's us iterate over to lists at the same time
for l, n in zip(letters, numbers):
print(f"{l} = {n}")
Plot each component separately.
fig, ax = plt.subplots(4, 1, figsize=(8,6), sharex=True)
decomposed_m = seasonal_decompose(df['co2'], model='multiplicative')
decomposed_a = seasonal_decompose(df['co2'], model='additive')
decomposed = decomposed_m
pos = (0.5, 0.9)
components =["observed", "trend", "seasonal", "resid"]
colors = ["tab:blue", "tab:orange", "tab:green", "tab:red"]
for axx, component, color in zip(ax, components, colors):
data = getattr(decomposed, component)
axx.plot(data, color=color)
axx.text(*pos, component, bbox=dict(facecolor='white', alpha=0.8),
transform=axx.transAxes, ha='center', va='top')
decomposed = decomposed_m
fig, ax = plt.subplots(1, 2, figsize=(10,6))
ax[0].plot(df['co2'], color="tab:blue", label="observed")
ax[0].plot(decomposed.trend * decomposed.resid, color="tab:orange", label="trend*resid")
ax[0].plot(decomposed.trend * decomposed.seasonal, color="tab:red", label="trend*seasonal")
ax[0].plot(decomposed.trend, color="black", label="trend")
ax[0].set(ylabel="CO$_2$ concentration (ppm)",
title="Mauna Loa CO$_2$ concentration")
ax[0].legend(frameon=False)
start = "2000-01-01"
end = "2003-01-01"
zoom = slice(start, end)
ax[1].plot(df.loc[zoom, 'co2'], color="tab:blue", label="observed")
ax[1].plot((decomposed.trend * decomposed.resid)[zoom], color="tab:orange", label="trend*resid")
ax[1].plot((decomposed.trend * decomposed.seasonal)[zoom], color="tab:red", label="trend*seasonal")
ax[1].plot(decomposed.trend[zoom], color="black", label="trend")
date_form = DateFormatter("%Y")
ax[1].xaxis.set_major_formatter(date_form)
ax[1].xaxis.set_major_locator(mdates.YearLocator(1))
ax[1].set_title("Components, 2000--2003");
