Time Series Components

import numpy as np, pandas as pd, matplotlib.pyplot as plt
idx=pd.date_range("2022-01-01",periods=36,freq="MS"); t=np.arange(36)
temp=pd.Series(26+0.05*t+5*np.sin(2*np.pi*t/12)+np.random.default_rng(0).normal(0,.6,36),idx)
roll=temp.rolling(12).mean(); diff=temp.diff()
print(temp.head()); print("Seasonal lag-12 autocorrelation:",round(temp.autocorr(12),3))
temp.plot(label="monthly temp"); roll.plot(label="12-mo rolling mean"); plt.legend(); plt.title("Trend + seasonality"); plt.show()