Having become familiar with the models that will allow us to predict time series, you probably have a question, which Python libraries will be used?

Firstly, in order to better understand the mathematical mechanism - you can implement one of the models yourself in Python.

While we will load the rest of the models through libraries such as statsmodels:

import matplotlib.pyplot as plt
import pandas as pd
import seaborn as sns
from statsmodels.tsa.api import acf, graphics, pacf
from statsmodels.tsa.ar_model import AutoReg, ar_select_order

sns.set_style("darkgrid")
pd.plotting.register_matplotlib_converters()
sns.mpl.rc("figure", figsize=(16, 6))
sns.mpl.rc("font", size=14)

data = pd.read_csv("HOUSTNSA.csv")
data = data.set_index("DATE")
housing = data.pct_change().dropna()
housing = 100 * housing.asfreq("MS")
fig, ax = plt.subplots()
ax = housing.plot(ax=ax)

mod = AutoReg(housing, 4, old_names=False)
res = mod.fit()

sel = ar_select_order(housing, 18, old_names=False)
sel.ar_lags
res = sel.model.fit()

fig = res.plot_predict(700, 840)

We have formed a prediction for the next hundred months in the plot above.

The above code uses a model that captures the last "pattern" of seasonality, i.e., the same repeating segment.