#!/usr/bin/env python
# coding: utf-8

# DO NOT EDIT
# Autogenerated from the notebook stl_decomposition.ipynb.
# Edit the notebook and then sync the output with this file.
#
# flake8: noqa
# DO NOT EDIT

# # Seasonal-Trend decomposition using LOESS (STL)
#
# This note book illustrates the use of `STL` to decompose a time series
# into three components: trend, season(al) and residual. STL uses LOESS
# (locally estimated scatterplot smoothing) to extract smooths estimates of
# the three components.  The key inputs into `STL` are:
#
# * `season` - The length of the seasonal smoother. Must be odd.
# * `trend` - The length of the trend smoother, usually around 150% of
# `season`.  Must be odd and larger than `season`.
# * `low_pass` - The length of the low-pass estimation window, usually the
# smallest odd number larger than the periodicity of the data.
#
# First we import the required packages, prepare the graphics environment,
# and prepare the data.

import matplotlib.pyplot as plt
import pandas as pd
import seaborn as sns
from pandas.plotting import register_matplotlib_converters

register_matplotlib_converters()
sns.set_style("darkgrid")

plt.rc("figure", figsize=(16, 12))
plt.rc("font", size=13)

# ## Atmospheric CO2
#
# The example in Cleveland, Cleveland, McRae, and Terpenning (1990) uses
# CO2 data, which is in the list below.  This monthly data (January 1959 to
# December 1987) has a clear trend and seasonality across the sample.

co2 = [
    315.58,
    316.39,
    316.79,
    317.82,
    318.39,
    318.22,
    316.68,
    315.01,
    314.02,
    313.55,
    315.02,
    315.75,
    316.52,
    317.10,
    317.79,
    319.22,
    320.08,
    319.70,
    318.27,
    315.99,
    314.24,
    314.05,
    315.05,
    316.23,
    316.92,
    317.76,
    318.54,
    319.49,
    320.64,
    319.85,
    318.70,
    316.96,
    315.17,
    315.47,
    316.19,
    317.17,
    318.12,
    318.72,
    319.79,
    320.68,
    321.28,
    320.89,
    319.79,
    317.56,
    316.46,
    315.59,
    316.85,
    317.87,
    318.87,
    319.25,
    320.13,
    321.49,
    322.34,
    321.62,
    319.85,
    317.87,
    316.36,
    316.24,
    317.13,
    318.46,
    319.57,
    320.23,
    320.89,
    321.54,
    322.20,
    321.90,
    320.42,
    318.60,
    316.73,
    317.15,
    317.94,
    318.91,
    319.73,
    320.78,
    321.23,
    322.49,
    322.59,
    322.35,
    321.61,
    319.24,
    318.23,
    317.76,
    319.36,
    319.50,
    320.35,
    321.40,
    322.22,
    323.45,
    323.80,
    323.50,
    322.16,
    320.09,
    318.26,
    317.66,
    319.47,
    320.70,
    322.06,
    322.23,
    322.78,
    324.10,
    324.63,
    323.79,
    322.34,
    320.73,
    319.00,
    318.99,
    320.41,
    321.68,
    322.30,
    322.89,
    323.59,
    324.65,
    325.30,
    325.15,
    323.88,
    321.80,
    319.99,
    319.86,
    320.88,
    322.36,
    323.59,
    324.23,
    325.34,
    326.33,
    327.03,
    326.24,
    325.39,
    323.16,
    321.87,
    321.31,
    322.34,
    323.74,
    324.61,
    325.58,
    326.55,
    327.81,
    327.82,
    327.53,
    326.29,
    324.66,
    323.12,
    323.09,
    324.01,
    325.10,
    326.12,
    326.62,
    327.16,
    327.94,
    329.15,
    328.79,
    327.53,
    325.65,
    323.60,
    323.78,
    325.13,
    326.26,
    326.93,
    327.84,
    327.96,
    329.93,
    330.25,
    329.24,
    328.13,
    326.42,
    324.97,
    325.29,
    326.56,
    327.73,
    328.73,
    329.70,
    330.46,
    331.70,
    332.66,
    332.22,
    331.02,
    329.39,
    327.58,
    327.27,
    328.30,
    328.81,
    329.44,
    330.89,
    331.62,
    332.85,
    333.29,
    332.44,
    331.35,
    329.58,
    327.58,
    327.55,
    328.56,
    329.73,
    330.45,
    330.98,
    331.63,
    332.88,
    333.63,
    333.53,
    331.90,
    330.08,
    328.59,
    328.31,
    329.44,
    330.64,
    331.62,
    332.45,
    333.36,
    334.46,
    334.84,
    334.29,
    333.04,
    330.88,
    329.23,
    328.83,
    330.18,
    331.50,
    332.80,
    333.22,
    334.54,
    335.82,
    336.45,
    335.97,
    334.65,
    332.40,
    331.28,
    330.73,
    332.05,
    333.54,
    334.65,
    335.06,
    336.32,
    337.39,
    337.66,
    337.56,
    336.24,
    334.39,
    332.43,
    332.22,
    333.61,
    334.78,
    335.88,
    336.43,
    337.61,
    338.53,
    339.06,
    338.92,
    337.39,
    335.72,
    333.64,
    333.65,
    335.07,
    336.53,
    337.82,
    338.19,
    339.89,
    340.56,
    341.22,
    340.92,
    339.26,
    337.27,
    335.66,
    335.54,
    336.71,
    337.79,
    338.79,
    340.06,
    340.93,
    342.02,
    342.65,
    341.80,
    340.01,
    337.94,
    336.17,
    336.28,
    337.76,
    339.05,
    340.18,
    341.04,
    342.16,
    343.01,
    343.64,
    342.91,
    341.72,
    339.52,
    337.75,
    337.68,
    339.14,
    340.37,
    341.32,
    342.45,
    343.05,
    344.91,
    345.77,
    345.30,
    343.98,
    342.41,
    339.89,
    340.03,
    341.19,
    342.87,
    343.74,
    344.55,
    345.28,
    347.00,
    347.37,
    346.74,
    345.36,
    343.19,
    340.97,
    341.20,
    342.76,
    343.96,
    344.82,
    345.82,
    347.24,
    348.09,
    348.66,
    347.90,
    346.27,
    344.21,
    342.88,
    342.58,
    343.99,
    345.31,
    345.98,
    346.72,
    347.63,
    349.24,
    349.83,
    349.10,
    347.52,
    345.43,
    344.48,
    343.89,
    345.29,
    346.54,
    347.66,
    348.07,
    349.12,
    350.55,
    351.34,
    350.80,
    349.10,
    347.54,
    346.20,
    346.20,
    347.44,
    348.67,
]
co2 = pd.Series(co2,
                index=pd.date_range("1-1-1959", periods=len(co2), freq="M"),
                name="CO2")
co2.describe()

# The decomposition requires 1 input, the data series. If the data series
# does not have a frequency, then you must also specify `period`. The
# default value for `seasonal` is 7, and so should also be changed in most
# applications.

from statsmodels.tsa.seasonal import STL

stl = STL(co2, seasonal=13)
res = stl.fit()
fig = res.plot()

# ## Robust Fitting
# Setting `robust` uses a data-dependent weighting function that re-
# weights data when estimating the LOESS (and so is using LOWESS). Using
# robust estimation allows the model to tolerate larger errors that are
# visible on the bottom plot.
#
# Here we use a series the measures the production of electrical equipment
# in the EU.

from statsmodels.datasets import elec_equip as ds

elec_equip = ds.load().data

# Next, we estimate the model with and without robust weighting.  The
# difference is minor and is most pronounced during the financial crisis of
# 2008. The non-robust estimate places equal weights on all observations and
# so produces smaller errors, on average.  The weights vary between 0 and 1.


def add_stl_plot(fig, res, legend):
    """Add 3 plots from a second STL fit"""
    axs = fig.get_axes()
    comps = ["trend", "seasonal", "resid"]
    for ax, comp in zip(axs[1:], comps):
        series = getattr(res, comp)
        if comp == "resid":
            ax.plot(series, marker="o", linestyle="none")
        else:
            ax.plot(series)
            if comp == "trend":
                ax.legend(legend, frameon=False)


stl = STL(elec_equip, period=12, robust=True)
res_robust = stl.fit()
fig = res_robust.plot()
res_non_robust = STL(elec_equip, period=12, robust=False).fit()
add_stl_plot(fig, res_non_robust, ["Robust", "Non-robust"])

fig = plt.figure(figsize=(16, 5))
lines = plt.plot(res_robust.weights, marker="o", linestyle="none")
ax = plt.gca()
xlim = ax.set_xlim(elec_equip.index[0], elec_equip.index[-1])

# ## LOESS degree
# The default configuration estimates the LOESS model with both a constant
# and a trend.  This can be changed to only include a constant by setting
# `COMPONENT_deg` to 0. Here the degree makes little difference except in
# the trend around the financial crisis of 2008.

stl = STL(elec_equip,
          period=12,
          seasonal_deg=0,
          trend_deg=0,
          low_pass_deg=0,
          robust=True)
res_deg_0 = stl.fit()
fig = res_robust.plot()
add_stl_plot(fig, res_deg_0, ["Degree 1", "Degree 0"])

# ## Performance
# Three options can be used to reduce the computational cost of the STL
# decomposition:
#
# * `seasonal_jump`
# * `trend_jump`
# * `low_pass_jump`
#
# When these are non-zero, the LOESS for component `COMPONENT` is only
# estimated ever `COMPONENT_jump` observations, and linear interpolation is
# used between points. These values should not normally be more than 10-20%
# of the size of `seasonal`, `trend` or `low_pass`, respectively.
#
# The example below shows how these can reduce the computational cost by a
# factor of 15 using simulated data with both a low-frequency cosinusoidal
# trend and a sinusoidal seasonal pattern.

import numpy as np

rs = np.random.RandomState(0xA4FD94BC)
tau = 2000
t = np.arange(tau)
period = int(0.05 * tau)
seasonal = period + ((period % 2) == 0)  # Ensure odd
e = 0.25 * rs.standard_normal(tau)
y = np.cos(t / tau * 2 * np.pi) + 0.25 * np.sin(t / period * 2 * np.pi) + e
plt.plot(y)
plt.title("Simulated Data")
xlim = plt.gca().set_xlim(0, tau)

# First, the base line model is estimated with all jumps equal to 1.

mod = STL(y, period=period, seasonal=seasonal)
res = mod.fit()
fig = res.plot(observed=False, resid=False)

# The jumps are all set to 15% of their window length. Limited linear
# interpolation makes little difference to the fit of the model.

low_pass_jump = seasonal_jump = int(0.15 * (period + 1))
trend_jump = int(0.15 * 1.5 * (period + 1))
mod = STL(
    y,
    period=period,
    seasonal=seasonal,
    seasonal_jump=seasonal_jump,
    trend_jump=trend_jump,
    low_pass_jump=low_pass_jump,
)
res = mod.fit()
fig = res.plot(observed=False, resid=False)

# ## Forecasting with STL
#
# ``STLForecast`` simplifies the process of using STL to remove
# seasonalities and then using a standard time-series model to forecast the
# trend and cyclical components.
#
# Here we use STL to handle the seasonality and then an ARIMA(1,1,0) to
# model the deseasonalized data. The seasonal component is forecast from the
# find full cycle where
#
# $$E[S_{T+h}|\mathcal{F}_T]=\hat{S}_{T-k}$$
#
# where $k= m - h + m \lfloor \frac{h-1}{m} \rfloor$. The forecast
# automatically adds the seasonal component forecast to the ARIMA forecast.

from statsmodels.tsa.arima.model import ARIMA
from statsmodels.tsa.forecasting.stl import STLForecast

elec_equip.index.freq = elec_equip.index.inferred_freq
stlf = STLForecast(elec_equip,
                   ARIMA,
                   model_kwargs=dict(order=(1, 1, 0), trend="t"))
stlf_res = stlf.fit()

forecast = stlf_res.forecast(24)
plt.plot(elec_equip)
plt.plot(forecast)
plt.show()

# ``summary`` contains information about both the time-series model and
# the STL decomposition.

print(stlf_res.summary())