# coding: utf-8

# DO NOT EDIT
# Autogenerated from the notebook tsa_arma_0.ipynb.
# Edit the notebook and then sync the output with this file.
#
# flake8: noqa
# DO NOT EDIT

# # Autoregressive Moving Average (ARMA): Sunspots data

import numpy as np
from scipy import stats
import pandas as pd
import matplotlib.pyplot as plt

import statsmodels.api as sm

from statsmodels.graphics.api import qqplot

# ## Sunspots Data

print(sm.datasets.sunspots.NOTE)

dta = sm.datasets.sunspots.load_pandas().data

dta.index = pd.Index(sm.tsa.datetools.dates_from_range('1700', '2008'))
del dta["YEAR"]

dta.plot(figsize=(12, 8))

fig = plt.figure(figsize=(12, 8))
ax1 = fig.add_subplot(211)
fig = sm.graphics.tsa.plot_acf(dta.values.squeeze(), lags=40, ax=ax1)
ax2 = fig.add_subplot(212)
fig = sm.graphics.tsa.plot_pacf(dta, lags=40, ax=ax2)

arma_mod20 = sm.tsa.ARMA(dta, (2, 0)).fit(disp=False)
print(arma_mod20.params)

arma_mod30 = sm.tsa.ARMA(dta, (3, 0)).fit(disp=False)

print(arma_mod20.aic, arma_mod20.bic, arma_mod20.hqic)

print(arma_mod30.params)

print(arma_mod30.aic, arma_mod30.bic, arma_mod30.hqic)

# * Does our model obey the theory?

sm.stats.durbin_watson(arma_mod30.resid.values)

fig = plt.figure(figsize=(12, 8))
ax = fig.add_subplot(111)
ax = arma_mod30.resid.plot(ax=ax)

resid = arma_mod30.resid

stats.normaltest(resid)

fig = plt.figure(figsize=(12, 8))
ax = fig.add_subplot(111)
fig = qqplot(resid, line='q', ax=ax, fit=True)

fig = plt.figure(figsize=(12, 8))
ax1 = fig.add_subplot(211)
fig = sm.graphics.tsa.plot_acf(resid.values.squeeze(), lags=40, ax=ax1)
ax2 = fig.add_subplot(212)
fig = sm.graphics.tsa.plot_pacf(resid, lags=40, ax=ax2)

r, q, p = sm.tsa.acf(resid.values.squeeze(), qstat=True)
data = np.c_[range(1, 41), r[1:], q, p]
table = pd.DataFrame(data, columns=['lag', "AC", "Q", "Prob(>Q)"])
print(table.set_index('lag'))

# * This indicates a lack of fit.

# * In-sample dynamic prediction. How good does our model do?

predict_sunspots = arma_mod30.predict('1990', '2012', dynamic=True)
print(predict_sunspots)

fig, ax = plt.subplots(figsize=(12, 8))
ax = dta.loc['1950':].plot(ax=ax)
fig = arma_mod30.plot_predict(
    '1990', '2012', dynamic=True, ax=ax, plot_insample=False)


def mean_forecast_err(y, yhat):
    return y.sub(yhat).mean()


mean_forecast_err(dta.SUNACTIVITY, predict_sunspots)

# ### Exercise: Can you obtain a better fit for the Sunspots model? (Hint:
# sm.tsa.AR has a method select_order)

# ### Simulated ARMA(4,1): Model Identification is Difficult

from statsmodels.tsa.arima_process import ArmaProcess

np.random.seed(1234)
# include zero-th lag
arparams = np.array([1, .75, -.65, -.55, .9])
maparams = np.array([1, .65])

# Let's make sure this model is estimable.

arma_t = ArmaProcess(arparams, maparams)

arma_t.isinvertible

arma_t.isstationary

# * What does this mean?

fig = plt.figure(figsize=(12, 8))
ax = fig.add_subplot(111)
ax.plot(arma_t.generate_sample(nsample=50))

arparams = np.array([1, .35, -.15, .55, .1])
maparams = np.array([1, .65])
arma_t = ArmaProcess(arparams, maparams)
arma_t.isstationary

arma_rvs = arma_t.generate_sample(nsample=500, burnin=250, scale=2.5)

fig = plt.figure(figsize=(12, 8))
ax1 = fig.add_subplot(211)
fig = sm.graphics.tsa.plot_acf(arma_rvs, lags=40, ax=ax1)
ax2 = fig.add_subplot(212)
fig = sm.graphics.tsa.plot_pacf(arma_rvs, lags=40, ax=ax2)

# * For mixed ARMA processes the Autocorrelation function is a mixture of
# exponentials and damped sine waves after (q-p) lags.
# * The partial autocorrelation function is a mixture of exponentials and
# dampened sine waves after (p-q) lags.

arma11 = sm.tsa.ARMA(arma_rvs, (1, 1)).fit(disp=False)
resid = arma11.resid
r, q, p = sm.tsa.acf(resid, qstat=True)
data = np.c_[range(1, 41), r[1:], q, p]
table = pd.DataFrame(data, columns=['lag', "AC", "Q", "Prob(>Q)"])
print(table.set_index('lag'))

arma41 = sm.tsa.ARMA(arma_rvs, (4, 1)).fit(disp=False)
resid = arma41.resid
r, q, p = sm.tsa.acf(resid, qstat=True)
data = np.c_[range(1, 41), r[1:], q, p]
table = pd.DataFrame(data, columns=['lag', "AC", "Q", "Prob(>Q)"])
print(table.set_index('lag'))

# ### Exercise: How good of in-sample prediction can you do for another
# series, say, CPI

macrodta = sm.datasets.macrodata.load_pandas().data
macrodta.index = pd.Index(
    sm.tsa.datetools.dates_from_range('1959Q1', '2009Q3'))
cpi = macrodta["cpi"]

# #### Hint:

fig = plt.figure(figsize=(12, 8))
ax = fig.add_subplot(111)
ax = cpi.plot(ax=ax)
ax.legend()

# P-value of the unit-root test, resoundingly rejects the null of a unit-
# root.

print(sm.tsa.adfuller(cpi)[1])