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#!/usr/bin/env python
# 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 matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import statsmodels.api as sm
from scipy import stats
from statsmodels.tsa.arima.model import ARIMA
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"))
dta.index.freq = dta.index.inferred_freq
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 = ARIMA(dta, order=(2, 0, 0)).fit()
print(arma_mod20.params)
arma_mod30 = ARIMA(dta, order=(3, 0, 0)).fit()
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(), fft=True, qstat=True)
data = np.c_[np.arange(1, 25), 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)
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, 0.75, -0.65, -0.55, 0.9])
maparams = np.array([1, 0.65])
# 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, 0.35, -0.15, 0.55, 0.1])
maparams = np.array([1, 0.65])
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.
lags = int(10 * np.log10(arma_rvs.shape[0]))
arma11 = ARIMA(arma_rvs, order=(1, 0, 1)).fit()
resid = arma11.resid
r, q, p = sm.tsa.acf(resid, nlags=lags, fft=True, qstat=True)
data = np.c_[range(1, lags + 1), r[1:], q, p]
table = pd.DataFrame(data, columns=["lag", "AC", "Q", "Prob(>Q)"])
print(table.set_index("lag"))
arma41 = ARIMA(arma_rvs, order=(4, 0, 1)).fit()
resid = arma41.resid
r, q, p = sm.tsa.acf(resid, nlags=lags, fft=True, qstat=True)
data = np.c_[range(1, lags + 1), 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])
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