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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Autoregressive Moving Average (ARMA)
Step1:  Generate some data from an ARMA process
Step2:  The conventions of the arma_generate function require that we specify a 1 for the zero-lag of the AR and MA parameters and that the AR parameters be negated.
Step3:  Now, optionally, we can add some dates information. For this example, we'll use a pandas time series.
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Python Code:
%matplotlib inline
import numpy as np
import pandas as pd
from statsmodels.graphics.tsaplots import plot_predict
from statsmodels.tsa.arima_process import arma_generate_sample
from statsmodels.tsa.arima.model import ARIMA
np.random.seed(12345)
Explanation: Autoregressive Moving Average (ARMA): Artificial data
End of explanation
arparams = np.array([0.75, -0.25])
maparams = np.array([0.65, 0.35])
Explanation: Generate some data from an ARMA process:
End of explanation
arparams = np.r_[1, -arparams]
maparams = np.r_[1, maparams]
nobs = 250
y = arma_generate_sample(arparams, maparams, nobs)
Explanation: The conventions of the arma_generate function require that we specify a 1 for the zero-lag of the AR and MA parameters and that the AR parameters be negated.
End of explanation
dates = pd.date_range("1980-1-1", freq="M", periods=nobs)
y = pd.Series(y, index=dates)
arma_mod = ARIMA(y, order=(2, 0, 2), trend="n")
arma_res = arma_mod.fit()
print(arma_res.summary())
y.tail()
import matplotlib.pyplot as plt
fig, ax = plt.subplots(figsize=(10, 8))
fig = plot_predict(arma_res, start="1999-06-30", end="2001-05-31", ax=ax)
legend = ax.legend(loc="upper left")
Explanation: Now, optionally, we can add some dates information. For this example, we'll use a pandas time series.
End of explanation
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