use autoregression on time series code example

Example 1: ar model python

# create and evaluate an updated autoregressive model
from pandas import read_csv
from matplotlib import pyplot
from statsmodels.tsa.ar_model import AutoReg
from sklearn.metrics import mean_squared_error
from math import sqrt
# load dataset
series = read_csv('daily-minimum-temperatures.csv', header=0, index_col=0, parse_dates=True, squeeze=True)
# split dataset
X = series.values
train, test = X[1:len(X)-7], X[len(X)-7:]
# train autoregression
window = 29
model = AutoReg(train, lags=29)
model_fit = model.fit()
coef = model_fit.params
# walk forward over time steps in test
history = train[len(train)-window:]
history = [history[i] for i in range(len(history))]
predictions = list()
for t in range(len(test)):
	length = len(history)
	lag = [history[i] for i in range(length-window,length)]
	yhat = coef[0]
	for d in range(window):
		yhat += coef[d+1] * lag[window-d-1]
	obs = test[t]
	predictions.append(yhat)
	history.append(obs)
	print('predicted=%f, expected=%f' % (yhat, obs))
rmse = sqrt(mean_squared_error(test, predictions))
print('Test RMSE: %.3f' % rmse)
# plot
pyplot.plot(test)
pyplot.plot(predictions, color='red')
pyplot.show()

Example 2: ar model python

# create and evaluate a static autoregressive model
from pandas import read_csv
from matplotlib import pyplot
from statsmodels.tsa.ar_model import AutoReg
from sklearn.metrics import mean_squared_error
from math import sqrt
# load dataset
series = read_csv('daily-minimum-temperatures.csv', header=0, index_col=0, parse_dates=True, squeeze=True)
# split dataset
X = series.values
train, test = X[1:len(X)-7], X[len(X)-7:]
# train autoregression
model = AutoReg(train, lags=29)
model_fit = model.fit()
print('Coefficients: %s' % model_fit.params)
# make predictions
predictions = model_fit.predict(start=len(train), end=len(train)+len(test)-1, dynamic=False)
for i in range(len(predictions)):
	print('predicted=%f, expected=%f' % (predictions[i], test[i]))
rmse = sqrt(mean_squared_error(test, predictions))
print('Test RMSE: %.3f' % rmse)
# plot results
pyplot.plot(test)
pyplot.plot(predictions, color='red')
pyplot.show()