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QuickStart Samples

ARIMA Models QuickStart Sample (IronPython)

Illustrates how to work with ARIMA time series models using classes in the Extreme.Statistics.TimeSeriesAnalysis namespace in IronPython.

```import numerics

from Extreme.Mathematics import *
from Extreme.Statistics import *
from Extreme.Statistics.TimeSeriesAnalysis import *

#/ Illustrates the use of the ArimaModel class to perform
#/ estimation and forecasting of ARIMA time series models..

# This QuickStart Sample fits an ARMA(2,1) model and
# an ARIMA(0,1,1) model to sunspot data.

# The time series data is stored in a numerical variable:
sunspots = NumericalVariable("sunspots", Vector([ \
100.8, 81.6, 66.5, 34.8, 30.6, 7, 19.8, 92.5, 154.4, \
125.9, 84.8, 68.1, 38.5, 22.8, 10.2, 24.1, 82.9, \
132, 130.9, 118.1, 89.9, 66.6, 60, 46.9, 41, 21.3, \
16, 6.4, 4.1, 6.8, 14.5, 34, 45, 43.1, 47.5, 42.2, \
28.1, 10.1, 8.1, 2.5, 0, 1.4, 5, 12.2, 13.9, 35.4, \
45.8, 41.1, 30.4, 23.9, 15.7, 6.6, 4, 1.8, 8.5, \
16.6, 36.3, 49.7, 62.5, 67, 71, 47.8, 27.5, 8.5, \
13.2, 56.9, 121.5, 138.3, 103.2, 85.8, 63.2, 36.8, \
24.2, 10.7, 15, 40.1, 61.5, 98.5, 124.3, 95.9, 66.5, \
64.5, 54.2, 39, 20.6, 6.7, 4.3, 22.8, 54.8, 93.8, \
95.7, 77.2, 59.1, 44, 47, 30.5, 16.3, 7.3, 37.3, 73.9 ]))

# ARMA models (no differencing) are constructed from
# the variable containing the time series data, and the
# AR and MA orders. The following constructs an ARMA(2,1)
# model:
model = ArimaModel(sunspots, 2, 1)

# The Compute methods fits the model.
model.Compute()

# The model's Parameters collection contains the fitted values.
# For an ARIMA(p,d,q) model, the first p parameters are the
# auto-regressive parameters. The last q parametere are the
# moving average parameters.
print "Parameter      Value  Std.Error  t-stat  p-Value"
for parameter in model.Parameters:
# Parameter objects have the following properties:
print "{0:10}{1:10.5f} {2:10.5f}{3:8.2f} {4:7.4f}".format( # Name, usually the name of the variable:
parameter.Name, # Estimated value of the parameter:
parameter.Value, # Standard error:
parameter.StandardError, # The value of the t statistic for the hypothesis that the parameter
# is zero.
parameter.Statistic, # Probability corresponding to the t statistic.
parameter.PValue)

# The log-likelihood of the computed solution is also available:
print "Log-likelihood: {0:.4f}".format(model.GetLogLikelihood())
# as is the Akaike Information Criterion (AIC):
print "AIC: {0:.4f}".format(model.GetAkaikeInformationCriterion())
# and the Baysian Information Criterion (BIC):
print "BIC: {0:.4f}".format(model.GetBayesianInformationCriterion())

# The Forecast method can be used to predict the next value in the series...
nextValue = model.Forecast()
print "One step ahead forecast: {0:.3f}".format(nextValue)

# or to predict a specified number of values:
nextValues = model.Forecast(5)
print "First five forecasts: ", nextValues.ToString("F3")

# An integrated model (with differencing) is constructed
# by supplying the degree of differencing. Note the order
# of the orders is the traditional one for an ARIMA(p,d,q)
# model (p, d, q).
# The following constructs an ARIMA(0,1,1) model:
model2 = ArimaModel(sunspots, 0, 1, 1)

# By default, the mean is assumed to be zero for an integrated model.
# We can override this by setting the EstimateMean property to True:
model2.EstimateMean = True

# The Compute methods fits the model.
model2.Compute()

# The mean shows up as one of the parameters.
print "Parameter      Value  Std.Error  t-stat  p-Value"
for parameter in model2.Parameters:
print "{0:10}{1:10.5f} {2:10.5f}{3:8.2f} {4:7.4f}".format(
parameter.Name, parameter.Value, parameter.StandardError, parameter.Statistic, parameter.PValue)

# We can also get the error variance:
print "Error variance: {0:.4f}".format(model2.ErrorVariance)

print "Log-likelihood: {0:.4f}".format(model2.GetLogLikelihood())
print "AIC: {0:.4f}".format(model2.GetAkaikeInformationCriterion())
print "BIC: {0:.4f}".format(model2.GetBayesianInformationCriterion())```