# We fix the parameter of the Cauchy model amplitude = [5] scale = [3] model = ot.CauchyModel(scale, amplitude) gp = ot.SpectralGaussianProcess(model, myTimeGrid) # Get a time series or a sample of time series # myTimeSeries = gp.getRealization() mySample = gp.getSample(1000) mySegmentNumber = 10 myOverlapSize = 0.3 # Build a spectral model factory myFactory = ot.WelchFactory(ot.Hanning(), mySegmentNumber, myOverlapSize) # Estimation on a TimeSeries or on a ProcessSample # myEstimatedModel_TS = myFactory.build(myTimeSeries) myEstimatedModel_PS = myFactory.buildAsUserDefinedSpectralModel(mySample) # Change the filtering window myFactory.setFilteringWindows(ot.Hamming()) # Get the FFT algorithm myFFT = myFactory.getFFTAlgorithm() # Get the frequencyGrid frequencyGrid = myEstimatedModel_PS.getFrequencyGrid() # With the model, we want to compare values
covmodel = ot.ExponentialModel(scale, amplitude) # Create a stationary Normal process with that covariance model process = ot.GaussianProcess(covmodel, tgrid) # Create a time series and a sample of time series tseries = process.getRealization() sample = process.getSample(1000) # %% # Build a factory of stationary covariance function covarianceFactory = ot.StationaryCovarianceModelFactory() # Set the spectral factory algorithm segmentNumber = 5 spectralFactory = ot.WelchFactory(ot.Hanning(), segmentNumber) covarianceFactory.setSpectralModelFactory(spectralFactory) # Check the current spectral factory print(covarianceFactory.getSpectralModelFactory()) # %% # Case 1 : Estimation on a ProcessSample # The spectral model factory computes the spectral density function # without using the block and overlap arguments of the Welch factories estimatedModel_PS = covarianceFactory.build(sample) # Case 2 : Estimation on a TimeSeries # The spectral model factory compute the spectral density function using
# We fix the parameter of the Cauchy model
amplitude = [5.0]
scale = [3.0]
model = ot.CauchyModel(amplitude, scale)
process = ot.SpectralGaussianProcess(model, tgrid)
# Get a time series or a sample of time series
tseries = process.getRealization()
sample = process.getSample(1000)
# %%
# Build a spectral model factory
segmentNumber = 10
overlapSize = 0.3
factory = ot.WelchFactory(ot.Hann(), segmentNumber, overlapSize)
# %%
# Estimation on a TimeSeries or on a ProcessSample
estimatedModel_TS = factory.build(tseries)
estimatedModel_PS = factory.build(sample)
# %%
# Change the filtering window
factory.setFilteringWindows(ot.Hamming())
# %%
# Get the frequencyGrid
frequencyGrid = ot.SpectralGaussianProcess(estimatedModel_PS,
tgrid).getFrequencyGrid()
# CASE 1 : we specify a (p,q) order
# Specify the order (p,q)
p = 4
q = 2
# Create the estimator
factory = ot.WhittleFactory(p, q)
print("Default spectral model factory = ", factory.getSpectralModelFactory())
# To set the spectral model factory
# For example, set WelchFactory as SpectralModelFactory
# with the Hann filtering window
# The Welch estimator splits the time series in four blocs without overlap
myFilteringWindow = ot.Hann()
mySpectralFactory = ot.WelchFactory(myFilteringWindow, 4, 0)
factory.setSpectralModelFactory(mySpectralFactory)
print("New spectral model factory = ", factory.getSpectralModelFactory())
# Estimate the ARMA model from a time series
# To get the quantified AICc, AIC and BIC criteria
arma42, criterion = factory.buildWithCriteria(tseries)
AICc, AIC, BIC = criterion[0:3]
print('AICc=', AICc, 'AIC=', AIC, 'BIC=', BIC)
arma42
# %%
# CASE 2 : we specify a range of (p,q) orders
# Range for p
pIndices = [1, 2, 4]