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Package Scientific :: Package Signals :: Module Models :: Class AutoRegressiveModel
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Class AutoRegressiveModel

Known Subclasses:

Auto-regressive model for stochastic process

This implementation uses the Burg algorithm to obtain the coefficients of the AR model.

Instance Methods
 
__init__(self, order, data, delta_t=1)
Scientific.Functions.Interpolation.InterpolatingFunction
correlation(self, nsteps)
Returns: the autocorrelation function of the process as estimated from the AR model
 
frictionConstant(self)
Returns: the friction constant of the process, i.e.
Scientific.Functions.Interpolation.InterpolatingFunction
memoryFunction(self, nsteps)
Returns: the memory function of the process as estimated from the AR model
Scientific.Function.Rational.RationalFunction
memoryFunctionZ(self)
Returns: the z-transform of the process' memory function
Scientific.Function.Rational.RationalFunction
memoryFunctionZapprox(self, den_order)
Returns: an approximation to the z-transform of the process' memory function that correponds to an expansion of the denominator up to order den_order
Numeric.array of complex
poles(self)
Returns: the poles of the model in the complex z-plane
float or complex
predictStep(self)
Calculates the linear prediction of the next step in the series.
Numeric.array of float
spectrum(self, omega)
Returns: the frequency spectrum of the process
Method Details

__init__(self, order, data, delta_t=1)
(Constructor)

 
Parameters:
  • order (int) - the order of the model
  • data (sequence of float or complex) - the time series
  • delta_t (float) - the sampling interval for the time series

correlation(self, nsteps)

 
Parameters:
  • nsteps (int) - the number of time steps for which the autocorrelation function is to be evaluated
Returns: Scientific.Functions.Interpolation.InterpolatingFunction
the autocorrelation function of the process as estimated from the AR model

frictionConstant(self)

 
Returns:
the friction constant of the process, i.e. the integral over the memory function

memoryFunction(self, nsteps)

 
Parameters:
  • nsteps (int) - the number of time steps for which the memory function is to be evaluated
Returns: Scientific.Functions.Interpolation.InterpolatingFunction
the memory function of the process as estimated from the AR model

memoryFunctionZ(self)

 
Returns: Scientific.Function.Rational.RationalFunction
the z-transform of the process' memory function

memoryFunctionZapprox(self, den_order)

 
Parameters:
  • den_order (int)
Returns: Scientific.Function.Rational.RationalFunction
an approximation to the z-transform of the process' memory function that correponds to an expansion of the denominator up to order den_order

poles(self)

 
Returns: Numeric.array of complex
the poles of the model in the complex z-plane

predictStep(self)

 

Calculates the linear prediction of the next step in the series. This step is appended internally to the current trajectory, making it possible to call this method repeatedly in order to obtain a sequence of predicted steps.

Returns: float or complex
the predicted step

spectrum(self, omega)

 
Parameters:
  • omega (Numeric.array of float) - the angular frequencies at which the spectrum is to be evaluated
Returns: Numeric.array of float
the frequency spectrum of the process

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