Class: Statsample::TimeSeries::Arima::KalmanFilter

Inherits:
Object
  • Object
show all
Includes:
GSL::MultiMin, Statsample::TimeSeries
Defined in:
lib/statsample-timeseries/arima/kalman.rb

Constant Summary

Constants included from Statsample::TimeSeries

VERSION

Instance Attribute Summary collapse

Class Method Summary collapse

Instance Method Summary collapse

Methods included from Statsample::TimeSeries

arima

Constructor Details

#initialize(ts = [], p = 0, i = 0, q = 0) ⇒ KalmanFilter

Creates a new KalmanFilter object and computes the likelihood


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# File 'lib/statsample-timeseries/arima/kalman.rb', line 25

def initialize(ts=[], p=0, i=0, q=0)
  @ts = ts.to_a
  @p = p
  @i = i
  @q = q
  ks #call the filter
end

Instance Attribute Details

#arObject (readonly)

Autoregressive coefficients


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# File 'lib/statsample-timeseries/arima/kalman.rb', line 20

def ar
  @ar
end

#iObject

Integerated part order


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# File 'lib/statsample-timeseries/arima/kalman.rb', line 15

def i
  @i
end

#maObject (readonly)

Moving average coefficients


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# File 'lib/statsample-timeseries/arima/kalman.rb', line 22

def ma
  @ma
end

#pObject

Autoregressive order


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# File 'lib/statsample-timeseries/arima/kalman.rb', line 13

def p
  @p
end

#qObject

Moving average order


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# File 'lib/statsample-timeseries/arima/kalman.rb', line 17

def q
  @q
end

#tsObject


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# File 'lib/statsample-timeseries/arima/kalman.rb', line 33

def ts
  Daru::Vector.new(@ts)
end

Class Method Details

.log_likelihood(params, timeseries, p, q) ⇒ Object

Log Likelihood

Computes Log likelihood on given parameters, ARMA order and timeseries

params

  • params: array of floats, contains phi/theta parameters

  • timeseries: timeseries object

  • p: integer, AR(p) order

  • q: integer, MA(q) order

Returns

LogLikelihood object

Usage

s = (1..100).map { rand }.to_ts p, q = 1, 0 ll = KalmanFilter.log_likelihood(, s, p, q) ll.log_likelihood #=> -22.66 ll.sigma #=> 0.232


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# File 'lib/statsample-timeseries/arima/kalman.rb', line 108

def self.log_likelihood(params, timeseries, p, q)
  Arima::KF::LogLikelihood.new(params, timeseries, p, q)
end

.T(r, k, p) ⇒ Object

Raises:

  • (NotImplementedError)

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# File 'lib/statsample-timeseries/arima/kalman.rb', line 113

def self.T(r, k, p)
  #=T
  #The coefficient matrix for the state vector in state equation
  # It's dimensions is r+k x r+k
  #==Parameters
  #* *r*: integer, r is max(p, q+1), where p and q are orders of AR and MA respectively
  #* *k*: integer, number of exogeneous variables in ARMA model
  #* *q*: integer, The AR coefficient of ARMA model

  #==References Statsmodels tsa, Durbin and Koopman Section 4.7
  raise NotImplementedError
end

Instance Method Details

#ksObject

Kalman Filter

Function which minimizes KalmanFilter.ll iteratively for initial parameters

Usage

@s = [-1.16025577,0.64758021,0.77158601,0.14989543,2.31358162,3.49213868,1.14826956,0.58169457,-0.30813868,-0.34741084,-1.41175595,0.06040081, -0.78230232,0.86734837,0.95015787,-0.49781397,0.53247330,1.56495187,0.30936619,0.09750217,1.09698829,-0.81315490,-0.79425607,-0.64568547,-1.06460320,1.24647894,0.66695937,1.50284551,1.17631218,1.64082872,1.61462736,0.06443761,-0.17583741,0.83918339,0.46610988,-0.54915270,-0.56417108,-1.27696654,0.89460084,1.49970338,0.24520493,0.26249138,-1.33744834,-0.57725961,1.55819543,1.62143157,0.44421891,-0.74000084 ,0.57866347,3.51189333,2.39135077,1.73046244,1.81783890,0.21454040,0.43520890,-1.42443856,-2.72124685,-2.51313877,-1.20243091,-1.44268002 ,-0.16777305,0.05780661,2.03533992,0.39187242,0.54987983,0.57865693,-0.96592469,-0.93278473,-0.75962671,-0.63216906,1.06776183, 0.17476059 ,0.06635860,0.94906227,2.44498583,-1.04990407,-0.88440073,-1.99838258,-1.12955558,-0.62654882,-1.36589161,-2.67456821,-0.97187696, -0.84431782 ,-0.10051809,0.54239549,1.34622861,1.25598105,0.19707759,3.29286114,3.52423499,1.69146333,-0.10150024,0.45222903,-0.01730516, -0.49828727, -1.18484684,-1.09531773,-1.17190808,0.30207662].to_ts
@kf=Statsample::TimeSeries::ARIMA.ks(@s,1,0,0)
#=> ks is implictly called in above operation
@kf.ar
#=> AR coefficients

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# File 'lib/statsample-timeseries/arima/kalman.rb', line 50

def ks
  initial = Array.new((@p+@q), 0.0)

  my_f = Proc.new{ |x, params|
    #In rb-gsl, params remain idle, x is varied upon
    #In R code, initial parameters varied in each iteration
    #my_func.set_params([(1..100).to_a.to_ts, p_value, q_value])
    timeseries = params[0]
    p,q = params[1], params[2]
    params = x
    #puts x
    -Arima::KF::LogLikelihood.new(x.to_a, timeseries, p, q).log_likelihood
    #KalmanFilter.ll(x.to_a, timeseries, p, q)
  }
  np = @p + @q
  my_func = Function.alloc(my_f, np)
  my_func.set_params([@ts, @p, @q])
  x = GSL::Vector.alloc(initial)
  ss = GSL::Vector.alloc(np)
  ss.set_all(0.1)

  minimizer = FMinimizer.alloc("nmsimplex", np)
  minimizer.set(my_func, x, ss)
  status = GSL::CONTINUE
  iter = 0
  while status == GSL::CONTINUE && iter < 100
    iter += 1
    begin
      status = minimizer.iterate
      status = minimizer.test_size(1e-2)
      x = minimizer.x
    rescue
      break
    end
  end
  @ar = (p > 0) ? x.to_a[0...p] : []
  @ma = (q > 0) ? x.to_a[p...(p+q)] : []
  x.to_a
end

#to_sObject


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# File 'lib/statsample-timeseries/arima/kalman.rb', line 37

def to_s
  sprintf("ARIMA model(p = %d, i = %d, q = %d) on series(%d elements) - [%s]",
          @p, @i, @q, @ts.size, @ts.to_a.join(','))
end