Class: Statsample::TimeSeries::Arima::KF::LogLikelihood

Inherits:
Object
  • Object
show all
Defined in:
lib/statsample-timeseries/arima/likelihood.rb

Instance Attribute Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(params, timeseries, p, q) ⇒ LogLikelihood

Returns a new instance of LogLikelihood.



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

def initialize(params, timeseries, p, q)
  @params = params
  @timeseries = timeseries
  @p = p
  @q = q
  ll
end

Instance Attribute Details

#aic ⇒ Object (readonly)

Gives AIC(Akaike Information Criterion) www.scss.tcd.ie/Rozenn.Dahyot/ST7005/13AICBIC.pdf



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

def aic
  @aic
end

#log_likelihood ⇒ Object (readonly)

Gives log likelihood value of an ARMA(p, q) process on given parameters



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# File 'lib/statsample-timeseries/arima/likelihood.rb', line 8

def log_likelihood
  @log_likelihood
end

#sigma ⇒ Object (readonly)

Gives sigma value of an ARMA(p,q) process on given parameters



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# File 'lib/statsample-timeseries/arima/likelihood.rb', line 11

def sigma
  @sigma
end

Instance Method Details

#ll ⇒ Object

Log likelihood link function.

iteratively minimized by simplex algorithm via KalmanFilter.ks Not meant to be used directly. Will make it private later.



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# File 'lib/statsample-timeseries/arima/likelihood.rb', line 28

def ll
  params, timeseries = @params, @timeseries
  p, q = @p, @q

  phi = []
  theta = []
  phi = params[0...p] if p > 0
  theta = params[(p)...(p + q)] if q > 0

  [phi, theta].each do |v|
    if v.size>0 and v.map(&:abs).inject(:+) > 1
      return
    end
  end

  m = [p, q].max
  h = Matrix.column_vector(Array.new(m,0))
  m.times do |i|
    h[i,0] = phi[i] if i< p
    h[i,0] = h[i,0] + theta[i] if i < q
  end

  t = Matrix.zero(m)
  #set_column is available in utility.rb
  t = t.set_column(0, phi)
  if(m > 1)
    t[0...(m-1), 1...m] = Matrix.I(m-1)
    #chances of extra constant 0 values as unbalanced column, so:
    t = Matrix.columns(t.column_vectors)
  end

  g = Matrix[[1]]
  a_t = Matrix.column_vector(Array.new(m,0))
  n = timeseries.size
  z = Matrix.row_vector(Array.new(m,0))
  z[0,0] = 1
  p_t = Matrix.I(m)
  v_t, f_t = Array.new(n,0), Array.new(n, 0)

  n.times do |i|
    v_t[i] = (z * a_t).map { |x| timeseries[i] - x }[0,0]

    f_t[i] = (z * p_t * (z.transpose)).map { |x| x + 1 }[0,0]

    k_t = ((t * p_t * z.transpose) + h).map { |x| x / f_t[i] }

    a_t = (t * a_t) + (k_t * v_t[i])
    l_t = t - k_t * z
    j_t = h - k_t

    p_t = (t * p_t * (l_t.transpose)) + (h * (j_t.transpose))
  end

  pot = v_t.map(&:square).zip(f_t).map { |x,y| x / y}.inject(:+)
  sigma_2 = pot.to_f / n.to_f

  f_t_log_sum = f_t.map { |x| Math.log(x) }.inject(:+)
  @log_likelihood = -0.5 * (n*Math.log(2*Math::PI) + n*Math.log(sigma_2) + f_t_log_sum + n)
  
  @sigma = sigma_2
  @aic = -(2 * @log_likelihood - 2*(p+q+1))
  #puts ("ll = #{-ll}")
  return @log_likelihood
end

#to_s ⇒ Object 



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# File 'lib/statsample-timeseries/arima/likelihood.rb', line 93

def to_s
  sprintf("LogLikelihood(p = %d, q = %d) on params: [%s]",
          @p, @q, @params.join(', '))
end