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.



17
18
19
20
21
22
23
 
# File 'lib/statsample-timeseries/arima/likelihood.rb', line 17

def initialize(params, timeseries, p, q)
  @params = params
  @timeseries = timeseries.to_a
  @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



15
16
17
 
# 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



8
9
10
 
# 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



11
12
13
 
# 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.



28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
 
# 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.quo 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 



92
93
94
95
 
# File 'lib/statsample-timeseries/arima/likelihood.rb', line 92

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