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module Statsample
module TimeSeries
module Arima
module KF
class LogLikelihood
#Gives log likelihood value of an ARMA(p, q) process on given parameters
attr_reader :log_likelihood
#Gives sigma value of an ARMA(p,q) process on given parameters
attr_reader :sigma
#Gives AIC(Akaike Information Criterion)
#https://www.scss.tcd.ie/Rozenn.Dahyot/ST7005/13AICBIC.pdf
attr_reader :aic
def initialize(params, timeseries, p, q)
@params = params
@timeseries = timeseries.to_a
@p = p
@q = q
ll
end
#===Log likelihood link function.
#iteratively minimized by simplex algorithm via KalmanFilter.ks
#Not meant to be used directly. Will make it private later.
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
def to_s
sprintf("LogLikelihood(p = %d, q = %d) on params: [%s]",
@p, @q, @params.join(', '))
end
end
end
end
end
end