kalman.rb

require 'daru'
require 'gnuplotrb'
require 'statsample-timeseries'

index = Daru::DateTimeIndex.date_range :start => '2012', :periods => 500
iteration_count = 500
actual_values = Daru::Vector.new(iteration_count.times.map { |j|  -0.37727 + j * j * 0.00001}, index: index)
noisy_data    = Daru::Vector.new(actual_values.map { |actual_val| rand * 0.6 - 0.3 + actual_val }, index: index)

GnuplotRB::Plot.new(
  [actual_values, with: 'line', title: 'Actual Values'],
  [noisy_data, with: 'line', title: 'Noisy Data'])
# This yields this graph: https://drive.google.com/file/d/0B5WTqLfjBC0pNFktTnhzSldOQmc/view?usp=sharing

# Inputs to KalmanFilter are: 
# Data to be passed into filter - noisy_data
# Autoregressive order - 2
# Integrated part order - 1
# Moving average order - 1
a=Statsample::TimeSeries::Arima::KalmanFilter.new(noisy_data, 2,1,1)

# Moving average coefficients
a.ma #=>[0.4]

# Autocorrelation coefficients
a.ar #=>[0.5, 0.0]