https://gyazo.com/5da375acbc3554a44e19f0e70c07597c

SP500-last-30-years-log-least-square-simulator.rb

require 'csv'

def least_square(ys)
  ave_x = ys.size / 2.0
  ave_y = ys.sum / ys.size.to_f

  a = ys.zip(0..).sum {|y, i| (i - ave_x) * (y - ave_y) } / ys.zip(0..).sum {|_, i| (i - ave_x) ** 2 }
  b = ave_y - a * ave_x
  [a, b]
end

# Download manually from https://finance.yahoo.com/quote/%5EGSPC/history?p=%5EGSPC
tuples = CSV.parse(File.read('/tmp/Downloads/^GSPC.csv'))[-251*30..] {|date, open, high, low, close, adj_close, volume|
  [date, close]
}

tuples = tuples.map {|date, close|
  [date, Math.log(close.to_f)]
}

(a, b) = least_square(tuples.map(&:last))
tuples = tuples.map.with_index {|(date, log_close), i|
  [date, log_close, a * i + b]
}
tuples.each do |date, log_close, log_ls|
  puts [date, Math.exp(log_close), Math.exp(log_ls)].join("\t")
end