日経平均相関計算

correlation.php

<?php

date_default_timezone_set('UTC');

function Parse($file, $shift = 0) {
  $data = explode("\n", trim(str_replace(
      ["\r\n", "\r"], "\n", file_get_contents($file))));
  array_shift($data);
  $output = [];
  foreach ($data as $row) {
    list($date, $value) = explode("\t", $row, 2);
    $time = strtotime($date);
    $output[date('Y-m-d', $time + $shift * 24 * 3600)] = floatval($value);
  }
  return $output;
}

$nikkei = Parse('nikkei.txt', -1);
$sp = Parse('sp.txt');
$usdjpy = Parse('usdjpy.txt');

$output = [];
foreach ($nikkei as $date => $value) {
  if (!isset($nikkei[$date]) ||
      !isset($sp[$date]) ||
      !isset($usdjpy[$date])) {
    continue;
  }
  $output[] = [
      'date' => $date,
      'nikkei' => $nikkei[$date],
      'sp' => $sp[$date],
      'usdjpy' => $usdjpy[$date]];
}

$names = ['nikkei', 'sp', 'usdjpy'];
$avgs = [];
for ($i = 0; $i < count($output); $i++) {
  $sum = [];
  for ($j = 3; $j < 10 && isset($output[$i + $j]); $j++) {
    $result = [];
    $ratio = sqrt($j);
    foreach ($names as $name) {
      $result[$name] =
          log($output[$i][$name] / $output[$i + $j][$name]) / $ratio;
    }
    $sum[''] += 1;
    foreach ($names as $name1) {
      $sum[$name1] += $result[$name1];
      foreach ($names as $name2) {
        $sum["$name1.$name2"] += $result[$name1] * $result[$name2];
      }
    }
  }
  $output[$i]['sum'] = $sum;
}

$output = array_values(array_reverse($output));
for ($i = 0; $i < count($output); $i++) {
  $last = $output[$i > 0 ? ($i - 1) : 0];
  $sum = [];
  for ($j = 0; $j < 60 && isset($output[$i + $j]); $j++) {
    foreach ($output[$i + $j]['sum'] as $key => $value) {
      $sum[$key] += $value;
    }
  }
  foreach ($sum as $key => $value) {
    if ($key === '') { continue; }
    $sum[$key] /= $sum[''];
  }
  echo "{$output[$i]['date']}";
  echo "\t";
  echo $output[$i]['nikkei'];
  echo "\t";
  echo $output[$i]['usdjpy'];
  echo "\t";
  echo $output[$i]['sp'];
  echo "\t";
  echo ($sum['nikkei.usdjpy'] - $sum['nikkei'] * $sum['usdjpy']) /
       sqrt(($sum['nikkei.nikkei'] - $sum['nikkei'] * $sum['nikkei']) *
            ($sum['usdjpy.usdjpy'] - $sum['usdjpy'] * $sum['usdjpy']));
  echo "\t";
  echo ($sum['nikkei.sp'] - $sum['nikkei'] * $sum['sp']) /
       sqrt(($sum['nikkei.nikkei'] - $sum['nikkei'] * $sum['nikkei']) *
            ($sum['sp.sp'] - $sum['sp'] * $sum['sp']));
  echo "\t";
  echo ($sum['nikkei.usdjpy'] - $sum['nikkei'] * $sum['usdjpy']) /
       ($sum['usdjpy.usdjpy'] - $sum['usdjpy'] * $sum['usdjpy']);
  echo "\t";
  echo ($sum['nikkei.sp'] - $sum['nikkei'] * $sum['sp']) /
       ($sum['sp.sp'] - $sum['sp'] * $sum['sp']);

  $output[$i]['nikkei/usdjpy'] =
      ($sum['nikkei.usdjpy'] - $sum['nikkei'] * $sum['usdjpy']) /
      ($sum['usdjpy.usdjpy'] - $sum['usdjpy'] * $sum['usdjpy']);
  $output[$i]['usdjpy~nikkei'] =
      $last['usdjpy~nikkei'] +
      floatval($last['nikkei/usdjpy']) *
      log($output[$i]['usdjpy'] / $last['usdjpy']);
  echo "\t";
  echo log($output[$i]['nikkei']) - $output[$i]['usdjpy~nikkei'];

  $output[$i]['nikkei/sp'] =
      ($sum['nikkei.sp'] - $sum['nikkei'] * $sum['sp']) /
      ($sum['sp.sp'] - $sum['sp'] * $sum['sp']);
  $output[$i]['sp~nikkei'] =
      $last['sp~nikkei'] +
      floatval($last['nikkei/sp']) *
      log($output[$i]['sp'] / $last['sp']);
  echo "\t";
  echo log($output[$i]['nikkei']) - $output[$i]['sp~nikkei'];

  $output[$i]['sp/nikkei'] =
      ($sum['nikkei.sp'] - $sum['nikkei'] * $sum['sp']) /
      ($sum['nikkei.nikkei'] - $sum['nikkei'] * $sum['nikkei']);
  $output[$i]['nikkei~sp'] =
      $last['nikkei~sp'] +
      floatval($last['sp/nikkei']) *
      log($output[$i]['nikkei'] / $last['nikkei']);
  echo "\t";
  echo log($output[$i]['sp']) - $output[$i]['nikkei~sp'];

  echo "\n";
}