title: Hayashi yoshida estimator for correlation not coming between -1 to 1
body: <p>I took two time series data with 141 data points in total with time stamps. i found out actual correlation between them which is about 0.97. Now i find the Hayashi Yoshida estimator for correlation. It comes greater than 3. The Hy correlation estimator should have given the correlation close to actual correlation.</p>
  
  <p>Though this HY correlation estimator is not bounded from-1 to 1 like actual correlation, still should not give it a better estimate? Is my data set too small?</p>
  
  <p>The Hayashi yohida correlation estimator is given in <a href="http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2225753" rel="nofollow noreferrer">http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2225753</a> 
  as 
  <img src="https://i.stack.imgur.com/Lo754.png" alt="enter image description here"></p>
  
  <p>data is :
  1,100,62<br>
  2,100.5,62<br>
  3,100.6,62<br>
  4,100.6,62.05<br>
  5,100.6,62.1<br>
  6,100.6,62.15<br>
  7,100.6,62.2<br>
  8,100.6,62.25<br>
  9,100.6,62.3<br>
  10,100.6,62.35<br>
  11,100.6,62.4<br>
  12,100.6,62.45<br>
  13,100.6,62.5<br>
  14,100.6,62.55<br>
  15,100.6,62.6<br>
  16,101.1,62.6<br>
  17,101.2,62.6<br>
  18,101.2,62.65<br>
  19,101.2,62.7<br>
  20,101.2,62.75<br>
  21,101.2,62.8<br>
  22,101.2,62.85<br>
  23,101.2,62.9<br>
  24,101.2,62.95<br>
  25,101.2,63<br>
  26,101.2,63.05<br>
  27,101.2,63.1<br>
  28,101.2,63.15<br>
  29,101.2,63.2<br>
  30,101.7,63.2<br>
  31,101.8,63.2<br>
  32,101.8,63.25<br>
  33,101.8,63.3<br>
  34,101.8,63.35<br>
  35,101.8,63.4<br>
  36,101.8,63.45<br>
  37,101.8,63.5<br>
  38,101.8,63.55<br>
  39,101.8,63.6<br>
  40,101.8,63.65<br>
  41,101.8,63.7<br>
  42,101.8,63.75<br>
  43,101.8,63.8<br>
  44,102.3,63.8<br>
  45,102.4,63.8<br>
  46,102.4,63.85<br>
  47,102.4,63.9<br>
  48,102.4,63.95<br>
  49,102.4,64<br>
  50,102.4,64.05<br>
  51,102.4,64.1<br>
  52,102.4,64.15<br>
  53,102.4,64.2<br>
  54,102.4,64.25<br>
  55,102.4,64.3<br>
  56,102.4,64.35<br>
  57,102.4,64.4<br>
  58,102.9,64.4<br>
  59,103,64.4<br>
  60,103,64.45<br>
  61,103,64.5<br>
  62,103,64.55<br>
  63,103,64.6<br>
  64,103,64.65<br>
  65,103,64.7<br>
  66,103,64.75<br>
  67,103,64.8<br>
  68,103,64.85<br>
  69,103,64.9<br>
  70,103,64.95<br>
  71,103,65<br>
  72,103.5,65<br>
  73,103.6,65<br>
  74,103.6,65.05<br>
  75,103.6,65.1<br>
  76,103.6,65.15<br>
  77,103.6,65.2<br>
  78,103.6,65.25<br>
  79,103.6,65.3<br>
  80,103.6,65.35<br>
  81,103.6,65.4<br>
  82,103.6,65.45<br>
  83,103.6,65.5<br>
  84,103.6,65.55<br>
  85,103.6,65.6<br>
  86,104.1,65.6<br>
  87,104.2,65.6<br>
  88,104.2,65.65<br>
  89,104.2,65.7<br>
  90,104.2,65.75<br>
  91,104.2,65.8<br>
  92,104.2,65.85<br>
  93,104.2,65.9<br>
  94,104.2,65.95<br>
  95,104.2,66<br>
  96,104.2,66.05<br>
  97,104.2,66.1<br>
  98,104.2,66.15<br>
  99,104.2,66.2<br>
  100,104.7,66.2<br>
  101,104.8,66.2<br>
  102,104.8,66.25<br>
  103,104.8,66.3<br>
  104,104.8,66.35<br>
  105,104.8,66.4<br>
  106,104.8,66.45<br>
  107,104.8,66.5<br>
  108,104.8,66.55<br>
  109,104.8,66.6<br>
  110,104.8,66.65<br>
  111,104.8,66.7<br>
  112,104.8,66.75<br>
  113,104.8,66.8<br>
  114,105.3,66.8<br>
  115,105.4,66.8<br>
  116,105.4,66.85<br>
  117,105.4,66.9<br>
  118,105.4,66.95<br>
  119,105.4,67<br>
  120,105.4,67.05<br>
  121,105.4,67.1<br>
  122,105.4,67.15<br>
  123,105.4,67.2<br>
  124,105.4,67.25<br>
  125,105.4,67.3<br>
  126,105.4,67.35<br>
  127,105.4,67.4<br>
  128,105.9,67.4<br>
  129,106,67.4<br>
  130,106,67.45<br>
  131,106,67.5<br>
  132,106,67.55<br>
  133,106,67.6<br>
  134,106,67.65<br>
  135,106,67.7<br>
  136,106,67.75<br>
  137,106,67.8<br>
  138,106,67.85<br>
  139,106,67.9<br>
  140,106,67.95<br>
  141,106,68  </p>