順序統計量再研究 - 模擬與交易.8

舉例而言，有價格數據資料八筆，依大小排序為 : X(1)、X(2)、...、X(7)、X(8)，定義全距(Range)=Max-Min=X(1)-X(8)=R(1,8)。 依此類推，R(3,6)就是X(3)-X(6)的距離，所以評估波動度的方法，又多了一個想法，就是R(1,8)/R(3,6)的比值，但因為運算便利考量，比值的檢定統計量改以R(1,8)的平方-R(3,6)的平方，透過標準常態分配亂數模擬，可以為此統計檢定量製表，以8筆資料為例，10萬次模擬的結果是，95%的顯著水準門檻值為16.85

MC程式碼構想如下 x=Average(High,8); y=StdDev(High,8); z[1]=(Highest(High,8)-x)/y; z[2]=(Lowest(High,8)-x)/y; z[3]=(NthHighest(3,High,8)-x)/y; z[4]=(NthHighest(6,High,8)-x)/y; u=Power(z[1]-z[2],2); v=Power(z[3]-z[4],2); If u-v16.85 then Buy next bar at Highest(High,8) stop;

Excel VBA參考程式碼如下 Public RankSort(1 To 8) As Variant Const FixConst As Variant = 0.398942284 '1/sqr(2*3.1415926) Public Sub avgRank() '模擬常態分配隨機變數的順序統計量期望值 Dim seed, seedCalc, nextSeed, NorValue As Variant Dim ArrNorRandom(1 To 8), x(1 To 100000) As Variant Dim iith, testNum, xTemp, yTemp As Long

For testNum = 1 To 100000 iith = 1 Do seed = Int(Rnd() * 1000000) seedCalc = ((seed - 500000) * 0.000001) * 8 '模擬4個標準差範圍的 N(0,1) 常態分配變數 NorValue = Format(FixConst * Exp(-0.5 * seedCalc * seedCalc), "0.000000") '常態分配機率函數的數值 nextSeed = 0 nextSeed = Int(0.001 * (seed * seed)) nextSeed = Format(0.000001 * nextSeed - Int(0.000001 * nextSeed), "0.000000") nextSeed = Int(1000000 * nextSeed) nextSeed = Int(((23 + iith * 0.01) * nextSeed + 1011 * iith)) Mod 999999 nextSeed = Format(nextSeed * 0.00001 * FixConst, "0.000000")

If (nextSeed) NorValue Then ArrNorRandom(iith) = seedCalc iith = iith + 1 End If Loop While iith = 8

'泡沫排序法 Dim swapTemp, ii, jj As Variant For jj = 0 To 6 For ii = 1 To 7 - jj If ArrNorRandom(ii) ArrNorRandom(ii + 1) Then swapTemp = "" swapTemp = ArrNorRandom(ii + 1) ArrNorRandom(ii + 1) = ArrNorRandom(ii) ArrNorRandom(ii) = swapTemp End If Next ii Next jj

xTemp = (ArrNorRandom(8) - ArrNorRandom(1)) * (ArrNorRandom(8) - ArrNorRandom(1)) yTemp = (ArrNorRandom(6) - ArrNorRandom(3)) * (ArrNorRandom(6) - ArrNorRandom(3)) x(testNum) = xTemp - yTemp Next 'For testNum = 1 To 100000

For jj = 0 To 4999 '資料數據共計10萬筆，求解第95001序位 For ii = 1 To 100000 - 1 - jj If x(ii) x(ii + 1) Then xTemp = 0 xTemp = x(ii + 1) x(ii + 1) = x(ii) x(ii) = xTemp End If Next ii Next jj

Debug.Print x(95001) End Sub