Attribute VB_Name = "bpassmod"
' Das Programm ist geschrieben von Kurt Annen, mehr unter www.web-reg.de'
' Wenn Ihnen das Programm gefällt, so schicken Sie mir bitte eine email: annen@web-reg.de'
' This program was written by Kurt Annen, see www.web-reg.de'
' If you like the program, please send me an email: annen@web-reg.de'

Option Explicit
Option Base 1

'Berechnet den "Standard"-Band-Pass-Filter durch eine Approximation, welche in '
'"The Band Pass Filter" by Lawrence J. Christiano and Terry J. Fitzgerald (1999)'
'beschrieben ist. Der Filter geht von einer Random-Walk-Zeitreihe mit Drift aus.'
'data = Zeitreihe'
'pl   = Minimalperiode'
'pu   = Maximalperiode'
'Für Quartaldaten: pl=6, pu=32; gibt alle Komponenten zwischen 1,5 und 8 Jahren wieder'
'Für Monatsdaten: pl=2, pu=24; gibt alle Komponenten, die unter 2 Jahren liegen wieder'

'This Filter computes the default Band-Pass-Filter using an approximation as discussed in'
'"The Band Pass Filter" by Lawrence J. Christiano and Terry J. Fitzgerald (1999)'
'This Filter assumes a Randome-Walk time-series with drift'
'data = time-series'
'pl   = minimum period'
'pu   = maximum period'
'Quarterly data: pl=6, pu=32 returns component with periods between 1.5 and 8 yrs.
'Monthly data:   pl=2, pu=24 returns component with all periods less than 2 yrs.'

Function bpass(data As Range, pl As Double, pu As Double)
Dim nobs As Integer, k As Integer, drift As Double, a As Double, b As Double
Dim bnot As Double, bhat As Double, AA() As Double, AAt() As Double
Dim l As Integer

Const pi As Double = 3.14159265358979

Dim datanew() As Double, BB() As Double

nobs = data.Rows.Count
ReDim datanew(nobs, 1)
    
For k = 1 To nobs Step 1
    datanew(k, 1) = data(k, 1)
Next k
    
'Drift wird entfernt'
'Removing drift'
    
drift = (datanew(nobs, 1) - datanew(1, 1)) / (nobs - 1)
For k = 1 To nobs Step 1
    datanew(k, 1) = datanew(k, 1) - (k - 1) * drift
Next k

'Die idealen B's werden berechnet und die Matrix AA wird erstellt'
'Create the ideal B's then construct the AA matrix'
b = 2 * pi / pl
a = 2 * pi / pu
bnot = (b - a) / pi
bhat = bnot / 2
ReDim BB(nobs, 1)

For k = 1 To nobs - 1 Step 1
    BB(k + 1, 1) = (Sin(k * b) - Sin(k * a)) / (k * pi)
Next k


BB(1, 1) = bnot

ReDim AAt(2 * nobs, 2 * nobs)
ReDim AA(nobs, nobs)
For k = 1 To nobs Step 1
    For l = 1 To nobs Step 1
        AAt(k, l + k - 1) = BB(l, 1)
           
        AAt(k + l - 1, k) = BB(l, 1)
    Next l
Next k

For k = 1 To nobs Step 1
    For l = 1 To nobs Step 1
        AA(k, l) = AAt(k, l)
    Next l
Next k


AA(1, 1) = bhat
AA(nobs, nobs) = bhat

For k = 1 To nobs - 1 Step 1
    AA(k + 1, 1) = AA(k, 1) - BB(k, 1)
    AA(nobs - k, nobs) = AA(k, 1) - BB(k, 1)
Next k
            
        
ReDim BB(nobs, 1)
        
'Berechnet den Filter aus AA'
'Computes the Filter using AA'
For k = 1 To nobs Step 1
    For l = 1 To nobs Step 1
        BB(k, 1) = BB(k, 1) + AA(k, l) * datanew(l, 1)
    Next l
Next k

bpass = BB
End Function