Kaufman Adaptive Moving Average

Kaufman Adaptive Moving Average KAMA

Comes with formula, calculation steps and VBA code

Introduction

The KAMA uses a smoothing constant in its calculation which requires the user to specify 3 integer values,

a) j, the number of periods to be used for the KAMA

b) Fast, the number of periods for a fast moving average

c) Slow, the number of periods for a slow moving average

Step 1: Calculate the change in direction in the last j periods.

Directional Change_t = Close_t – Close_t-j, Close j days ago

Step 2: Sum the absolute of daily change in direction.

Total Range = Absolute (Close_t – Close_t-1) + Absolute (Close_t-1 – Close_t-2) + … + Absolute (Close_t-j+1 – Close_t-j)

Step 3: Calculate the Efficiency Ratio

Efficiency Ratio = Absolute (Directional Change / Total Range)

If the market closed up every day for the last j days, the Efficiency Ratio will be 1. If the market remained unchanged for the last j days despite moving up and down, the Efficiency Ratio will be 0.

Step 4: Calculate the fast and slow smoothing constant

Fast Smoothing Constant, FSC = 2 / (Fast + 1)

Slow Smoothing Constant, SSC = 2 / (Slow + 1)

Step 5: Calculate Weighted Smoothing Constant

Weighted Smoothing Constant, WSC = Efficiency Ratio x (FSC – SSC) + SSC

Hence, the Weighted Smoothing Constant shifts between FSC and SSC based on the Efficiency Ratio, i.e. how will the market has been trending in the last n days.

Step 6: Square the WSC

C = WSC x WSC

C is used in the next step to calculate KAMA. Squaring it reduces the sensitivity of the KAMA to market fluctuations.

Step 7: Calculate KAMA

KAMA = C x (Close_t – KAMA_t-1) + KAMA_t-1

= C x Close_t + (1 – C) x KAMA_t-1

The very first KAMA of a series can be the close or a simple moving average. Compare the above to the formula for the exponential moving average,

EMA = alpha x Price + (1 – alpha) x EMA_t-1

Recall that the alpha in EMA is calculated as 1 / (j + 1), which is the same formula to be used for the calculation of FSC and SSC.

FSC = 1 / (Fast + 1) Slow = 1 / (Slow + 1)

Thus, the KAMA indicator can be thought of as the combination of 2 different exponential moving averages, dynamically adjusting its responsiveness based on the Efficiency Ratio and the fast and slow smoothing constants dictated.

VBA Code

Method A: Using UDFs

Method A creates a custom function that can be called from the formula bar. Enter in any cell, "=KAMA([j+1 periods of prices], [n the fast EMA smoothing period], [k the slow EMA smoothing period], [the prior period KAMA])"

Sub AddUDF()

Application.MacroOptions macro:="KAMA", _

Description:="Returns Kaufman Adaptive Moving Average" & Chr(10) & Chr(10) & _

"Select last j+1 periods of Close for efficiency ratio, n the fast EMA smoothing period," & Chr(10) & _

"k the slow EMA smoothing period and last KAMA", _

Category:="Technical Indicators"

End Sub

Public Function KAMA(close_, n, k, KAMAYesterday)

'Calculate Efficiency Ratio

j = WorksheetFunction.Count(close_) - 1

dir_chg = close_(j + 1, 1) - close_(1, 1)

tot_rng = 0

For a = 1 To j

tot_rng = tot_rng + Abs(close_(a + 1, 1) - close_(a, 1))

Next a

EffRatio = Abs(dir_chg / tot_rng)

FSC = 2 / (n + 1)

SSC = 2 / (k + 1)

C = (EffRatio * (FSC - SSC) + SSC) ^ 2

KAMA = C * close_(j + 1, 1) + (1 - C) * KAMAYesterday

End Function

Method B

Method B produces the daily directional change, absolute daily directional change, efficiency ratio, KAMA smoothing constant C and KAMA. You start by running the Runthis sub which passes your inputs to the KAMA_1 sub.

Sub Runthis()

Dim close1 As Range, output As Range, n As Long

Dim k As Long, j As Long

Set close1 = Range("E2:E11955")

Set output = Range("H2:H11955")

n = 5 'number of periods for fast EMA

k = 10 'number of periods for slow EMA

j = 5 'The number of periods used in calculating efficiency ratio

KAMA_1 close1, output, n, k, j

End Sub

Sub KAMA_1(close1 As Range, output As Range, n As Long, k As Long, j As Long)

output(0, 1).Value = "Directional Change"

lastclose = close1(1, 1).Address(False, False)

currentclose = close1(2, 1).Address(False, False)

output(2, 1).Value = "=" & currentclose & "-" & lastclose

output(0, 2).Value = "Abs Dir Chg"

dirchg = output(2, 1).Address(False, False)

output(2, 2).Value = "=abs(" & dirchg & ")"

Range(output(2, 1), output(2, 2)).Copy output

output(0, 3).Value = "Efficiency Ratio"

dirsum = Range(output(2, 1), output(j + 1, 1)).Address(False, False)

absdirsum = Range(output(2, 2), output(j + 1, 2)).Address(False, False)

output(j + 1, 3).Value = "=abs(sum(" & dirsum & ")/sum(" & absdirsum & "))"

FSC = "2/(" & n & "+1)"

SSC = "2/(" & k & "+1)"

effrange = output(j + 1, 3).Address(False, False)

output(0, 4).Value = "C"

output(j + 1, 4) = "=(" & effrange & "*(" & FSC & "-" & SSC & ")+" & SSC & ")^2"

C1 = output(j + 1, 4).Address(False, False)

lastKAMA = output(j, 5).Address(False, False)

output(0, 5).Value = "KAMA"

output(j + 1, 5) = "=" & C1 & "*" & close1(j + 1, 1).Address(False, False) & "+(1-" & C1 & ")*" & lastKAMA

Range(output(j + 1, 3), output(j + 1, 5)).Copy output.Offset(0, 2)

output(j + 1, 5) = "=" & C1 & "*" & close1(j + 1, 1).Address(False, False) & "+(1-" & C1 & ")*" & close1(j, 1)

Range(output(1, 3), output(j, 5)).Clear

Range(output(1, 1), output(1, 2)).Clear

End Sub

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