Hull Moving Average

Hull Moving Average HMA

Comes with formula, calculation step and VBA code

The Hull moving average for n periods is calculated as such

HMA = WMA of (2 x WMA for last n/2 periods – WMA for last n periods) for last k periods

, where

1. k =square root of n rounded to a whole number
2. n/2 is also rounded to a whole number.
3. and the WMA refers to a weighted moving average.

Both n is specified by the user. A single WMA will often lag behind current prices if n is large. On the other hand, too small a value of n will lead to an unsmooth moving average which might give false signals. On closer observation, the HMA consists of 3 steps to reduce lags and smooth the kinks in a typical moving average.

1. Reduce the period by half using WMA for the last n/2 periods to reduce the lag effect.
2. Make the HMA even more responsive by adding (WMA for last n/2 periods – WMA for last n periods) to the WMA for the last n/2 periods in step 1.
3. Smooth the output of 2 by applying a WMA of square root n periods.

VBA Code

Method A

The Hull moving average is a series of nested weighted moving averages. Using the WMA custom function for calculating weighted moving averages, the Hull moving average can be calculated following the steps below without a custom function of its own.

1. Calculate the n periodweighted moving average of a series "=WMA(price for n periods)"
2. Calculate the n/2 period weighted moving average of a series"=WMA(price for n/2 periods)". Round n/2 to the nearest whole number
3. Create a time series with 2*WMA from Step 2 - WMA from Step 1
4. The HMA is the WMA of the series in Step 3. "=WMA(Step 3 outputs fo k period)"

Method B

Method B automates the entire process in Method A using sub routines. It produces in 4 columns the respective outputs from Step 1 to Step 4 of Method A.

Sub Runthis()

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

Dim k As Long

Set close1 = Range("E2:E11955")

Set output = Range("H2:H11955")

n = 5 'number of historical periods to look at

'needed for certain indicators

k = 10 'number of historical periods to look at

'needed for certain indicators as slow average

HMA_1 close1, output, n, k

End Sub

Sub WMA_1(close1 As Range, output As Range, n As Long)

For a = 1 To n

output(a, 1).Value = a

Next a

numrange = Range(output(1, 1), output(n, 1)).Address

pricerange = Range(close1(1, 1), close1(n, 1)).Address(False, False)

output(n, 2).Value = "=sumproduct(" & numrange & "," & pricerange & ")/(" & n & "*(" & n & "+1)/2)"

output(n, 2).Copy output.Offset(0, 1)

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

End Sub

Sub HMA_1(close1 As Range, output As Range, n As Long, k As Long)

WMA_1 close1, output, n

Dim j As Long

j = WorksheetFunction.Round(n / 2, 0)

WMA_1 close1, output.Offset(0, 2), j

WMAn = output(n, 2).Address(False, False)

WMAj = output(n, 4).Address(False, False)

output(n, 5).Value = "=" & WMAn & "-" & WMAj

output(n, 5).Copy output.Offset(0, 4)

Range(output(1, 5), output(n - 1, 5)).Clear

WMA_1 output.Offset(0, 4), output.Offset(0, 5), k

End Sub

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