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Helper I

## Tricky Calculated Column - Calling any math gurus!

Hello,

I have a table of data that has two columns: ‘Week Number’ and ‘Rolling 4 Week Total’. I’ve made a simple example below. I don’t have data for weeks before - starting value for Week 1 is unknown.

 Week Number Rolling 4 Week Total 88 35 89 35 90 42 91 43 92 42 93 45 94 44 95 53 96 59 97 49 98 43 99 37 100 34

I’m hoping there’s an equation for a calculated column that can calculate the ‘Actual Week Total’ – example results in table below. It may not be possible! I’d prefer in M but can work with DAX if easier. The real table is millions of rows long, with many products, markets and weeks.

 Week Number Rolling 4 Week Total Actual Week Total 88 35 10 89 35 12 90 42 15 91 43 6 92 42 9 93 45 15 94 44 14 95 53 15 96 59 15 97 49 5 98 43 8 99 37 9 100 34 12

Dan

1 ACCEPTED SOLUTION
Super User

It is possible to derive Actual Week Total values, but there is not a unique solution.

If you begin with rolling 4 week totals, you can specify an initial set of 3 weeks' actual values, then the remaining weeks can be determined.

I have attached a small example using DAX since it was easier to knock together, but I think this is really a job for Power Query.

Here is the code for the calculated column I created. You can see the initial condition in the InitialCondition variable. The exact weeks covered by the initial condition could be adjusted.

``````Actual Week Total =
-- Number of weeks summed in each Rolling Total
VAR RollingWeeks = 4
-- This table should have a row count = ( RollingWeeks - 1 )
VAR InitialCondition =
DATATABLE (
"WeekNum", INTEGER,
"Actual", DOUBLE,
{
{ 88, 10 },
{ 89, 10 },
{ 90, 10 }
}
)
VAR InitialConditionMaxWeek =
MAXX ( InitialCondition, [WeekNum] )
VAR InitialConditionMinWeek =
MINX ( InitialCondition, [WeekNum] )
VAR InitialConditionSum =
SUMX (
InitialCondition,
[Actual]
)
VAR ActualAfterInitial =
LOOKUPVALUE (
Data[Rolling 4 Week Total],
Data[Week Number], InitialConditionMaxWeek + 1
)
- InitialConditionSum
VAR InitialConditionExtended =
UNION (
InitialCondition,
ROW (
"WeekNum", InitialConditionMaxWeek + 1,
"Actual", ActualAfterInitial
)
)
VAR CurrentWeek = Data[Week Number]
VAR ActualWeekTotal =
IF (
CurrentWeek <= InitialConditionMaxWeek + 1,
MAXX (
FILTER ( InitialConditionExtended, [WeekNum] = CurrentWeek ),
[Actual]
),
VAR BaseWeekRow =
FILTER (
InitialConditionExtended,
MOD ( [WeekNum], RollingWeeks ) = MOD ( CurrentWeek, RollingWeeks )
)
VAR BaseWeek =
SELECTCOLUMNS ( BaseWeekRow, "WeekNum", [WeekNum] )
VAR BaseWeekActual =
SELECTCOLUMNS ( BaseWeekRow, "Actual", [Actual] )
VAR DifferenceWeeks =
TREATAS (
GENERATESERIES ( BaseWeek + RollingWeeks, CurrentWeek, RollingWeeks ),
Data[Week Number]
)
VAR Differences =
CALCULATE (
SUMX (
Data,
VAR CurrentWeekInner = Data[Week Number]
VAR PreviousWeekInner = CurrentWeekInner - 4
RETURN
Data[Rolling 4 Week Total]
- LOOKUPVALUE ( Data[Rolling 4 Week Total], Data[Week Number], PreviousWeekInner )
),
DifferenceWeeks,
REMOVEFILTERS ()
)
RETURN
BaseWeekActual + Differences
)

RETURN ActualWeekTotal``````

The basic formula I applied (after doing some algebra) is:

Let x(n) be the actual value for week n.

Let R(n) be the rolling total for week n.

Let D(n) = R(n) - R(n-1) (i.e. the difference between two consecutive rolling totals).

Then assume we have initial condition specified for weeks k, k+1 and k+2 (in the case of 4 week rolling totals), that is we know x(k), x(k+1), x(k+2).

Then x(k+3) = R(k+3) - [ x(k) + x(k+1) + x(k+2) ].

Then the pattern after this is

x(k+4) = x(k) + D(k+4)

x(k+5) = x(k+1) + D(k+5)

x(k+6) = x(k+2) + D(k+6)

x(k+7) = x(k+3) +  D(k+7)

x(k+8) = x(k) + D(k+4) + D(k+8)

x(k+9) = x(k+1) + D(k+5) + D(k+9)

....

In other words, each x(n) is the sum of a "base value" x(i) taken from x(k) to x(k+3), such that n is equivalent to i modulo 4, plus a sequence of differences R(n), R(n-4),.... at regular intervals.

(this can be expressed more precisely but hopefully makes sense).

Given that you have multiple dimensions to worry about (products, markets etc), you would need to do these calculations at the right level of granularity.

Does the above logic seem right?

I can come back to you with an M example of this as well later on 🙂

Regards

Owen Auger
Blog
2 REPLIES 2
Super User

It is possible to derive Actual Week Total values, but there is not a unique solution.

If you begin with rolling 4 week totals, you can specify an initial set of 3 weeks' actual values, then the remaining weeks can be determined.

I have attached a small example using DAX since it was easier to knock together, but I think this is really a job for Power Query.

Here is the code for the calculated column I created. You can see the initial condition in the InitialCondition variable. The exact weeks covered by the initial condition could be adjusted.

``````Actual Week Total =
-- Number of weeks summed in each Rolling Total
VAR RollingWeeks = 4
-- This table should have a row count = ( RollingWeeks - 1 )
VAR InitialCondition =
DATATABLE (
"WeekNum", INTEGER,
"Actual", DOUBLE,
{
{ 88, 10 },
{ 89, 10 },
{ 90, 10 }
}
)
VAR InitialConditionMaxWeek =
MAXX ( InitialCondition, [WeekNum] )
VAR InitialConditionMinWeek =
MINX ( InitialCondition, [WeekNum] )
VAR InitialConditionSum =
SUMX (
InitialCondition,
[Actual]
)
VAR ActualAfterInitial =
LOOKUPVALUE (
Data[Rolling 4 Week Total],
Data[Week Number], InitialConditionMaxWeek + 1
)
- InitialConditionSum
VAR InitialConditionExtended =
UNION (
InitialCondition,
ROW (
"WeekNum", InitialConditionMaxWeek + 1,
"Actual", ActualAfterInitial
)
)
VAR CurrentWeek = Data[Week Number]
VAR ActualWeekTotal =
IF (
CurrentWeek <= InitialConditionMaxWeek + 1,
MAXX (
FILTER ( InitialConditionExtended, [WeekNum] = CurrentWeek ),
[Actual]
),
VAR BaseWeekRow =
FILTER (
InitialConditionExtended,
MOD ( [WeekNum], RollingWeeks ) = MOD ( CurrentWeek, RollingWeeks )
)
VAR BaseWeek =
SELECTCOLUMNS ( BaseWeekRow, "WeekNum", [WeekNum] )
VAR BaseWeekActual =
SELECTCOLUMNS ( BaseWeekRow, "Actual", [Actual] )
VAR DifferenceWeeks =
TREATAS (
GENERATESERIES ( BaseWeek + RollingWeeks, CurrentWeek, RollingWeeks ),
Data[Week Number]
)
VAR Differences =
CALCULATE (
SUMX (
Data,
VAR CurrentWeekInner = Data[Week Number]
VAR PreviousWeekInner = CurrentWeekInner - 4
RETURN
Data[Rolling 4 Week Total]
- LOOKUPVALUE ( Data[Rolling 4 Week Total], Data[Week Number], PreviousWeekInner )
),
DifferenceWeeks,
REMOVEFILTERS ()
)
RETURN
BaseWeekActual + Differences
)

RETURN ActualWeekTotal``````

The basic formula I applied (after doing some algebra) is:

Let x(n) be the actual value for week n.

Let R(n) be the rolling total for week n.

Let D(n) = R(n) - R(n-1) (i.e. the difference between two consecutive rolling totals).

Then assume we have initial condition specified for weeks k, k+1 and k+2 (in the case of 4 week rolling totals), that is we know x(k), x(k+1), x(k+2).

Then x(k+3) = R(k+3) - [ x(k) + x(k+1) + x(k+2) ].

Then the pattern after this is

x(k+4) = x(k) + D(k+4)

x(k+5) = x(k+1) + D(k+5)

x(k+6) = x(k+2) + D(k+6)

x(k+7) = x(k+3) +  D(k+7)

x(k+8) = x(k) + D(k+4) + D(k+8)

x(k+9) = x(k+1) + D(k+5) + D(k+9)

....

In other words, each x(n) is the sum of a "base value" x(i) taken from x(k) to x(k+3), such that n is equivalent to i modulo 4, plus a sequence of differences R(n), R(n-4),.... at regular intervals.

(this can be expressed more precisely but hopefully makes sense).

Given that you have multiple dimensions to worry about (products, markets etc), you would need to do these calculations at the right level of granularity.

Does the above logic seem right?

I can come back to you with an M example of this as well later on 🙂

Regards

Owen Auger
Blog
Helper I

Wow,

I really like this approach. I hadn’t thought of specifying a starting point, and given I’m working with years of data, it will work a treat.

Very well explained and detailed solution too. I am blown away!

In terms of granularity, I will create a ‘key’ to group products and markets.

Many thanks for all your time and effort in explaining this, I'm sure it will help others too!

Cheers!

Dan

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