cascadeProjectionValues with cascadeType = "step"¶
Note
In the examples below, whenever a valuation date is mentioned, we only use the month name, for brevity. Instead
of February, you would write something like DATE(2021,2,28) or EOMONTH(DATE(2021,2,1),0).
Equivalence with mapProjectionValues¶
At each time step, a value is read from a different projection node. It can be written as an equivalent
piecewise-defined function containing different calls to mapProjectionValues:
cascadeProjectionValues(varName, valnType, hLevel, January, March, 1, 0, 0, "step", "sum")
│ │ │ └──┬────────────────┘ │ │
@t=1, lookup January from: mapProjectionValues(varName, valnType, hLevel, January, 0, "sum")
@t=2, lookup February from: mapProjectionValues(varName, valnType, hLevel, February, 0, "sum")
@t=3, lookup March from: mapProjectionValues(varName, valnType, hLevel, March, 0, "sum")
With valnDateMonthsShift
When using valnDateMonthsShift, the precedent at each time step changes.
With valnDateMonthsShift=-1, each time step reads from the previous month's projection node, except at the beginning,
where it reads from the first projection node:
cascadeProjectionValues(varName, valnType, hLevel, January, March, 1, -1, 0, "step", "sum")
│ │ │ └──┬─────────────────┘ │ │
@t=1, lookup January from: mapProjectionValues(varName, valnType, hLevel, January, 0, "sum")
@t=2, lookup February from: mapProjectionValues(varName, valnType, hLevel, January, 0, "sum")
@t=3, lookup March from: mapProjectionValues(varName, valnType, hLevel, February, 0, "sum")
@t=1 would lookup January from a precedent with a December valuation date, but that's not part of the January
– March series. So it uses the first projection node instead, which has a January valuation date.
With valnDateMonthsShift=1, each time step reads from the next month's projection node, except at the end,
where it reads from the last projection node:
cascadeProjectionValues(varName, valnType, hLevel, January, March, 1, 1, 0, "step", "sum")
│ │ │ └──┬────────────────┘ │ │
@t=1, lookup January from: mapProjectionValues(varName, valnType, hLevel, February, 0, "sum")
@t=2, lookup February from: mapProjectionValues(varName, valnType, hLevel, March, 0, "sum")
@t=3, lookup March from: mapProjectionValues(varName, valnType, hLevel, March, 0, "sum")
@t=3 would lookup March from a precedent with an April valuation date, but that's not part of the January
– March series. So it uses the last projection node instead, which has a March valuation date.
With timeShift
When using timeShift, the lookup at each time step changes:
cascadeProjectionValues(varName, valnType, hLevel, January, March, 1, 0, 1, "step", "sum")
│ │ │ └──┬────────────────┘ │ │
@t=1, lookup February from: mapProjectionValues(varName, valnType, hLevel, January, 1, "sum")
@t=2, lookup March from: mapProjectionValues(varName, valnType, hLevel, February, 1, "sum")
@t=3, lookup April from: mapProjectionValues(varName, valnType, hLevel, March, 1, "sum")
Examples¶
The examples below are all demonstrated in this example workbook.
Say you have a model with a single hierarchy node. There are some projection nodes using valuation type valnTypeData
that contains some data in variable VarA. The starting projection node uses valuation type valnTypeCpv and valuation
date January.
Simple example¶
The variable named VarASimple has the following formula:
cascadeProjectionValues("VarA","valnTypeData",1,February,April,1,0,0,"step","sum")
The precedents will be:
| # | Valuation type | Valuation date |
|---|---|---|
| 1 | valnTypeData |
February |
| 2 | valnTypeData |
March |
| 3 | valnTypeData |
April |
Say the precedents contain the following results:
Precedent 1
| t | Date | varA |
|---|---|---|
| 1 | February | \(x_1\) |
| 2 | March | \(x_2\) |
| 3 | April | \(x_3\) |
| 4 | May | \(x_4\) |
Precedent 2
| t | Date | varA |
|---|---|---|
| 1 | March | \(y_1\) |
| 2 | April | \(y_2\) |
| 3 | May | \(y_3\) |
| 4 | June | \(y_4\) |
Precedent 3
| t | Date | varA |
|---|---|---|
| 1 | April | \(z_1\) |
| 2 | May | \(z_2\) |
| 3 | June | \(z_3\) |
| 4 | July | \(z_4\) |
The results for this variable will be:
| t | Date | VarASimple | Explanation |
|---|---|---|---|
| 1 | January | N/A |
Look up January in precedent with February valuation date (There is no precedent with valuation date January). Precedent #1 does not have data for January. |
| 2 | February | \(x_1\) | Look up February in precedent with February valuation date. This is t=1 from precedent #1. |
| 3 | March | \(y_1\) | Look up March in precedent with March valuation date. This is t=1 from precedent #2. |
| 4 | April | \(z_1\) | Look up April in precedent with April valuation date. This is t=1 from precedent #3. |
| 5 | May | \(z_2\) | Look up May in precedent with April valuation date (There is no precedent with valuation date May). This is t=2 from precedent #3. |
| 6 | June | \(z_3\) | Look up June in precedent with April valuation date (There is no precedent with valuation date June). This is t=3 from precedent #3. |
With valnDateMonthsShift¶
Variable VarAValnDateShift has the following formula:
cascadeProjectionValues("VarA","valnTypeData",1,February,April,1,-1,0,"step","sum")
This is the same as the simple example, but with valnDateMonthsShift=-1. The precedents are the
same, but at each time step, a precedent will be used that has a valuation date corresponding to the previous month
instead of the current month.
The results for this variable will be:
| t | Date | VarAValnDateShift | Explanation |
|---|---|---|---|
| 1 | January | N/A |
Look up January in precedent with February valuation date (There is no precedent with valuation date December). Precedent #1 does not have data for January. |
| 2 | February | \(x_1\) | Look up February in precedent with February valuation date (There is no precedent with valuation date January). This is t=1 from precedent #1. |
| 3 | March | \(x_2\) | Look up March in precedent with February valuation date. This is t=2 from precedent #1. |
| 4 | April | \(y_2\) | Look up April in precedent with March valuation date. This is t=2 from precedent #2. |
| 5 | May | \(z_2\) | Look up May in precedent with April valuation date. This is t=2 from precedent #3. |
| 6 | June | \(z_3\) | Look up June in precedent with April valuation date (There is no precedent with valuation date May). This is t=3 from precedent #3. |
With timeShift¶
Variable VarATimeShift has the following formula:
cascadeProjectionValues("VarA","valnTypeData",1,February,April,1,0,1,"step","sum")
This is the same as the simple example, but with timeShift=1. The precedents are the same, and the
same precedent is used at each time step as in the simple example. However, at each time step, the
date of a different time step is looked up from the precedent.
The results for this variable will be:
| t | Date | VarATimeShift | Explanation |
|---|---|---|---|
| 1 | January | \(x_1\) | Look up February in precedent with February valuation date (There is no precedent with valuation date January). This is t=1 from precedent #1. |
| 2 | February | \(x_2\) | Look up March in precedent with February valuation date. This is t=2 from precedent #1. |
| 3 | March | \(y_2\) | Look up April in precedent with March valuation date. This is t=2 from precedent #2. |
| 4 | April | \(z_2\) | Look up May in precedent with April valuation date. This is t=2 from precedent #3. |
| 5 | May | \(z_3\) | Look up June in precedent with April valuation date (There is no precedent with valuation date May). This is t=3 from precedent #3. |
| 6 | June | \(z_4\) | Look up July in precedent with April valuation date (There is no precedent with valuation date June). This is t=4 from precedent #3. |
With valnDateMonthsShift and timeShift¶
Variable VarAValnDateShiftTimeShift has the following formula:
cascadeProjectionValues("VarA","valnTypeData",1,February,April,1,-1,1,"step","sum")
This combines the valuation date shift example and the time shift example. Please ensure that you understand both before reading this example.
The precedents are the same as in the simple example. Akin to the valuation date shift example, at each time step, a precedent will be used that has a valuation date corresponding to the previous month instead of the current month. Akin to the time shift example, at each time step, the date of a different time step is looked up from the precedent.
The results for this variable will be:
| t | Date | VarAValnDateShiftTimeShift | Explanation |
|---|---|---|---|
| 1 | January | \(x_1\) | Look up February in precedent with February valuation date (There is no precedent with valuation date December). This is t=1 from precedent #1. |
| 2 | February | \(x_2\) | Look up March in precedent with February valuation date (There is no precedent with valuation date January). This is t=2 from precedent #1. |
| 3 | March | \(x_3\) | Look up April in precedent with February valuation date. This is t=3 from precedent #1. |
| 4 | April | \(y_3\) | Look up May in precedent with March valuation date. This is t=3 from precedent #2. |
| 5 | May | \(z_3\) | Look up June in precedent with April valuation date. This is t=3 from precedent #3. |
| 6 | June | \(z_4\) | Look up July in precedent with April valuation date (There is no precedent with valuation date May). This is t=4 from precedent #3. |