duration.TTC: Duration - Data Weighting and "TTC" Calculation
In RTransProb: Analyze and Forecast Credit Migrations

Description Usage Arguments Details Value Author(s) Examples

Calculating Through-the-Cycle generator matrix and transition counts using duration method

1	duration.TTC(lstCnt,lstFirmYears)

`lstCnt`	off-diagonal transition counts (matrix) for each time-step
`lstFirmYears`	firm years each time-step

Given data representing x off-diagonal transition counts for each time-step, this function combines those data to obtain average counts for each time-step, in such a way as to preserve the information while implementing a weighting scheme that would allow for the weighting of the historical experiences.

Let T(m,y) and F(m,y) represent the off-diagonal transition matrix and 'firm-years' vector, for month = m and year = y, respectively. Then,

T(m,y) = \{T_{ij}(m,y)\}_{i,j\,=\,1,…,K}

F(m,y) = \{F_{i}(m,y)\}_{i\,=\,1,…,K}

Many credit risk models require a long-run average PD estimate. This has been interpreted as meaning the data from multiple years should be combined and in a method capable of supporting some form of weighting of samples. The three methods of weighting considered for data generated via the duration method are:

Scale the number of transitions and firm counts/years using the a single year count to preserve dynamics, then average transitions and firms counts/years separately to create a generator matrix.
Estimate the single-year quantities (generator matrices for each time-step), then average across years
Average transition matrices from each time-step

The Markov property allows for direct weighting as each year can be regarded as distinct.

`CLW`	Count Level Weighting - Construct TTC transition matrix from aggregate scaled and weighted counts data (transitions and 'firm-years').
`PTMLW`	Periodic Transition Matrix Level Weighting - Construct TTC transition matrix using the average of the weighted transition matrices from each time-step (Scaling is performed at the transition matrix level for each time-step).
`PGMLW`	Periodic Generator Matrix Level Weighting - Construct TTC transition matrix using the average of the weighted Generator matices from each time-step (Scaling is performed at the generator matrix level for each time-step).
`UUPTM`	Unscaled and UnWeighted Periodic Transition Matrices - Construction of unscaled and unweighted periodic transition matrices from unscaled and unweighted generator matrices for each time-step .
`WGM`	Weighted Generator Matrix - Average generator matrix from each time-step.
`SWT`	Scaled and Weighted Transitions - aggregate scaled and weighted transitions
`SWFY`	Scaled and Weighted Firm Years - aggregate scaled and weighted firm years

Abdoulaye (Ab) N'Diaye

## Not run: 

#Set parameters
startDate  <- "2000-01-01"
endDate    <- "2005-01-01"
method       <- "duration"   
snapshots <- 4
interval <-  0
Example1<-getPIT(data,startDate, endDate,method, snapshots, interval)

ExampleTTC1<-duration.TTC(Example1$lstCntMat,Example1$lstInitVec)


## End(Not run)