tcsrec {FoReco} | R Documentation |
Heuristic first-temporal-then-cross-sectional cross-temporal forecast reconciliation
Description
The cross-temporal forecast reconciliation procedure by
Kourentzes and Athanasopoulos (2019) can be viewed as an ensemble
forecasting procedure which exploits the simple averaging of different
forecasts. First, for each time series the forecasts at any temporal
aggregation order are reconciled using temporal hierarchies
(thfrec()
), then time-by-time cross-sectional
reconciliation is performed (htsrec()
). The
projection matrices obtained at this step are then averaged and used to
cross-sectionally reconcile the forecasts obtained at step 1, by this way
fulfilling both cross-sectional and temporal constraints.
Usage
tcsrec(basef, thf_comb, hts_comb, res, avg = "KA", ...)
Arguments
basef |
(\(n \times h(k^\ast+m)\)) matrix of base forecasts to be reconciled, \(\widehat{\mathbf{Y}}\); \(n\) is the total number of variables, \(m\) is the highest time frequency, \(k^\ast\) is the sum of (a subset of) (\(p-1\)) factors of \(m\), excluding \(m\), and \(h\) is the forecast horizon for the lowest frequency time series. Each row identifies a time series, and the forecasts are ordered as [lowest_freq' ... highest_freq']'. |
hts_comb , thf_comb |
Type of covariance matrix (respectively
(\(n \times n\)) and (\((k^\ast + m) \times (k^\ast + m)\))) to
be used in the cross-sectional and temporal reconciliation. More details in
|
res |
(\(n \times N(k^\ast + m)\)) matrix containing the residuals
at all the temporal frequencies ordered [lowest_freq' ... highest_freq']'
(columns) for each variable (row), needed to estimate the covariance matrix
when |
avg |
If |
... |
Any other options useful for |
Details
This function performs a two-step cross-temporal forecast reconciliation using
the covariance matrices chosen by the user. If the combinations used by Kourentzes and Athanasopoulos (2019) are
wished, thf_comb
must be set equal to either "struc"
or "wlsv"
,
and hts_comb
equal to either "shr"
or "wls"
.
Warning, the two-step heuristic reconciliation allows considering non negativity constraints only in the first step. This means that non-negativity is not guaranteed in the final reconciled values.
Value
The function returns a list with two elements:
recf |
(\(n \times h(k^\ast + m)\)) reconciled forecasts matrix, \(\widetilde{\mathbf{Y}}\). |
M |
Matrix which transforms the uni-dimensional reconciled forecasts of step 1 (projection approach) . |
References
Di Fonzo, T., and Girolimetto, D. (2023), Cross-temporal forecast reconciliation: Optimal combination method and heuristic alternatives, International Journal of Forecasting, 39(1), 39-57.
Kourentzes, N., Athanasopoulos, G. (2019), Cross-temporal coherent forecasts for Australian tourism, Annals of Tourism Research, 75, 393-409.
Schäfer, J.L., Opgen-Rhein, R., Zuber, V., Ahdesmaki, M., Duarte Silva, A.P., Strimmer, K. (2017), Package ‘corpcor’, R package version 1.6.9 (April 1, 2017), https://CRAN.R-project.org/package= corpcor.
Schäfer, J.L., Strimmer, K. (2005), A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics, Statistical Applications in Genetics and Molecular Biology, 4, 1.
Stellato, B., Banjac, G., Goulart, P., Bemporad, A., Boyd, S. (2020). OSQP: An Operator Splitting Solver for Quadratic Programs, Mathematical Programming Computation, 12, 4, 637-672.
Stellato, B., Banjac, G., Goulart, P., Boyd, S., Anderson, E. (2019), OSQP: Quadratic Programming Solver using the ‘OSQP’ Library, R package version 0.6.0.3 (October 10, 2019), https://CRAN.R-project.org/package=osqp.
See Also
Other reconciliation procedures:
cstrec()
,
ctbu()
,
htsrec()
,
iterec()
,
lccrec()
,
octrec()
,
tdrec()
,
thfrec()
Examples
data(FoReco_data)
obj <- tcsrec(FoReco_data$base, m = 12, C = FoReco_data$C,
thf_comb = "acov", hts_comb = "shr", res = FoReco_data$res)