FoReco (version 0.1.1)

cstrec: Heuristic first-cross-sectional-then-temporal cross-temporal forecast reconciliation

Description

The order of application of the two reconciliation steps proposed by Kourentzes and Athanasopoulos (2019), implemented in the function tcsrec, may be inverted. The function cstrec performs cross-sectional reconciliation (htsrec) first, then temporal reconciliation (thfrec), and finally applies the average of the projection matrices obtained in the second step to the one dimensional reconciled values obtained in the first step.

Usage

cstrec(basef, m, C, thf_comb, hts_comb, Ut, nb, res, W, Omega,
       mse = TRUE, corpcor = FALSE, nn = FALSE,
       settings = osqpSettings(verbose = FALSE, eps_abs = 1e-5,
       eps_rel = 1e-5, polish_refine_iter = 100, polish = TRUE))

Arguments

basef

(n x h(k* + m)) matrix of base forecasts to be reconciled; n is the total number of variables, m is the highest frequency, k* is the sum of (p-1) factors of m, excluding m, and h is the forecast horizon. Each row identifies, a time series, and the forecasts are ordered as [lowest_freq' ... highest_freq']'.

m

Highest available sampling frequency per seasonal cycle (max. order of temporal aggregation).

C

(na x nb) cross-sectional (contemporaneous) matrix mapping the bottom level series into the higher level ones.

thf_comb

Type of the ((k* + m) x (k* + m)) covariance matrix to be used in the temporal reconciliation, see more in comb param of thfrec.

hts_comb

Type of the (n x n) covariance matrix to be used in the cross-sectional reconciliation, see more in comb param of htsrec.

Ut

Zero constraints cross-sectional (contemporaneous) kernel matrix \((\textbf{U}'\textbf{Y} = \mathbf{0})\) spanning the null space valid for the reconciled forecasts. It can be used instead of parameter C, but in this case nb (n = na + nb) is needed. If the hierarchy admits a structural representation, Ut has dimension (na x n).

nb

Number of bottom time series; if C is present, nb is not used.

res

(n x N(k* + 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 hts_comb = {"wls", "shr", "sam"} and/or hts_comb = {"wlsv", "wlsh", "acov", "strar1", "sar1", "har1", "shr", "sam"}. The rows must be in the same order as basef.

W

This option permits to directly enter the covariance matrix in the cross-sectional reconciliation, see more in W param of htsrec.

Omega

This option permits to directly enter the covariance matrix in the reconciliation through temporal hierarchies, see more in Omega param of thfrec.

mse

Logical value: TRUE (default) calculates the covariance matrix of the in-sample residuals (when necessary) according to the original hts and thief formulation: no mean correction, T as denominator.

corpcor

Logical value: TRUE if corpcor (Sch<U+00E4>fer et al., 2017) must be used to shrink the sample covariance matrix according to Sch<U+00E4>fer and Strimmer (2005), otherwise the function uses the same implementation as package hts.

nn

Logical value, TRUE if non-negative reconciled forecasts are wished. Warning, the two-step heuristic reconciliation allows non negativity constraints only in the first step. This means that non-negativity is not guaranteed in the final reconciled values.

settings

Settings for osqp (object osqpSettings). The default options are: verbose = FALSE, eps_abs = 1e-5, eps_rel = 1e-5, polish_refine_iter = 100 and polish = TRUE. For details, see the osqp documentation (Stellato et al., 2019).

Value

The function returns a list with two elements:

recf

(n x h(k* + m)) reconciled forecasts matrix.

M

Projection matrix (projection approach).

References

Di Fonzo, T., Girolimetto, D. (2020), Cross-Temporal Forecast Reconciliation: Optimal Combination Method and Heuristic Alternatives, Department of Statistical Sciences, University of Padua, arXiv:2006.08570.

Kourentzes, N., Athanasopoulos, G. (2019), Cross-temporal coherent forecasts for Australian tourism, Annals of Tourism Research, 75, 393-409.

Sch<U+00E4>fer, 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.

Sch<U+00E4>fer, 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. (2018). OSQP: An Operator Splitting Solver for Quadratic Programs, arXiv:1711.08013.

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.

Examples

# NOT RUN {
data(FoReco_data)
obj <- cstrec(FoReco_data$base, m = 12, C = FoReco_data$C, thf_comb = "acov",
              hts_comb = "shr", res = FoReco_data$res)

# }