ctmo function

Cross-temporal middle-out reconciliation

The cross-temporal middle-out forecast reconciliation combines top-down (cttd ) and bottom-up (ctbu ) methods in the cross-temporal framework for genuine hierarchical/grouped time series. Given the base forecasts of an intermediate cross-sectional level $l$ and aggregation order $k$, it performs

• a top-down approach for the aggregation orders $\geq k$ and cross-sectional levels $\geq l$;
• a bottom-up approach, otherwise.

ctmo(base, agg_mat, agg_order, id_rows = 1, order = max(agg_order),
     weights, tew = "sum", normalize = TRUE)

Arguments

• base: A ($n_l \times hk$) numeric matrix containing the $l$-level base forecasts of temporal aggregation order $k$; $n_l$ is the number of variables at level $l$, $k$ is an aggregation order (a factor of $m$, and $1<k<m$), $m$ is the max aggregation order, and $h$ is the forecast horizon for the lowest frequency time series.
• agg_mat: A ($n_a \times n_b$) numeric matrix representing the cross-sectional aggregation matrix. It maps the $n_b$ bottom-level (free) variables into the $n_a$ upper (constrained) variables.
• agg_order: Highest available sampling frequency per seasonal cycle (max. order of temporal aggregation, $m$), or a vector representing a subset of $p$ factors of $m$.
• id_rows: A numeric vector indicating the $l$-level rows of agg_mat.
• order: The intermediate fixed aggregation order $k$.
• weights: A ($n_b \times hm$) numeric matrix containing the proportions for each high-frequency bottom time series; $n_b$ is the total number of high-frequency bottom variables, $m$ is the max aggregation order, and $h$ is the forecast horizon for the lowest frequency time series.
• tew: A string specifying the type of temporal aggregation. Options include: "sum" (simple summation, default), "avg" (average), "first" (first value of the period), and "last" (last value of the period).
• normalize: If TRUE (default), the weights will sum to 1.

Returns

A ($n \times h(k^\ast+m)$) numeric matrix of cross-temporal reconciled forecasts.

Examples

set.seed(123)
# Aggregation matrix for Z = X + Y, X = XX + XY and Y = YX + YY
A <- matrix(c(1,1,1,1,1,1,0,0,0,0,1,1), 3, byrow = TRUE)
# (2 x 6) base forecasts matrix (simulated), forecast horizon = 3
# and intermediate aggregation order k = 2 (max agg order = 4)
baseL2k2 <- rbind(rnorm(3*2, 5), rnorm(3*2, 5))

# Same weights for different forecast horizons, agg_order = 4
fix_weights <- matrix(runif(4*4), 4, 4)
reco <- ctmo(base = baseL2k2, id_rows = 2:3, agg_mat = A,
             order = 2, agg_order = 4, weights = fix_weights)

# Different weights for different forecast horizons
h_weights <- matrix(runif(4*4*3), 4, 3*4)
recoh <- ctmo(base = baseL2k2, id_rows = 2:3, agg_mat = A,
             order = 2, agg_order = 4, weights = h_weights)

See Also

Middle-out reconciliation: csmo(), temo()

Cross-temporal framework: ctboot(), ctbu(), ctcov(), ctlcc(), ctrec(), cttd(), cttools(), iterec(), tcsrec()