temo function

Temporal middle-out reconciliation

The middle-out forecast reconciliation for temporal hierarchies combines top-down (tetd ) and bottom-up (tebu ) methods. Given the base forecasts of an intermediate temporal aggregation order $k$, it performs

• a top-down approach for the aggregation orders $\<k$;
• a bottom-up approach for the aggregation orders $\>k$.

temo(base, agg_order, order = max(agg_order), weights, tew = "sum",
     normalize = TRUE)

Arguments

• base: A ($hk \times 1$) numeric vector containing the temporal aggregated base forecasts of order $k$; $k$ 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_order: Highest available sampling frequency per seasonal cycle (max. order of temporal aggregation, $m$), or a vector representing a subset of $p$ factors of $m$.
• order: The intermediate fixed aggregation order $k$.
• weights: A ($hm \times 1$) numeric vector containing the proportions for the high-frequency time series; $m$ 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 ($h(k^\ast+m) \times 1$) numeric vector of temporal reconciled forecasts.

Examples

set.seed(123)
# (6 x 1) base forecasts vector (simulated), forecast horizon = 3
# and intermediate aggregation order k = 2 (max agg order = 4)
basek2 <- rnorm(3*2, 5)
# Same weights for different forecast horizons
fix_weights <- runif(4)
reco <- temo(base = basek2, order = 2, agg_order = 4, weights = fix_weights)

# Different weights for different forecast horizons
h_weights <- runif(4*3)
recoh <- temo(base = basek2, order = 2, agg_order = 4, weights = h_weights)

See Also

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

Temporal framework: teboot(), tebu(), tecov(), telcc(), terec(), tetd(), tetools()