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 \(>k\).

## Usage

```
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.

## 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)
```