Top-down forecast reconciliation for a univariate time series, where the forecast of the most aggregated temporal level is disaggregated according to a proportional scheme (weights). Besides fulfilling any aggregation constraint, the top-down reconciled forecasts should respect two main properties:

the top-level value remains unchanged;

all the bottom time series reconciled forecasts are non-negative.

## Arguments

- base
A (\(hm \times 1\)) numeric vector containing the temporal aggregated base forecasts of order \(m\); \(m\) 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 \(m\).

- 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)
# (2 x 1) top base forecasts vector (simulated), forecast horizon = 2
topf <- rnorm(2, 10)
# Same weights for different forecast horizons
fix_weights <- runif(4)
reco <- tetd(base = topf, agg_order = 4, weights = fix_weights)
# Different weights for different forecast horizons
h_weights <- runif(4*2)
recoh <- tetd(base = topf, agg_order = 4, weights = h_weights)
```