The goal of DOSPorfolio is to provide a simple interface for computing portfolio weights according to the dynamic weighting scheme from (Bodnar, Parolya, and Thorsén 2021).

The development version can be installed from GitHub with:

```
# install.packages("devtools")
::install_github("Statistics-In-Portfolio-Theory/DOSportfolio") devtools
```

This is a very simple example which shows you how use the package:

```
library(DOSPortfolio)
<- 25*2
n <- 15
p # Simulate data
<- sqrt(5/3) * matrix(rt(n*p, df=5), ncol=p, nrow=n)
data # specify the allocation points. The DOSPortfolio class will validate what is
# "ok" allocation periods.
<- c(25, 42)
reallocation_points <- DOSPortfolio(data, reallocation_points))
(portfolios #> $weights
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0.08697641 0.07240871 0.018210965 0.0800573 0.06954698 0.07120553
#> [2,] 0.09185841 0.07378896 0.006563325 0.0832761 0.07023934 0.07229657
#> [,7] [,8] [,9] [,10] [,11] [,12]
#> [1,] 0.05088562 0.006348246 0.06908115 0.08272137 0.08722852 0.06232573
#> [2,] 0.04709222 -0.008150919 0.06966153 0.08658055 0.09217112 0.06128227
#> [,13] [,14] [,15]
#> [1,] 0.08156509 0.08208267 0.07935573
#> [2,] 0.08514633 0.08578832 0.08240588
#>
#> $shrinkage_type
#> [1] "non-overlapping"
#>
#> attr(,"class")
#> [1] "DOSPortfolio"
```

The variable `portfolios`

is a “DOSPortfolio” class whose
documentation can be viewed by `?DOSPortfolio`

. The
constructor `DOSPortfolio()`

looks for violations against the
assumptions made in the reference. Here is an example when things does
not work

```
<- c(37, 42)
reallocation_points # observe that there is little data between the first and second allcoation
# point. Its actually to little since p > n_2, e.g. 15 > 42 - 37.
# This will cause an error
DOSPortfolio(data, reallocation_points)
#> Error: Non-overlapping estimator can not handle concentration ratios above one.
#> Consider excluding one (or more) break point(s) or provide more data.
```

However, by using the the argument
`shrinkage_type="overlapping"`

we can make it work!

```
DOSPortfolio(data, reallocation_points, shrinkage_type = "overlapping")
#> $weights
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0.08409633 0.07159444 0.025082350 0.07815841 0.06913853 0.07056188
#> [2,] 0.09300762 0.07411387 0.003821481 0.08403381 0.07040232 0.07255340
#> [,7] [,8] [,9] [,10] [,11] [,12]
#> [1,] 0.05312349 0.01490185 0.06873876 0.08044469 0.08431269 0.06294131
#> [2,] 0.04619926 -0.01156401 0.06979815 0.08748900 0.09333460 0.06103664
#> [,13] [,14] [,15]
#> [1,] 0.07945238 0.07989656 0.07755632
#> [2,] 0.08598935 0.08666063 0.08312389
#>
#> $shrinkage_type
#> [1] "overlapping"
#>
#> attr(,"class")
#> [1] "DOSPortfolio"
```

If you want to learn to more why this is then you can have a look at
the *“introduction”* vignette or read the paper!

- Create summary function so that one can construct summaries of the portfolios as done in (Bodnar, Parolya, and Thorsén 2021).
- Include test on finite fourth moment, summary function to generate table from the article?
- Setup so that the portfolio estimators can work with the
`tsibble`

package? - Extend theory to mean-variance portfolio and Shrinkage estimators.

Bodnar, Taras, Nestor Parolya, and Erik Thorsén. 2021. “Dynamic
Shrinkage Estimation of the High-Dimensional Minimum-Variance
Portfolio.” *arXiv Preprint arXiv:2106.02131*. https://arxiv.org/abs/2106.02131.