precise 0.5.16

Online covariance, precision, portfolios and ensembles

precise

Online covariance and precision forecasting, portfolios, and model ensembles with ongoing benchmarking.

Covariance TLDR: "Functions that forecast covariance in online fashion"

Here y is a vector:

from precise.skaters.covariance.ewapm import ewa_pm_emp_scov_r005_n100 as f 
s = {}
for y in ys:
    x, x_cov, s = f(s=s, y=y)

This package contains lots of different "f"s. There is a LISTING_OF_COV_SKATERS with links to the code.

Portfolio TLDR: "Functions that update portfolio weights in online fashion"

Here y is a vector:

    from precise.skaters.managers.schurmanagers import schur_weak_pm_t0_d0_r025_n50_g100_long_manager as mgr
    s = {}
    for y in ys:
        w, s = mgr(s=s, y=y)

This package contains lots of "mgr"'s. There is a LISTING_OF_MANAGERS with links to respective code.

Ensembles, mixtures of experts TLDR: "They are just portfolios"

Read this article exploring the connection between portfolio theory and combining models, or the colab notebook on which is is based.

$$ M6 Contest example entries $$

This package includes scripts to create entries for the lucrative M6 Financial Forecasting competition.

1. See precise/examples_m6
2. Register at the m6 competition.
3. Buy me, or the authors of PyPortfolio-Lib and PyPortfolioOpt, lots of beers when you win.

Install

pip install precise 

or for latest:

pip install git+https://github.com/microprediction/precise.git

Trouble?

pip install --upgrade pip
pip install --upgrade scipy
pip insatll --upgrade precise 

More about covariance skaters and their Elos

Similar in style to skaters used in the timemachines package, this package may be thought of as a collection of covariance prediction functions taking one vector at a time, and also the prior state, and spitting out a prediction mean vector x, a prediction covariance x_cov, and a posterior state whose interpretation is the responsibility of the skater, not the caller.

See /examples_basic_usage. And yes, this mildly unusual convention requires the caller to maintain state from one call to the next: See the timemachines faq for justification of this style. The running_empirical_covariance colab notebook also illustrates the simple usage pattern.

Cov skater listing and Elo ratings

• Peruse the listing
• Or hunt for skaters in precise/skaters/covariance.
• Run the Elo ratings colab notebook which may, or may not, help guide your shortlisting.

Interpreting covariance skater names

Examples:

Skater name	Location	Meaning
buf_huber_pcov_d1_a1_b2_n50	skaters/covariance/bufhuber	Applies an approach that exploits Huber pseudo-means to a buffer of data of length 50 in need of differencing once, with generalized Huber loss parameters a=1, b=2.
buf_sk_ld_pcov_d0_n100	skaters/covariance/bufsk	Applies sk-learn's implementation of Ledoit-Wolf to stationary buffered data of length 100
ewa_pm_emp_scov_r01	skaters/covariance/ewapartial	Performs an incremental, recency-weighted sample covariance estimate that exploits partial moments. Uses a memory parameter r=0.01

Broad calculation style categories

Shorthand	Interpretation	Incremental ?
buf	Performs classical batch calculation on a fixed window of data each time	No
win	Performs incremental fixed window calculation.	Yes
run	Running calculation weighing all observations equally	Yes
ewa	Running calculation weighing recent observations more	Yes

Methodology hints (can be combined)

Shorthand	Inspiration
emp	"Empirical" (not shrunk or augmented)
lz	Le-Zhong variable-by-variable updating
lw	Ledoit-Wolf
pm	Partial moments
huber	Generalized Huber pseudo-mean
oas	Oracle approximating shrinkage.
gl	Graphical Lasso
mcd	Minimum covariance determinant
weak	Novel shrinkage method by yours truly

Intended main target (more than one may be produced in the state)

Shorthand	Intent
scov	Sample covariance
pcov	Population covariance
spre	Inverse of sample covariance
ppre	Inverse of population covariance

Differencing hints:

Shorthand	Intent
d0	For use on stationary, ideally IID data
d1	For use on data that is iid after taking one difference

Stand-alone covariance utilities

If you are hunting for useful functions for independent use (i.e. not "skating") then I suggest rummaging in

• covarianceutil
• locationutil
• portfolioutil

or the "factory" modules, perhaps.

More on portfolio managers and their Elos

Hopefully it is clear that portfolio techniques map to other uses like smarter stacking of time-series forecasting methods. But this part is too fluid to document thoroughly. See the portfolio directories in skaters and also the managers. Managers are just like cov skaterse except they emit portfolio holdings and state.

    s = {}
    for y in ys:
        w, s = mgr(s=s, y=y)

Most managers pair a cov skater with a "static" portfolio construction estimator, although that may change. For provisional Elo ratings of managers see the example script that collates manager Elo ratings. Here are some portfolio and manager hints:

PyPortfolioOpt	Intent
ppo	Uses the PyPortfolioOpt package
ppo_vol	... and minimum volatility therein
ppo_quad	... and maximum quadratic utility therein
ppo_sharpe	... and maximum Sharpe ratio therein

Riskfolio-Lib	Intent
rpl	Uses the RiskFolio-Lib package
rpl_hrp	... and Hierarchical Risk Parity therein
rlp_hrp_cdar	... and Conditional Drawdown at Risk of uncompounded cumulative returns
rlp_hrp_flpm	... and First Lower Partial Moment therein
	... et cetera (see the rest)

Homespun	Intent
diag	Use only diagonal entries of cov
weak	Method that "weakens" some cov entries to make portfolio long only
hrp	Varieties of hierarchical allocation
hrp_diag_diag	... and uses "diag" allocation/portfolio, like Lopez de Prado's 2016 paper
hrp_weak_weak	... and uses "weak" allocation and also "weak" portfolio construction.
schur	Homespun method that exploits Schur complements
schur_weak_diag	... and uses weak allocation and diag portfolio at the leaves

At present "weak" and "schur" are the only methods you may have trouble finding implemented elsewhere. The latter is my attempt to unify seemingly disparate approaches: namely those using a global optimization versus those using divide and conquer.

Model ensembles, stacking, mixtures of experts et cetera

Same thing, sort of. See this notebook example or these examples.

Miscellaneous remarks

• Here is some related, and potentially related, literature.
• This is a piece of the microprediction project aimed at creating millions of autonomous critters to democratize AI, should you ever care to cite the same. The uses include mixtures of experts models for time-series analysis, buried in timemachines somewhere.
• If you just want univariate calculations, and don't want numpy as a dependency, there is momentum. However if you want univariate forecasts of the variance of something, as distinct from mere online calculations of the same, you might be better served by the timemachines package. In particular I would suggest checking the time-series elo ratings and the "special" category in particular, as various kinds of empirical moment time-series (volatility etc) are used to determine those ratings.
• The name of this package refers to precision matrices, not numerical precision. This isn't a source of high precision covariance calculations per se. The intent is more in forecasting future realized covariance. Perhaps I'll include some more numerically stable methods from this survey to make the name more fitting. Pull requests are welcome!
• The intent is that methods are parameter free. However some not-quite autonomous methods admit a few parameters (the factories). A few might even use just one additional scalar parameter r with a space-filling curve convention - somewhat akin to the tuning of skaters explained here in the timemachines package).
• I use Elo ratings, despite the shortcomings, because comparisions are extremely time intensive. Match results are recorded in hashed files for easy parallelization and avoidance of git merging. You can run the battle scripts if you like. See these examples for instance. To make a different battle you modify the name of the script and nothing else. Pull requests for match results are welcome.

Disclaimer

Not investment advice. Not M6 entry advice. Just a bunch of code subject to the MIT License disclaimers.