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Evaluation and standardization of popular time series packages

Project description

timemachines teststsa tbats prophet orbit neuralprophet pmd pydlm elo-ratings License: MIT

Fast, incremental, pure-functional, time-series forecasting (article)

Use popular forecasting packages with one line of code, or view their Elo ratings

What's different:

  • Simple canonical functional use of some functionality from packages like fbprophet, pmdarima, tbats, tsa, pmdarima, neuralprophet and their ilk. Sadly most of these are slow but...

  • Simple fast accurate alternatives to popular time series packages that are often faster, lighter and more accurate (e.g. thinking)

  • Simple, ongoing empirical evaluation. See the leaderboards in the accompanying repository timeseries-elo-ratings. Assessment is always out of sample and uses live, constantly updating real-world data from

  • Simple k-step ahead forecasts in functional style involving one line of code.

  • Simple tuning with one line of code facilitated by HumpDay, which provides canonical functional use of scipy.optimize, ax-platform, hyperopt, optuna, platypus, pymoo, pySOT, skopt, dlib, nlopt, bayesian-optimization, nevergrad and more.

  • Simple evaluation with one line of code using metrics like RMSE or energy distances.

  • Simple stacking of models with one line of code. The functional form makes other types of model combination easy as well.

  • Simpler deployment. There is no state, other that that explicitly returned to the caller. For many models state is a pure Python dictionary and thus trivially converted to JSON and back.


Nothing to slow you down!

Here time series "models" are plain old functions. Those functions have a "skater" signature, facilitating "skating". One might say that skater functions suggest state machines for sequential assimilation of observations (as a data point arrives, forecasts for 1,2,...,k steps ahead, with corresponding standard deviations are emitted). However here the caller is expected to maintain state from one invocation (data point) to the next. See the FAQ if this seems odd.

New contributor guide:


Running a model and plotting it

from import hospital_with_exog
from timemachines.skatertools.visualization.priorplot import prior_plot
import matplotlib.pyplot as plt

# Get some data - including variables known in advance:
k = 1
y, a = hospital_with_exog(k=k, n=450, offset=True)

# Run the model and plot it 
prior_plot(f=fbprophet_exogenous, k=k, y=y, n=450, n_plot=50)

The Skater signature

  x, w, s = f(   y:Union[float,[float]],               # Contemporaneously observerd data, 
                                                     # ... including exogenous variables in y[1:], if any. 
            s=None,                                  # Prior state
            k:float=1,                               # Number of steps ahead to forecast. Typically integer. 
            a:[float]=None,                          # Variable(s) known in advance, or conditioning
            t:float=None,                            # Time of observation (epoch seconds)
            e:float=None,                            # Non-binding maximal computation time ("e for expiry"), in seconds
            r:float=None)                            # Hyper-parameters ("r" stands for for hype(r)-pa(r)amete(r)s in R^n)

The function is intended to be applied repeatedly. For example one could harvest a sequence of the model predictions as follows:

def posteriors(f,y):
    s = {}       
    x = list()
    for yi in y: 
        xi, xi_std, s = f(yi,s)
    return x

or see the prominently positioned Notice the use of s={} on first invocation.

Skater "y" argument

A skater function f takes a vector y, where the quantity to be predicted is y[0] and there may be other, simultaneously observed variables y[1:] deemed helpful in predicting y[0].

Skater "s" argument

The state. Pass empty dict the first time.

Skater "k" argument

Determines the length of the term structure of predictions (and also their standard deviations) that will be returned. This cannot be varied from one invocation to the next.

Skater "a" argument

A vector of known-in-advance variables.

Skater "t" argument

Epoch time of the observation.

Skater "e" argument ("expiry")

Seconds allowed for computation. See remark below.

Skater "r" argument ("hype(r) pa(r)amete(r)s")

A scalar in the closed interval [0,1] represents all hyper-parameters. See comments below.

Return values

Two vectors and the posterior state. The first set of k numbers can be interpreted as a point estimate (but need not be) and the second is typically suggestive of a symmetric error std, or width. However a broader interpretation is possible wherein a skater suggests a useful affine transformation of the incoming data and nothing more.

      -> x     [float],    # A vector of point estimates, or anchor points, or theos
         x_std [float]     # A vector of "scale" quantities (such as a standard deviation of expected forecast errors) 
         s    Any,         # Posterior state, intended for safe keeping by the callee until the next invocation 

In returning state, the intent is that the caller might carry the state from one invocation to the next verbatim. This is arguably more convenient than having the predicting object maintain state, because the caller can "freeze" the state as they see fit, as when making conditional predictions. This also eyes lambda-based deployments and encourages tidy use of internal state - not that we succeed when calling down to statsmodels (though prophet, and others including the home grown models use simple dictionaries, making serialization trivial).

You'll notice also that parameter use seems limited. This is deliberate. A skater is morally a "bound" model (i.e. fixed hyper-parameters) and ready to use. Any fitting, estimation or updating is the skater's internal responsibility. That said, it is sometimes useful to enlarge the skater concept to include hyper-parameters, as this enourages a more standardized way to expose and fit them. It remains the responsibility of the skater designer to ensure that the parameter space is folded into (0,1) is a somewhat sensible way.

The use of a single scalar for hyper-parameters may seem unnatural, but is slighly less unnatural if conventions are followed that inflate [0,1] into the square [0,1]^2 or the cube [0,1]^3. See the functions to_space and from_space. This also makes it trivial for anyone to design black box optimization routines that can work on any skater, without knowing its working. The humpday package makes this trivial - albeit time-consuming.

The use of e is a fairly weak convention that many skaters ignore. In theory, a large expiry e can be used as a hint to the callee that there is time enough to do a 'fit', which we might define as anything taking longer than the usual function invocation. A zero might suggest that there isn't even time for a "proper" prediction to be made, and we are still in the burn-in period as far as assessment or usage is concerned. However, this is between the caller and it's priest really - or its prophet we should say. Some skaters, such as the Facebook prophet skater, do a full 'fit' every invocation so this is meaningless. Other skaters don't even have a separate notion of 'fit' versus 'update' because everything is incremental.

Summary of conventions:

  • State

    • The caller, not the callee, persists state from one invocation to the next
    • The caller passes s={} the first time, and the callee initializes state
    • State can be mutable for efficiency (e.g. it might be a long buffer) or not.
    • State should, ideally, be JSON-friendly.
  • Observations: target, and contemporaneous exogenous

    • If y is a vector, the target is the first element y[0]
    • The elements y[1:] are contemporaneous exogenous variables, not known in advance.
    • Missing data can be supplied to some skaters, as np.nan.
    • Most skaters will accept scalar y and a if there is only one of either.
  • Variables known k-steps in advance, or conditioning variables:

    • Pass the vector argument a that will occur in k-steps time (not the contemporaneous one)
    • Remark: In the case of k=1 there are different interpretations that are possible beyond "business day", such as "size of a trade" or "joystick up" etc.
  • Hyper-Parameter space:

    • A float r in (0,1).
    • This package provides functions to_space and from_space, for expanding to R^n using space filling curves, so that the callee's (hyper) parameter optimization can still exploit geometry, if it wants to.

See FAQ or file an issue if anything offends you greatly.

Related illustrations


We've moved to bare-bones dependencies because some timeseries packages are not keeping up with changes to dependent packages (as with STAN releases), or operating system or hardware quirks (like Apple M1 for example), and also because the statistical evidence for their inclusion is less than overwhelming (ahem. So ...

pip install --upgrade pip
pip install timemachines

This gives you access to the home grown packages and to scipy/tsa models. Those perform well. The popular packages and some others are not added by default. But add them manually if you want to use them:

pip install prophet
pip install neuralprophet
pip install pydlm
pip install divinity
pip install pmdarima

Add matplotlib if you want to use plotting utilities provides

pip install matplotlib 

Add microprediction if you want to use live data

pip install microprediction   

Apple M1

A fluid situation. You might try adding the pip argument to skip pep517 if you run into trouble on M1 chips

pip install whatever --no-use-pep517

Tuning hyper-params


If you'd like to contribute to this standardizing and benchmarking effort, here are some ideas:

If you are the maintainer of a time series package, we'd love your feedback and if you take the time to submit a PR here that incorporates your library, do yourself a favor and also enable "supporting" on your repo. Nothing here is put forward as the right way to write time series packages - more a way of exposing their functionality for comparisons. If you are interested in design thoughts for time series maybe participate in this thread.



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