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Evaluation and standardization of popular time series packages

Project description

timemachines simpletsa darts sktime tbats simdkalman prophet orbit neuralprophet pmd pydlmtcn river divinityLicense: MIT

Fast, incremental, time-series prediction

... and some slow options. Use popular forecasting packages with one line of code in a sequence-to-sequence calling syntax. Or just browse their Elo ratings to help decide which to try out first. There's also a recommendation colab notebook you can open and run.

What's different:

  • Simple k-step ahead forecasts in functional style There are no "models" here requiring setup, only forecast functions:

     x, x_hat, s = f(y,s,k)

    These functions are called skaters. What they do is sometimes called sequence-to-sequence prediction.

  • Simple canonical use of some functionality from packages like river, pydlm, tbats, pmdarima, statsmodels.tsa, neuralprophet, Facebook Prophet, Uber's orbit, Facebook's greykite and more.

  • Simple fast accurate alternatives to popular time series packages. For example the thinking skaters perform well in the Elo ratings, and much better than the brand names. See the article comparing them to Facebook prophet and Neural Prophet.

  • Ongoing, incremental, empirical evaluation. Again, see the leaderboards produced by the accompanying repository timeseries-elo-ratings. Assessment is always out of sample and uses live, constantly updating real-world data from

  • Simple stacking, ensembling and combining of models. The function form makes it easy to do this with one line of code, quite often (again, see for an illustration, or

  • Simpler deployment. There is no state, other that that explicitly returned to the caller. For skaters relying only on the timemachines and river packages (the fast ones), the state is a pure Python dictionary trivially converted to JSON and back (for instance in a web application). See the FAQ for a little more discussion.


Nothing to slow you down!

To emphasize, in this package a time series "model" is a plain old function taking scalars and lists as arguments. 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:



The suggested install is:

pip install --upgrade pip
pip install --upgrade numpy
pip install --upgrade timemachines

In colab you might need to

pip unisntall numpy
pip install --upgrade numpy 

Then check the Elo ratings or otherwise decide which packages you want to utilize - they aren't in by default.

pip install --upgrade darts
pip install --ugprade sktime
pip install --upgrade tbats
pip install --upgrade orbit-ml
pip install --upgrade pydlm
pip install --upgrade divinity
pip install --upgrade pmdarima
pip install --upgrade prophet
pip install --upgrade neuralprophet
pip install --upgrade greykite
pip install --upgrade orbit-ml
pip install --upgrade git+

Then add matplotlib if you want to use plotting utilities provides

pip install matplotlib 

And add microprediction if you want to use live data (e.g. for training)

pip install --upgrade microprediction   

My policy at the moment is that online, incremental libraries get installed automatically (e.g. river) and so does statsmodels because so many other packages depend on it. However other batch-style packages need more statistical justification. See my review of prophet for example, which is slow and probably only suited to rare situations where the generative model is a very close match.

Nuts and bolts. The apple m1 install situation is fluid. I'd suggest you first get numpy, cython, pandas to work. You might try adding the pip argument to skip pep517 if you run into trouble:

pip install whatever --no-use-pep517

TCN surrogates.

To train and use surrogate models build with keras-tcn and live data

pip install --upgrade keras-tcn
pip install --upgrade tf2onnx
pip install --upgrade onnxruntime
pip install --upgrade microprediction

Honestly this isn't quite ready for prime time.

Quick start

My hope is that the utilities also serve as demonstrations of how to use any given skater in this library. If f is a skater then you call it repeatedly:

from timemachines.skaters.simple.thinking import thinking_slow_and_fast 
import numpy as np
y = np.cumsum(np.random.randn(1000))
s = {}
x = list()
for yi in y:
    xi, x_std, s = thinking_slow_and_fast(y=yi, s=s, k=3)

This will accumulate 3-step ahead prediction vectors. Or to plot actual data:

from timemachines.skaters.simple.thinking import thinking_slow_and_slow
from timemachines.skatertools.visualization.priorplot import prior_plot
from import hospital
import matplotlib.pyplot as plt
y = hospital(n=200)

There's more in examples/basic_usage.

The Skater signature

Okay, here's a little more about "skater" functions. I'm repeating myself somewhat but the good thing is, this is the only thing you need to know. Morally this package is a mere collection of skater functions and they all operate like this:

  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)

Evidently, 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. The convention is that the caller passes the skater an empty dict on the first invocation, or to reset it. Thus the callee must initialize state if it receives an empty dictionary. It should return to the caller anything it will need for the next invocation. Skaters are pure in that sense.

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. You can also use the "a" argument for conditional prediction. This is a nice advantage of keeping skaters pure - though the caller might need to make a copy of the prior state if she intends to reuse it.

Skater "t" argument

Epoch time of the observation.

Skater "e" argument ("expiry")

Suggests a number of seconds allowed for computation, though skater's don't necessarily comply. See remarks 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 

For many skaters the x_std is, as is suggested, indicative of one standard deivation.

 x, x_std, x = f( .... )   # skater
 x_up = [ xi+xstdi for xi,xstdi in zip(x,xstd) ]
 x_dn = [ xi-xstdi for xi,xstdi in zip(x,xstd) ]

then very roughly the k'th next value should, with 5 out of 6 times, below the k'th entry in x_up There isn't any capability to indicate three numbers (e.g. for asymmetric conf intervals around the mean).

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.

More on the e argument ...

The use of e is a fairly weak convention. 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 negative e suggests that there isn't even time for a "proper" prediction to be made, never mind a model fit. It suggests that we are still in a burn-in period where the caller doesn't care too much, if at all, about the quality of prediction. The callee (i.e. the skater) should, however, process this observation somehow because this is the only way it can receive history. There won't be another chance. Thus some skaters will use e<0 as a hint to dump the obervation into a buffer so it can be used in the next model fit. They return a naive forecast, confident that this won't matter.

Some skaters are so fast that a separate notion of 'fit' versus 'update' is irrelevant. Other skaters will periodically fit whether or not e>0 is passed.

The "e" conventions are useful for testing and assessment. You'll notice that the Elo rating code passes a sequence of e's something looking like:

 -1, -1, -1, ... -1 1000 1000 1000 1000 1000 ...

because it wants to allow the skaters to receive some history before they are evaluated. On the other hand, waiting for Facebook prophet to fit itself 500 times is a bit like waiting for the second coming of Christ.

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

Tuning hyper-params

It's also dead easy (though possibly time-consuming) to hyper-optimize skaters offline. By convention they only admit a single hyper-parameter, if any. This means you can, with one line of code use HumpDay to call down to scipy.optimize, ax-platform, hyperopt, optuna, platypus, pymoo, pySOT, skopt, dlib, nlopt, bayesian-optimization, nevergrad or your favourite black-box optimizer.


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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