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Evaluation and standardization of popular time series packages

Project description

timemachines simplepycarettsa successor darts greykite sktime tbats simdkalman prophet orbit neuralprophet pmd pydlm merlion river divinitypycaret License: MIT

Autonomous, univariate, k-step ahead time-series forecasting functions assigned Elo ratings

You can:

  1. Use some of the functionality of a subset of the popular python time-series packages with one line of code.
  2. Find faster, lighter, lesser-known alternatives like thinking_fast_and_slow that might be as accurate for your purpose.
  3. Use various combinations (composition, stacking et cetera) or make your own.
  4. Peruse Elo ratings or use them programatically.
  5. Adopt the use of forever functions that get better over time without your doing anything.
  6. Join our slack and ask questions (try the knowledge center if that invite has expired or asks you for an email).

There's also a recommendation colab notebook you can open and run. This project is intended to help you select packages, strategies and even hyper-params. But it does not replace the packages themselves. Possibly one of the best uses is applying these skater functions to the residuals of your existing models.


See Also FAQ and slack invite


The cautious person proceeds...

pip install --upgrade pip
pip install --upgrade numpy
pip install --upgrade timemachines
pip install --upgrade scikit-learn 
pip install --upgrade scipy 

(You can scrape by without the last two as they are only used for metrics)

On colab you might need to do this if it still has an old numpy:

!pip uninstall numpy
!pip install --upgrade numpy 

Next (optional)...

pip install --upgrade statsmodels

(Many packages wrap statsmodels.tsa)

Next (optional)...

pip install tensorflow

You may get better performance by first installing tensorflow following the instructions and perhaps reading this thread.

Next (optional)... some subset of the following:

pip install --upgrade darts
pip install --upgrade river 
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 successor
pip install --upgrade neuralprophet
pip install --upgrade greykite
pip install --upgrade git+
pip install --upgrade salesforce-merlion
pip install --upgrade pycaret-ts-alpha

You may wish to first check the Elo ratings to get a vague idea of accuracy and speed, and which packages you wish to install. On some hardware you may need to resort to conda-forge for some packages if you run into trouble, for example

conda install -c conda-forge lightgbm


pip install matplotlib 

Optional: (e.g. for training, testing etc)

pip install --upgrade microprediction   

On some systems pystan is flaky, thus also prophet, thus also things wrapping prophet. You'll need an older pystan (unless things have changed). Maybe read my review of prophet before spending too much install agony there. The apple silicon (m1) install situation is particularly fluid. I revert to anaconda miniforge as noted above. But see also this thread and keep open the possibility of the --no-use-pep517 option.

pip install whatever --no-use-pep517


The package is setup for pytest and we rely pretty heavily on Github actions. You may wish to use act to run the Github actions locally.

Quick start

This package is just a collection of skaters. My hope is that the utilities also serve as demonstrations of how to use any given "skater". The intent is that you call them repeatedly to process one data point at a time.

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.

Skating advantages

There are important limitations to this package ... but also some alleged strengths:

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

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

    These functions are called skaters. Now this is Python and s is mutable, but philosophically this is a pure function.

  • 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 often 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.

NO CLASSES. NO DATAFRAMES. NO CEREMONY. NO HEAVY DEPENDENCIES. There's not much to slow you down here.

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.

The Skater signature

So, here's a tiny bit more detail about the signature adopted by all skaters in this package.

  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) 

As noted, 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

Notice the use of s={} on first invocation. Also as noted above, there are prominently positioned utilities for processing full histories - though there isn't much beyond what you see above.

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 for pre-skaters only)

A real skater doesn't have any hyper-parameters. It's the job of the designer to make it fully autonomous. The small concession made here is the notion of a pre-skater: one with a single float hyperparameter in the closed interval [0,1]. Pre-skaters squish all tunable parameters into this interval. That's a bit tricky, so some rudimentary conventions and space-filling functions are provided. See tuning.

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 pre-skaters



        title = {{Timemachines: A Python Package for Creating and Assessing Autonomous Time-Series Prediction Algorithms}},
        year = {2021},
        author = {Peter Cotton},
        url = {}

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