Evaluation and standardization of popular time series packages
Project description
timemachines
Fast, incremental, timeseries prediction
Use popular forecasting packages with one line of code. Or just browse their Elo ratings to help decide which to try out first.
What's different:

Simple kstep 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.

Simple canonical use of some functionality from packages like river, pydlm, tbats, pmdarima, statsmodels.tsa, neuralprophet, Facebook Prophet, Uber orbit 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 timeserieseloratings. Assessment is always out of sample and uses live, constantly updating realworld data from microprediction.org.

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 thinking.py for an illustration, or prophetskaterscomposed.py).

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
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:
See CONTRIBUTE.md
Install
The suggested install is:
pip install upgrade pip
pip install timemachines
Then check the Elo ratings to decide which packages you want to utilize  they aren't in by default.
pip install river
pip install tbats
pip install orbitml
pip install pydlm
pip install divinity
pip install pmdarima
pip install prophet
pip install neuralprophet
Then add matplotlib if you want to use plotting utilities provides
pip install matplotlib
And add microprediction if you want to use live data
pip install microprediction
I'm reluctant to put anything beyond statsmodels in the timemachines package requirements until there is statistical justification. See my review of prophet for example, which is seemingly both slow and innacurate (but on the other hand, river won't slow you down). By the way, 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 nousepep517
Quick start
My hope is that the skating.py 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)
x.append(xi)
This will accumulate 3step 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 timemachines.skatertools.data.real import hospital
import matplotlib.pyplot as plt
y = hospital(n=200)
prior_plot(f=thinking_slow_and_slow,y=y)
plt.show()
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, # Nonbinding maximal computation time ("e for expiry"), in seconds
r:float=None) # Hyperparameters ("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)
x.append(xi)
return x
or see the prominently positioned skating.py. 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 knowninadvance 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 hyperparameters. 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 lambdabased 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 hyperparameters) 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 hyperparameters, 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 hyperparameters 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 timeconsuming.
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 burnin 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 JSONfriendly.

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 ksteps in advance, or conditioning variables:
 Pass the vector argument a that will occur in ksteps 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.

HyperParameter 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
 See examples
Tuning hyperparams
It's also dead easy (though possibly timeconsuming) to hyperoptimize skaters offline. By convention they only admit a single hyperparameter, if any. This means you can, with one line of code use HumpDay to call down to scipy.optimize, axplatform, hyperopt, optuna, platypus, pymoo, pySOT, skopt, dlib, nlopt, bayesianoptimization, nevergrad or your favourite blackbox optimizer.
 See examples/tuning
 See tuning
Contribute
If you'd like to contribute to this standardizing and benchmarking effort, here are some ideas:
 Read the contributor guide
 See the list of popular time series packages ranked by download popularity.
 Think about the most important hyperparameters and consider "warming up" the mapping (0,1)>hyperparams by testing on real data. There is a tutorial on retrieving live data, or use the real data package, if that's simpler.
 The comparison of hyperparameter optimization packages might also be helpful.
 Read the contributor guide
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.
FAQ
See FAQ
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