State machines for time-series. (Use popular packages with one line of code)

What's different:

  • Simple canoncial use of some functionality from packages like fbprophet, pmdarima, tsa and their ilk.

  • Simple k-step ahead forecasts in functional style involving one line of code.
    Time series "models" are synomymous with functions that 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.

  • 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.

  • Simple, ongoing empirical evaluation. See the leaderboards in
    the accompanying repository timemachines-testing listing Elo ratings
    for skaters with no unassigned hyper-parameters. Assessment is always out of sample and uses live, constantly updating real-world data
    from microprediction.org.

  • 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!

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 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. 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")

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
no separate notion of 'fit' versus 'update' because everything is incremental.

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

A scalar in the closed interval [0,1] represents all hyper-parameters. This step 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.

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).

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.



pip install timemachines
pip install microprediction   (if you want to use live data)

Running a model and plotting it

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

# Get some data
k = 1
y, a = hospital_with_exog(k=k, n=450, offset=True)

# Run the model and plot it 
err2 = prior_plot(f=fbprophet_exogenous, k=k, y=y, n=450, n_plot=50)


Tuning hyper-params