mojolearn.AutoARIMA#

class mojolearn.AutoARIMA(endog)[source]#

Bases: object

Automatic ARIMA order selection for a batch of series.

Chooses, per series, the differencing order d by the KPSS test and then the (p, q, P, Q) orders and intercept with the least information criterion, following cuML’s AutoARIMA.search; fit() then fits each chosen model with ARIMA. Every candidate order is fitted on all the series that share a d as one batch; on a tie the first order tried wins.

endog is laid out one series per row, (batch_size, n_obs); cuML’s AutoARIMA takes series in columns, so transpose to call it the same way. Fitting is maximum likelihood only.

Parameters:

endog (array-like of shape (batch_size, n_obs) or (n_obs,)) – The series, float32. float64 raises TypeError.

Variables:

  • d_ (ndarray of shape (batch_size,), int64) – Differencing order chosen for each series. Set by search().

  • order_ (ndarray of shape (batch_size, 8), int64) – Chosen (p, d, q, P, D, Q, s, k) per series, k 1 with an intercept. Set by search().

  • ic_ (ndarray of shape (batch_size,), float64) – Information criterion of the chosen order. Set by search().

  • models (list) – Distinct chosen models as ((p, d, q), (P, D, Q, s), k).

Examples

>>> import numpy as np, mojolearn
>>> y = np.random.default_rng(0).standard_normal((8, 120)).cumsum(axis=1).astype(np.float32)
>>> model = mojolearn.AutoARIMA(y).search(d=range(2), p=range(3), q=range(3)).fit()
>>> model.forecast(10).shape
(8, 10)
__init__(endog)[source]#

Methods

fit([h, maxiter, method, truncate])

Fit the chosen model of every series.

forecast(nsteps[, level])

Forecast nsteps past the end of every series.

predict([start, end, level])

In-sample (and out-of-sample) predictions from start to end.

search([s, d, D, p, q, P, Q, fit_intercept, ...])

Select the orders for every series.
search(s=None, d=range(0, 3), D=range(0, 2), p=range(1, 4), q=range(1, 4), P=range(0, 3), Q=range(0, 3), fit_intercept='auto', ic='aicc', test='kpss', seasonal_test='seas', h=1e-08, maxiter=20, method='auto', truncate=0)[source]#

Select the orders for every series.

Parameters:

  • s (int or None, default None) – Seasonal period. None, 0 or 1 means non-seasonal (then D, P and Q are 0).

  • d (int or iterable of int, default range(3)) – Differencing options; a list must be 0, 1, ..., d_max. With one value it is used for every series; otherwise the KPSS test picks d per series.

  • D (int or iterable of int, default range(2)) – Seasonal differencing; with s set, give one value (the seasonal test over several values is not supported).

  • p, q (int or iterable of int, default range(1, 4)) – Non-seasonal AR and MA order options, clipped to [0, 4] (or [0, s - 1] when seasonal).

  • P, Q (int or iterable of int, default range(3)) – Seasonal AR and MA order options, clipped to [0, 4] (0 when non-seasonal).

  • fit_intercept (bool or “auto”, default “auto”) – Whether candidates include an intercept.

  • ic ({“aic”, “aicc”, “bic”}, default “aicc”) – Information criterion.

  • test ({“kpss”}, default “kpss”) – Stationarity test for d.

  • seasonal_test (str, default “seas”) – Only used with several D options, which are not supported.

  • h (float, default 1e-8) – Only the default is supported.

  • maxiter (int, default 20) – Optimizer iterations per candidate fit.

  • method ({“auto”, “ml”}, default “auto”) – Fitting method; maximum likelihood. "css" and "css-ml" raise NotImplementedError.

  • truncate (int, default 0) – Only 0 is supported.

Returns:

self

Raises:

  • ValueError – For an unknown ic or test, or an order option with no valid value.

  • NotImplementedError – For css methods, a non-default h or truncate, several D options with a season, or a d list that is not 0..d_max.

fit(h=1e-08, maxiter=1000, method='ml', truncate=0)[source]#

Fit the chosen model of every series.

Call search() first.

Parameters:

  • h (float, default 1e-8) – Only the default is supported.

  • maxiter (int, default 1000) – Optimizer iterations.

  • method ({“ml”}, default “ml”) – Maximum likelihood only.

  • truncate (int, default 0) – Only 0 is supported.

Returns:

self

Raises:

RuntimeError – If search() has not been called.

predict(start=0, end=None, level=None)[source]#

In-sample (and out-of-sample) predictions from start to end.

Parameters:

  • start (int, default 0) – First index to predict.

  • end (int or None, default None) – One past the last index; None means n_obs.

  • level (None) – Prediction intervals are not supported; anything other than None raises NotImplementedError.

Returns:

ndarray of shape (batch_size, end - start), float32

forecast(nsteps, level=None)[source]#

Forecast nsteps past the end of every series.

Parameters:

  • nsteps (int) – Forecast horizon.

  • level (None) – Prediction intervals are not supported; anything other than None raises NotImplementedError.

Returns:

ndarray of shape (batch_size, nsteps), float32