Time series#

The time-series models forecast future values of a series from its past, or split a series into trend and seasonal parts. Most of them fit a whole batch of series at once: pass a 2-D array with one series per row, and each series gets its own parameters.

Use	Estimators
ARIMA and seasonal ARIMA	`ARIMA`, `AutoARIMA`
Exponential smoothing	`ETS`, `ExponentialSmoothing`, `DampedETS`
Theta methods	`Theta`, `AutoTheta`, `OptimizedTheta`, `DynamicTheta`, `DynamicOptimizedTheta`
Intermittent demand	`CrostonClassic`, `CrostonOptimized`, `CrostonSBA`
Several series that move together	`VAR`
Volatility	`GARCH`
Trend and season decomposition	`STL`
Trend, seasonality and holidays	`ProphetForecaster`

ARIMA#

The data goes to fit, not to the constructor. forecast(steps) returns one row of forecasts per series.

import numpy as np
import mojolearn

y = np.random.default_rng(0).standard_normal((16, 200)).cumsum(axis=1).astype(np.float32)

model = mojolearn.ARIMA(order=(1, 1, 1)).fit(y)
print(model.forecast(10).shape)       # (16, 10)

AutoARIMA searches over orders for each series and picks the best by an information criterion:

auto = mojolearn.AutoARIMA(y).search(d=range(2), p=range(3), q=range(3)).fit()
print(auto.forecast(10).shape)

Exponential smoothing and theta#

ETS, Theta and their relatives fit on fit(y) and forecast h steps with predict(h), which returns a dictionary with the forecasts under "mean".

t = np.arange(120, dtype=np.float32)
series = 50 + 0.2 * t + 5 * np.sin(2 * np.pi * t / 12).astype(np.float32)

ets = mojolearn.ETS(season_length=12, model="AAA", damped=False).fit(series)
print(ets.predict(12)["mean"].shape)  # (12,)

theta = mojolearn.Theta(season_length=12).fit(series)
print(theta.predict(12)["mean"])

Decomposition#

parts = mojolearn.STL(series, period=12).fit()
trend, seasonal, resid = parts.trend, parts.seasonal, parts.resid

Saving a model#

ARIMA and ExponentialSmoothing save to a file and load back:

model.save("arima.npz")
loaded = mojolearn.ARIMA.load("arima.npz")

Devices and numeric modes#

In identical mode, mojolearn returns the same bits on Apple, NVIDIA and AMD GPUs. identical is the default. On Apple GPUs you can choose fast instead, which is tuned for speed and does not promise identical bits: call mojolearn.set_numeric_mode() with "fast". See Numeric modes.