ARIMA¶

durbyn provides manual ARIMA/SARIMA specification and automatic model selection via AutoARIMA.

ARIMA — Manual Specification¶

from durbyn import ARIMA

# Non-seasonal ARIMA(1,1,1)
model = ARIMA(order=(1, 1, 1)).fit(y, m=1)
fc = model.forecast(h=12, level=[80, 95])

# Seasonal ARIMA(2,1,1)(0,1,0)
model = ARIMA(
    order=(2, 1, 1),
    seasonal_order=(0, 1, 0),
).fit(y, m=12)
fc = model.forecast(h=12)

Parameters¶

Parameter	Type	Default	Description
`order`	`tuple[int, int, int]`	`(0, 0, 0)`	Non-seasonal `(p, d, q)` orders
`seasonal_order`	`tuple[int, int, int] \\| None`	`None`	Seasonal `(P, D, Q)` orders
`include_mean`	`bool`	`True`	Include mean/intercept term
`method`	`str`	`"CSS-ML"`	Estimation method: `"CSS-ML"`, `"ML"`, `"CSS"`
`transform_pars`	`bool`	`True`	Transform parameters for stationarity
`lambda_`	`float \\| bool \\| None`	`None`	Box-Cox parameter
`biasadj`	`bool \\| None`	`None`	Bias adjustment for Box-Cox

With External Regressors¶

ARIMA supports external regressors (xreg) via the X parameter at fit time:

import numpy as np
from durbyn import ARIMA

# Training data with regressors
y = np.random.randn(100)
X = np.random.randn(100, 2)  # 2 regressors

model = ARIMA(order=(1, 1, 0)).fit(y, m=12, X=X)

# Future regressors must be provided (not yet wired through forecast)
fc = model.forecast(h=12)

AutoARIMA — Automatic Selection¶

Searches over ARIMA model space using information criteria.

from durbyn import AutoARIMA

# Default: stepwise search with AICc
model = AutoARIMA().fit(y, m=12)
fc = model.forecast(h=12, level=[80, 95])

# With constraints
model = AutoARIMA(
    max_p=3,
    max_q=3,
    d=1,          # fix differencing order
    D=1,          # fix seasonal differencing
    seasonal=True,
    stepwise=True,
    ic="bic",
).fit(y, m=12)

Parameters¶

Parameter	Type	Default	Description
`d`	`int \\| None`	`None`	Differencing order. `None` for auto
`D`	`int \\| None`	`None`	Seasonal differencing. `None` for auto
`max_p`	`int`	`5`	Maximum AR order
`max_q`	`int`	`5`	Maximum MA order
`max_P`	`int`	`2`	Maximum seasonal AR order
`max_Q`	`int`	`2`	Maximum seasonal MA order
`max_order`	`int`	`5`	Maximum total p + q + P + Q
`max_d`	`int`	`2`	Maximum differencing order
`max_D`	`int`	`1`	Maximum seasonal differencing
`stationary`	`bool`	`False`	Restrict to stationary models
`seasonal`	`bool`	`True`	Include seasonal terms
`stepwise`	`bool`	`True`	Use stepwise search (faster)
`trace`	`bool`	`False`	Print search progress
`approximation`	`bool`	`True`	Use CSS approximation during search
`ic`	`str`	`"aicc"`	Information criterion: `"aicc"`, `"aic"`, `"bic"`
`test`	`str`	`"adf"`	Unit root test: `"adf"`, `"kpss"`, `"pp"`
`seasonal_test`	`str`	`"ocsb"`	Seasonal unit root test
`allowmean`	`bool`	`True`	Allow mean/intercept
`allowdrift`	`bool`	`True`	Allow drift term
`lambda_`	`float \\| bool \\| None`	`None`	Box-Cox parameter
`biasadj`	`bool \\| None`	`None`	Bias adjustment

Example: Full Workflow¶

from durbyn import AutoARIMA

y = [112, 118, 132, 129, 121, 135, 148, 148, 136, 119, 104, 118,
     115, 126, 141, 135, 125, 149, 170, 170, 158, 133, 114, 140,
     145, 150, 178, 163, 172, 178, 199, 199, 184, 162, 146, 166]

model = AutoARIMA(ic="aicc").fit(y, m=12)

# Inspect the model
print(model.summary)
print(f"Residuals std: {model.residuals.std():.2f}")

# Forecast
fc = model.forecast(h=12, level=[80, 95])
df = fc.to_dataframe()
print(df)