BATS / TBATS¶

BATS (Box-Cox, ARMA errors, Trend, Seasonality) and TBATS (Trigonometric BATS) handle complex seasonal patterns, including multiple seasonal periods.

BATS¶

from durbyn import BATS

# Single seasonal period
model = BATS().fit(y, m=12)
fc = model.forecast(h=12, level=[80, 95])

# Multiple seasonal periods (pass a list as m)
model = BATS().fit(y, m=[24, 168])  # daily + weekly
fc = model.forecast(h=24)

# With specific components
model = BATS(
    use_box_cox=True,
    use_trend=True,
    use_damped_trend=True,
    use_arma_errors=True,
).fit(y, m=12)

Parameters¶

Parameter	Type	Default	Description
`use_box_cox`	`bool \\| None`	`None`	Use Box-Cox transform. `None` for auto
`use_trend`	`bool \\| None`	`None`	Include trend. `None` for auto
`use_damped_trend`	`bool \\| None`	`None`	Damp the trend. `None` for auto
`use_arma_errors`	`bool`	`True`	Model errors as ARMA process
`bc_lower`	`float`	`0.0`	Box-Cox lower bound
`bc_upper`	`float`	`1.0`	Box-Cox upper bound
`biasadj`	`bool`	`False`	Bias adjustment

TBATS¶

Extends BATS with trigonometric representation for seasonal components, enabling non-integer seasonal periods.

from durbyn import TBATS

# Non-integer seasonal periods
model = TBATS().fit(y, m=[12.5, 52.18])
fc = model.forecast(h=12, level=[80, 95])

# Standard usage
model = TBATS(
    use_box_cox=True,
    use_damped_trend=True,
).fit(y, m=12)
fc = model.forecast(h=24)

Parameters¶

Same as BATS:

Parameter	Type	Default	Description
`use_box_cox`	`bool \\| None`	`None`	Use Box-Cox transform. `None` for auto
`use_trend`	`bool \\| None`	`None`	Include trend. `None` for auto
`use_damped_trend`	`bool \\| None`	`None`	Damp the trend. `None` for auto
`use_arma_errors`	`bool`	`True`	Model errors as ARMA process
`bc_lower`	`float`	`0.0`	Box-Cox lower bound
`bc_upper`	`float`	`1.0`	Box-Cox upper bound
`biasadj`	`bool`	`False`	Bias adjustment

When to Use BATS vs TBATS¶

Feature	BATS	TBATS
Integer seasonal periods	Yes	Yes
Non-integer seasonal periods	No	Yes
Multiple seasonal periods	Yes	Yes
Speed	Faster	Slower
Very long seasonal periods	Limited	Better

Tip

Use BATS when you have integer seasonal periods (e.g., monthly data with m=12). Use TBATS when you have non-integer or very long seasonal periods (e.g., hourly data with m=[24, 168.25]).