ARIMA Models

AutoRegressive Integrated Moving Average - models dependencies between observations.

Model	Description
ARIMA	Classic ARIMA with manual parameter specification
AutoARIMA	Automatic ARIMA with (p,d,q) selection

Showing 2 of 2

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ARIMA

Classic ARIMA model with manual parameter specification.

Parameters

Parameter	Type	Required	Description
p	INTEGER	Yes	AR (autoregressive) order
d	INTEGER	Yes	Differencing order
q	INTEGER	Yes	MA (moving average) order
seasonal_period	INTEGER	No	For seasonal ARIMA
P	INTEGER	No	Seasonal AR order
D	INTEGER	No	Seasonal differencing
Q	INTEGER	No	Seasonal MA order

Example

-- Non-seasonal ARIMA(1,1,1)
SELECT * FROM anofox_fcst_ts_forecast(
    'sales_data',
    'date',
    'sales',
    'ARIMA',
    28,
    MAP{'p': '1', 'd': '1', 'q': '1'}
);

-- Seasonal ARIMA(1,1,1)(1,1,1)[7]
SELECT * FROM anofox_fcst_ts_forecast(
    'weekly_data',
    'date',
    'value',
    'ARIMA',
    28,
    MAP{'p': '1', 'd': '1', 'q': '1', 'P': '1', 'D': '1', 'Q': '1', 'seasonal_period': '7'}
);

Best for: Complex patterns when you know the appropriate order.

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AutoARIMA

Automatic ARIMA with (p,d,q) parameter selection using information criteria.

Parameters

Parameter	Type	Default	Description
seasonal_period	INTEGER	auto	Seasonal period
max_p	INTEGER	5	Maximum AR order
max_d	INTEGER	2	Maximum differencing order
max_q	INTEGER	5	Maximum MA order

Example

SELECT * FROM anofox_fcst_ts_forecast(
    'sales_data',
    'date',
    'sales',
    'AutoARIMA',
    28,
    MAP{'seasonal_period': '7'}
);

Best for: Complex patterns, long-term forecasts, automatic tuning.

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Parameter Selection Guide

Scenario	p	d	q
Stationary data	1-2	0	1-2
Trending data	1-2	1	1-2
Strong trend	1-2	2	1-2
Random walk	0	1	0

When to Use ARIMA vs AutoARIMA

Scenario	Recommended
Known order from domain expertise	ARIMA
Exploratory analysis	AutoARIMA
Production pipeline	AutoARIMA
Performance-critical	ARIMA (faster)
Many time series	AutoARIMA