SAP HANA Predictive Analysis Library (PAL)

Prerequisite
No missing or null data in the inputs.
ARIMATRAIN
This function generates ARIMA or ARIMAX training model.
ARIMA Model
An ARIMA model is a universalization of an auto regressive moving average (ARMA) model. The integrated
part is mainly applied to induce stationary when data show evidence of non-stationary.
An ARIMA (p, d, q) model can be expressed as:
Φ(B)(1−B) d (Y t −c)=Θ(B)ε t , t∈Z
An ARMA (p, q) model can be expressed as:
Φ(B)(Y t −c)=Θ(B)ε t , t∈Z
ε t ~i.i.d.N(0,σ 2 )
Where B is lag operator (backward shift operator), c is the mean of the series data,
Φ(B)=1−φ 1 B−φ 2 B 2 −…−φ p B p , p ≥ 0
Θ(B)=1+θ 1 B+θ 2 B 2 +…+ θ q B q , q ≥ 0
ARIMAX Model
An ARIMAX model is a universalization of an ARMAX model. The integrated part is mainly applied to induce
stationary when data show evidence of non-stationary.
An ARIMAX (p, d, q) model can be expressed as:
Φ(B)(1−B) d (Y t −c)=H T (1−B) d X t +Θ(B)ε t , t∈Z
An ARMAX (p, q) model can be expressed as:
Φ(B)Y t =H T X t +Θ(B)ε t , t∈Z
ε t ~i.i.d.N(0,σ 2 )
Where B is lag operator (backward shift operator), X t is a covariate vector at time t, and H is its coefficient
vector.
In PAL, the ARIMATRAIN algorithm first converts the original non-stationary time series data to a new
stationary time series data by the integrated step, and then ARIMA fits the stationary time series data to an
ARMA model, and ARIMAX fits the stationary time series data to an ARMAX model.
PAL provides two parameter estimation methods: conditional sum of squares (CSS or conditional maximum
likelihood estimation) and maximum likelihood estimation (MLE).
SARIMA Model
SAP HANA Predictive Analysis Library (PAL)
PAL Functions P U B L I C 321