ARIMAX Statement

ARIMAX <options> ;

An ARIMAX statement can be used to find an appropriate ARIMAX specification.

The HPFDIAGNOSE procedure performs the intermittency test first. If the series is intermittent, an intermittent demand model is fitted to the data and the ARIMAX statement is not applicable. If the series is not intermittent, an ARIMAX model is fitted to the data.

If a model statement is not specified, the HPFDIAGNOSE procedure diagnoses ARIMAX and exponential smoothing models if the series is not intermittent, but diagnoses an intermittent demand model if the series is intermittent.

The following options can be used in the ARIMAX statement.

PERROR=(number : number)

specifies the range of the AR order for obtaining the error series used in the MINIC method. The default is (maxp:maxp+maxq).

P=(number : number) (number : number)

specifies the range of the nonseasonal and seasonal AR orders. The default is (0:5)(0:2).

Q=(number : number) (number : number)

specifies the range of the nonseasonal and seasonal MA orders. The default is (0:5)(0:2).

DEN=(number : number)

specifies the range of the denominator order of the transfer function. The default is (0:2).

NUM=(number : number)

specifies the range of the numerator order of the transfer function. The default is (0:2).

CRITERION=AIC | SBC

specifies the criterion for the tentative ARMA order selection. The default is CRITERION=SBC.

SIGLEVEL=value

specifies the significance level to use as a cutoff value to decide the AR and MA orders. The SIGLEVEL=value should be in (0,1). The SIGLEVEL= option overrides the value of SIGLEVEL= option in the HPFDIAGNOSE statement.

ESTMETHOD=CLS | ULS | ML

specifies the method for choosing the tentative ARMA orders (Choi 1992; Tsay and Tiao 1984).

CLS

conditional least squares method. This option is the default.

ULS

unconditional least squares method

ML

maximum likelihood method

METHOD=ESACF | MINIC | SCAN

specifies the method for choosing the tentative ARMA orders (Choi 1992; Tsay and Tiao 1984).

ESACF

extended sample autocorrelation function

MINIC

minimum information criterion. This option is the default.

SCAN

smallest canonical correlation analysis

OUTLIER=(options)

specifies outlier detection in an ARIMAX model (de Jong and Penzer 1998).

DETECT=YES

includes outliers detected in a model if the model that includes the outliers is successfully diagnosed.

DETECT=MAYBE

includes outliers detected in a model if the model that includes the outliers is successfully diagnosed and has a smaller criterion than the model without outliers. This option is the default.

DETECT=NO

no outlier detection is performed.

FILTER=FULL | SUBSET

chooses a model for outlier detection. If FILTER=FULL, then use a full model. If FILTER=SUBSET, then use a subset model that includes nonseasonal AR and MA filters only. If the data have no seasonality, then the outlier detection is not affected by the FILTER= option. FILTER=FULL is the default.

MAXNUM=number

includes up to MAXNUM= value outliers in a model. MAXNUM=2 is the default.

MAXPCT=value

includes up to MAXPCT= value outliers in a model. MAXPCT=2 is the default. If MAXNUM=5 and MAXPCT=10, the number of the outliers is where is the length of the time series with beginning and ending missing values removed.

TYPE=option | (options)

specifies the type of outliers. If the TYPE= option is not specified, then both AO and LS types are searched for outliers. The options are as follows.

AO

specifies additive outliers.

LS

specifies level shift outliers.

TLS(value,...,value)

specifies temporary level shift outliers. The value is a duration of a temporary level shift and should be greater than or equal to 2. Examples are TYPE=TLS(2) and TYPE=TLS(3,9,15).

SIGLEVEL=value

specifies the cutoff value for outlier detection. The SIGLEVEL=value should be in (0,1). The SIGLEVEL=0.01 is the default. The SIGLEVEL= option overrides the value of SIGLEVEL= option in the HPFDIAGNOSE statement.

ENTRYPCT=number

specifies a threshold to check the percentage increment of the criterion between two candidate models. The ENTRYPCT=value should be in (0,100); the default is ENTRYPCT=0.1. The ENTRYPCT= option overrides the value of the ENTRYPCT= option in the HPFDIAGNOSE statement.

If the OUTLIER= option is not specified, the HPFDIAGNOSE performs the outlier detection with the OUTLIER=(DETECT=MAYBE MAXNUM=2 MAXPCT=2 SIGLEVEL=0.01) option as default.

If the PREFILTER=EXTREME option is specified in the PROC HPFDIAGNOSE statement and extreme values are found, then these values are potential outliers. With the PREFILTER=EXTREME option, outliers might be detected even if the DETECT=NO option is specified and more than number of outliers can be detected even if the MAXNUM= option is specified.

IDENTIFYORDER=ARIMA | REG | BOTH

IDENTIFY=ARIMA | REG | BOTH

specifies the identification order when inputs and events are specified.

ARIMA

finds an ARIMA model for the error series first and then chooses significant inputs and events. This option is the default.

REG

finds a regression model first and then decides the AR and MA polynomial orders.

BOTH

fits models by using the two methods and determines the better model.

REFINEPARMS=( options )

specifies to refine insignificant parameters of the final model, identify the factors to refine, and identify the order of factors.

SIGLEVEL=

specifies the cutoff value for all refining insignificant parameters. The SIGLEVEL=value should be between (0,1); SIGLEVEL=0.4 is the default.

FACTOR=ALL

refines the parameters for all factors. This option is the default.

FACTOR=ARMA

refines the parameters for ARMA factor.

FACTOR=EVENT

refines the parameters for EVENT factor.

FACTOR=INPUT

refines the parameters for INPUT factor.

Using parentheses, more than one option can be specified. For example, the option FACTOR=( ARMA EVENT ) refines the parameters for ARMA and EVENT.

The FIRST and SECOND options take one of the factors ARMA, EVENT, and INPUT.

FIRST=

specifies the factor which refines first.

SECOND=

specifies the factor which refines second.

The default order of refining is ARMA, EVENT, INPUT.

NOINT

NOCONSTANT

suppresses the intercept (constant) term.