Superclasses:
Create ARIMA or ARIMAX time series model
arima
creates model objects for stationary or unit
root nonstationary linear time series model. This includes
moving average (MA), autoregressive (AR), mixed autoregressive and moving average (ARMA),
integrated (ARIMA), multiplicative seasonal, and linear time series models that include a
regression component (ARIMAX).
Specify models with known coefficients, estimate coefficients with data using
estimate
, or simulate models with simulate
. By default, the
variance of the innovations is a positive scalar, but you can specify any supported conditional
variance model, such as a GARCH model.
creates an ARIMA model of degrees
zero.Mdl
= arima
creates a nonseasonal linear time series model using autoregressive degree Mdl
=
arima(p
,D
,q
)p
,
differencing degree D
, and moving average degree q
.
Mdl = arima(
creates a linear time
series model using additional options specified by one or more Name,Value
)Name,Value
pair arguments. Name
is the property name and Value
is the
corresponding value. Name
must appear inside single quotes
(''
). You can specify several namevalue pair arguments in any order as
Name1,Value1,...,NameN,ValueN
.
You can only use these arguments for nonseasonal models. For seasonal models, use the namevalue syntax.

Positive integer indicating the degree of the nonseasonal autoregressive polynomial. 

Nonnegative integer indicating the degree of nonseasonal integration in the linear time series. 

Positive integer indicating the degree of the nonseasonal moving average polynomial. 
Specify optional
commaseparated pairs of Name,Value
arguments. Name
is
the argument name and Value
is the corresponding value.
Name
must appear inside quotes. You can specify several name and value
pair arguments in any order as
Name1,Value1,...,NameN,ValueN
.

Cell vector of nonseasonal autoregressive coefficients corresponding to a stable
polynomial. When specified without Default: Cell vector of 

Vector of positive integer lags associated with the Default: Vector of integers 1,2,... to the degree of the nonseasonal autoregressive polynomial. 

Real vector of coefficients corresponding to the regression component in an ARIMAX conditional mean model. Default: 

Scalar constant in the linear time series. Default: 

Nonnegative integer indicating the degree of the nonseasonal differencing lag operator polynomial (the degree of nonseasonal integration) in the linear time series. Default: 

Conditional probability distribution of the innovation process.
Default: 

Cell vector of nonseasonal moving average coefficients corresponding to an invertible
polynomial. When specified without Default: Cell vector of 

Vector of positive integer lags associated with the Default: Vector of integers 1,2,... to the degree of the nonseasonal moving average polynomial. 

Cell vector of seasonal autoregressive coefficients corresponding to a stable
polynomial. When specified without Default: Cell vector of 

Vector of positive integer lags associated with the Default: Vector of integers 1,2,... to the degree of the seasonal autoregressive polynomial. 

Cell vector of seasonal moving average coefficients corresponding to an invertible
polynomial. When specified without Default: Cell vector of 

Vector of positive integer lags associated with the Default: Vector of integers 1,2,... to the degree of the seasonal moving average polynomial. 

Nonnegative integer indicating the degree of the seasonal differencing lag operator polynomial in the linear time series model. Default: 

Positive scalar variance of the model innovations, or a supported conditional variance
model object (e.g., a Default: 

String scalar or character vector describing the model. By default, this argument
describes the parametric form of the model, for example, 
Each AR
, SAR
, MA
,
and SMA
coefficient is associated with an underlying
lag operator polynomial and is subject to a nearzero tolerance exclusion
test. That is, the software compares each coefficient to the default
lag operator zero tolerance, 1e12
. If the magnitude
of a coefficient is greater than 1e12
, then the
software includes it in the model. Otherwise, the software considers
the coefficient sufficiently close to 0, and excludes it from the
model. For additional details, see LagOp
.
Specify the lags associated with the seasonal polynomials SAR
and SMA
in
the periodicity of the observed data, and not as multiples of the Seasonality
parameter.
This convention does not conform to standard Box and Jenkins [1] notation, but it is a more flexible
approach for incorporating multiplicative seasonality.

Cell vector of nonseasonal autoregressive coefficients corresponding to a stable
polynomial. Associated lags are 1,2,... to the degree of the nonseasonal autoregressive
polynomial, or as specified in 

Real vector of regression coefficients corresponding to a regression component. 

Scalar constant in the linear time series model. 

Nonnegative integer indicating the degree of nonseasonal integration in the linear time series. 
 String scalar for the model description. 

Data structure for the conditional probability distribution of the innovation process.
The field 

Cell vector of nonseasonal moving average coefficients corresponding to an invertible
polynomial. Associated lags are 1,2,... to the degree of the nonseasonal moving average
polynomial, or as specified in 

Degree of the compound autoregressive polynomial.
The property 

Degree of the compound moving average polynomial. The property 

Cell vector of seasonal autoregressive coefficients corresponding to a stable polynomial.
Associated lags are 1,2,... to the degree of the seasonal autoregressive polynomial, or as
specified in 

Cell vector of seasonal moving average coefficients corresponding to an invertible
polynomial. Associated lags are 1,2,... to the degree of the seasonal moving average
polynomial, or as specified in 

Nonnegative integer indicating the seasonal differencing polynomial degree in the linear time series model. 

Positive scalar variance of the model innovations, or a supported conditional variance
model (e.g., a 
estimate  Estimate ARIMA or ARIMAX model parameters 
filter  Filter disturbances using ARIMA or ARIMAX model 
forecast  Forecast ARIMA or ARIMAX model responses or conditional variances 
impulse  Impulse response function 
infer  Infer ARIMA or ARIMAX model residuals or conditional variances 
(To be removed) Display parameter estimation results for ARIMA or ARIMAX models  
simulate  Monte Carlo simulation of ARIMA or ARIMAX models 
summarize  Display ARIMA model estimation results 
Value. To learn how value classes affect copy operations, see Copying Objects (MATLAB).