Superclasses:
Create regression model with ARIMA time series errors
regARIMA
creates a regression model with ARIMA time
series errors to maintain the sensitivity interpretation of regression
coefficients.
By default, the time series errors (also called unconditional disturbances) are independent, identically distributed, mean 0 Gaussian random variables. If the errors have an autocorrelation structure, then you can specify models for them. The models include:
moving average (MA)
autoregressive (AR)
mixed autoregressive and moving average (ARMA)
integrated (ARIMA)
multiplicative seasonal (SARIMA)
Specify error models containing known coefficients to:
creates a regression model
with degree 0 ARIMA errors and no regression coefficient.Mdl
= regARIMA
creates a regression model with errors modeled by a nonseasonal, linear time series with
autoregressive degree Mdl
= regARIMA(p
,D
,q
)p
, differencing degree D
,
and moving average degree q
.
creates a regression model with ARIMA errors using additional options specified by one
or more Mdl
= regARIMA(Name,Value
)Name,Value
pair arguments. Name
can also
be a property name and Value
is the corresponding value.
Name
must appear inside single quotes (''
).
You can specify several Name,Value
pair arguments in any order as
Name1,Value1,...,NameN,ValueN
.
For regression models with nonseasonal ARIMA errors, use p
,
D
, and q
. For regression models with
seasonal ARIMA errors, use Name,Value
pair arguments.

Nonseasonal, autoregressive polynomial degree for the error model, specified as a positive integer. 

Nonseasonal integration degree for the error model, specified as a nonnegative integer. 

Nonseasonal, moving average polynomial degree for the error model, specified as a positive integer. 
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
.

Regression model intercept, specified as the commaseparated pair
consisting of Default:  

Regression model coefficients associated with the predictor data,
specified as the commaseparated pair consisting of
Default:  

Nonseasonal, autoregressive coefficients for the error model,
specified as the commaseparated pair consisting of
Default: Cell vector of  

Nonseasonal, moving average coefficients for the error model,
specified as the commaseparated pair consisting of
Default: Cell vector of  

Lags associated with the Default: Vector of integers 1,2,...,p, the nonseasonal, autoregressive polynomial degree.  

Lags associated with the Default: Vector of integers 1,2,...,q, the nonseasonal moving average polynomial degree.  

Seasonal, autoregressive coefficients for the error model,
specified as the commaseparated pair consisting of
Default: Cell vector of  

Seasonal, moving average coefficients for the error model,
specified as the commaseparated pair consisting of
Default: Cell vector of  

Lags associated with the Default: Vector of integers 1,2,...,p_{s}, the seasonal, autoregressive polynomial degree.  

Lags associated with the Default: Vector of integers 1,2,...,q_{s}, the seasonal moving average polynomial degree.  

Nonseasonal differencing polynomial degree (i.e., nonseasonal
integration degree) for the error model, specified as the
commaseparated pair consisting of Default:  

Seasonal differencing polynomial degree for the error model,
specified as the commaseparated pair consisting of
Default:  

Variance of the model innovations
ε_{t}, specified as
the commaseparated pair consisting of Default:  

Conditional probability distribution of the innovation process,
specified as the commaseparated pair consisting of
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 of the error model. Associated lags are
1,2,...,p, which is the nonseasonal, autoregressive
polynomial degree, or as specified in 

Real vector of regression coefficients corresponding to the columns of the predictor data matrix. 

Nonnegative integer indicating the nonseasonal integration degree of the error model. 
 String scalar for the model description. 

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

Scalar intercept in the error model. 

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

Scalar, compound autoregressive polynomial degree of the error model.


Scalar, compound moving average polynomial degree of the error model.


Cell vector of seasonal autoregressive coefficients corresponding to a
stable polynomial of the error model. Associated lags are
1,2,...,p_{s}, which is the
seasonal autoregressive polynomial degree, or as specified in


Cell vector of seasonal moving average coefficients corresponding to an
invertible polynomial of the error model. Associated lags are
1,2,...,q_{s}, which is the
seasonal moving average polynomial degree, or as specified in


Nonnegative integer indicating the seasonal differencing polynomial degree for the error model. 

Positive scalar variance of the model innovations. 
arima  Convert regression model with ARIMA errors to ARIMAX model 
estimate  Estimate parameters of regression models with ARIMA errors 
filter  Filter disturbances through regression model with ARIMA errors 
forecast  Forecast responses of regression model with ARIMA errors 
impulse  Impulse response of regression model with ARIMA errors 
infer  Infer innovations of regression models with ARIMA errors 
(To be removed) Display estimation results for regression models with ARIMA errors  
simulate  Monte Carlo simulation of regression model with ARIMA errors 
summarize  Display estimation results of regression model with ARIMA errors 
Value. To learn how value classes affect copy operations, see Copying Objects (MATLAB).
[1] Box, G. E. P., G. M. Jenkins, and G. C. Reinsel. Time Series Analysis: Forecasting and Control. 3rd ed. Englewood Cliffs, NJ: Prentice Hall, 1994.