regARIMA class
Superclasses:
Create regression model with ARIMA time series errors
Description
regARIMA
creates a regression model with ARIMA time series errors to maintain the sensitivity interpretation of regression coefficients. To create an ARIMA model containing a linear regression component for exogenous predictors (ARIMAX), see arima
.
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:
Construction
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
.
Input Arguments
Note
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 pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Namevalue arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.

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
The coefficients in 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
The coefficients in Default: Cell vector of  

Seasonal, moving average coefficients for the error model, specified as the commaseparated pair consisting of
The coefficients in 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, 
Note
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.
Properties

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. 
Object Functions
estimate  Estimate parameters of regression models with ARIMA errors 
infer  Infer innovations of regression models with ARIMA errors 
summarize  Display estimation results of regression model with ARIMA errors 
simulate  Monte Carlo simulation of regression model with ARIMA errors 
filter  Filter disturbances through regression model with ARIMA errors 
impulse  Generate regression model with ARIMA errors impulse response function (IRF) 
forecast  Forecast responses of regression model with ARIMA errors 
arima  Convert regression model with ARIMA errors to ARIMAX model 
Copy Semantics
Value. To learn how value classes affect copy operations, see Copying Objects.
Examples
More About
References
[1] Box, George E. P., Gwilym M. Jenkins, and Gregory C. Reinsel. Time Series Analysis: Forecasting and Control. 3rd ed. Englewood Cliffs, NJ: Prentice Hall, 1994.