regARIMA
Create regression model with ARIMA time series errors
Description
The regARIMA
function returns a regARIMA
object specifying the functional form and storing the parameter values of a regression model with ARIMA time series
errors for a univariate response process
yt.
Because they completely specify the model structure, the key components of a
regARIMA
object are the:
Regression model coefficients c and β
Polynomial degrees of the ARIMA disturbances ut, for example, the AR polynomial degree p and the degree of integration D
Given only polynomial degrees, the regression model contains only a constant.
All parameters, such as the model constant, and error model coefficients and
innovation-distribution parameters, are unknown and estimable unless you specify their values.
regARIMA
determines the number of coefficients in the regression model
by the number of variables in the supplied predictor data or by other specifications.
To estimate a model containing unknown parameter values, pass the model and data to the
estimate
object function. To work with an estimated or fully specified
regARIMA
object, pass it to an object function.
Alternatively, you can:
Create and work with
regARIMA
model objects interactively by using Econometric Modeler.Create a standard ARIMA model containing exogenous predictors (ARIMAX). For more details, see the
arima
function and Alternative ARIMA Model Representations.Create a Bayesian linear regression model by using the
bayeslm
function.
Creation
Description
creates a regression model
containing degree 0 ARIMA disturbances. The regression model contains an intercept; the
software determines the number of regression coefficients when you fit the model to data
by using Mdl
= regARIMAestimate
. The innovations are iid Gaussian
random variables with a mean of 0 and unknown variance.
creates a regression model with
ARIMA(Mdl
= regARIMA(p
,D
,q
)p
,D
,q
)
disturbances. The disturbance model contains nonseasonal AR polynomial lags from 1 through
p
, a degree D
nonseasonal integration polynomial,
and nonseasonal MA polynomial lags from 1 through q
. The regression
model contains an intercept; the software determines the number of regression coefficients
when you fit the model to data by using estimate
. The innovations are iid Gaussian random variables with a mean of 0
and unknown variance.
This shorthand syntax provides an easy way to create a model template in which you specify the degrees of the nonseasonal polynomials explicitly. The model template is suited for unrestricted parameter estimation. After you create a model, you can alter property values using dot notation.
sets properties and polynomial lags
using name-value arguments. For example, Mdl
= regARIMA(Name=Value
)regARIMA(ARLags=[1 4],AR={0.5
–0.1})
creates a regression model containing an unknown model intercept and
innovations variance, and AR(4) disturbances, where the lag 1 nonseasonal AR coefficient
is –0.5
and the lag 4 nonseasonal AR coefficient is
0.1
.
This longhand syntax allows you to create more flexible models. For example, you can
create a regression model with seasonal errors by using only longhand syntax.
regARIMA
infers all disturbance model polynomial degrees from the
properties that you set. Therefore, property values that correspond to polynomial degrees
must be consistent with each other.
Input Arguments
The shorthand syntax provides an easy way for you to create model templates of regression models with nonseasonal ARIMA errors. Model templates are suitable for unrestricted parameter estimation. For example, to create a regression model with ARMA(2,1) errors containing an unknown model intercept and innovations variance, enter:
Mdl = regARIMA(2,0,1);
p
— Nonseasonal autoregressive polynomial degree
nonnegative integer
Nonseasonal autoregressive polynomial degree for the error model, specified as a nonnegative integer.
Data Types: double
D
— Degree of nonseasonal integration
nonnegative integer
Degree of nonseasonal integration (the degree of the nonseasonal differencing
polynomial) for the error model, specified as a nonnegative integer. The
D
input argument sets the property D.
Data Types: double
q
— Nonseasonal moving average polynomial degree
nonnegative integer
Nonseasonal moving average polynomial degree for the error model, specified as a nonnegative integer.
Data Types: double
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Name-value 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.
The longhand syntax enables you to create seasonal error models or models in which
some or all coefficients are known. During estimation, estimate
imposes equality constraints on any known parameters.
Example: regARIMA(ARLags=[1 4],AR={0.5 –0.1})
creates a regression
model containing an unknown model intercept and innovations variance, and AR(4)
disturbances, where the lag 1 nonseasonal AR coefficient is –0.5
and
the lag 4 nonseasonal AR coefficient is 0.1
, symbolically, .
ARLags
— Lags associated with nonseasonal AR polynomial coefficients
1:numel(AR)
(default) | numeric vector of unique positive integers
Lags associated with the nonseasonal AR polynomial coefficients for the error model ut, specified as a numeric vector of unique positive integers. The maximum lag is p.
AR{
is the coefficient of lag
j
}ARLags(
, where
j
)AR
is the value of the property AR.
Example: ARLags=4
specifies the nonseasonal AR polynomial .
Example: ARLags=1:4
specifies the nonseasonal AR polynomial .
Example: ARLags=[1 4]
specifies the nonseasonal AR polynomial
Data Types: double
MALags
— Lags associated with nonseasonal MA polynomial coefficients
1:numel(MA)
(default) | numeric vector of unique positive integers
Lags associated with the nonseasonal MA polynomial coefficients for the error model ut, specified as a numeric vector of unique positive integers. The maximum lag is q.
MA{
is the coefficient of lag
j
}MALags(
, where
j
)MA
is the value of the property MA.
Example: MALags=3
specifies the nonseasonal MA polynomial .
Example: MALags=1:3
specifies the nonseasonal MA polynomial
Example: MALags=[1 3]
specifies the nonseasonal MA polynomial .
Data Types: double
SARLags
— Lags associated with seasonal AR polynomial coefficients
1:numel(SAR)
(default) | numeric vector of unique positive integers
Lags associated with the seasonal AR polynomial coefficients for the error model ut, specified as a numeric vector of unique positive integers. The maximum lag is ps.
SAR{
is the coefficient of lag
j
}SARLags(
, where
j
)SAR
is the value of the property SAR.
Specify SARLags
as the periodicity of the observed data, not
as multiples of the Seasonality property.
This convention does not conform to standard Box and Jenkins [1] notation, but it is more flexible for incorporating multiplicative
seasonality.
Example: SARLags=[4 8]
specifies the seasonal AR polynomial
Data Types: double
SMALags
— Lags associated with seasonal MA polynomial coefficients
1:numel(SMA)
(default) | numeric vector of unique positive integers
Lags associated with the seasonal MA polynomial coefficients for the error model ut, specified as a numeric vector of unique positive integers. The maximum lag is qs.
SMA{
is the coefficient of lag
j
}SMALags(
, where
j
)SMA
is the value of the property SMA.
Specify SMALags
as the periodicity of the observed data, not
as multiples of the Seasonality property.
This convention does not conform to standard Box and Jenkins [1] notation, but it is more flexible for incorporating multiplicative
seasonality.
Example: SMALags=4
specifies the seasonal MA polynomial
Data Types: double
Note
Polynomial degrees are not estimable. If you do not specify a polynomial degree, or
regARIMA
cannot infer it from other specifications,
regARIMA
does not include the polynomial in the model.
Properties
You can set writable property values when you create the model object by using name-value argument syntax, or after you create the model object by using dot notation. For example, to create the fully specified regression model with ARMA(2,1) disturbances
enter:
Mdl = regARIMA(Intercept=1,Beta=[3; 5],AR={0.3 -0.15},MA=0.2); Mdl.Variance = 1;
Note
NaN
-valued properties indicate estimable parameters. Numeric properties indicate equality constraints on parameters during model estimation. Coefficient vectors can contain both numeric andNaN
-valued elements.You can specify polynomial coefficients as vectors in any orientation, but
regARIMA
stores them as row vectors.
Regression Model Properties
Intercept
— Regression model intercept c
NaN
(default) | numeric scalar
Regression model intercept c, specified as a numeric scalar.
Example: Intercept=1
Data Types: double
Beta
— Regression model coefficients β
empty row vector []
(default) | numeric vector
Regression component coefficients β associated with predictor variables xt, specified as a numeric vector.
The default indicates one of the following conditions:
estimate
infers the size ofBeta
from the number of columns of the specified predictor dataX
. Therefore, if you plan to fit all regression coefficients to data, you do not need to specifyBeta
.The model does not include regression coefficients.
Example: Beta=[0.5 NaN 3]
specifies three regression coefficients.
During estimation, estimate
fixes
β1 to 5 and
β3 to 3, and it fits
β2 to the data associated with the second
predictor variable.
Data Types: double
Error Model Properties
P
— Compound AR polynomial degree
nonnegative integer
This property is read-only.
Compound AR polynomial degree of the error model, specified as a nonnegative integer.
P
does not necessarily conform to standard Box and Jenkins
notation [1] because P
captures the degrees of the nonseasonal and seasonal AR
polynomials (properties AR
and SAR
,
respectively), nonseasonal integration (property D
), and
seasonality (property Seasonality
). Explicitly,
P
= p + D +
ps + s.
P
conforms to Box and Jenkins notation for models without
integration or a seasonal AR component (D
= 0
and SAR
= {}
).
P
specifies the number of lagged observations required to
initialize the AR components of the model.
Data Types: double
Q
— Compound MA polynomial degree
nonnegative integer
This property is read-only.
Compound MA polynomial degree of the error model, specified as a nonnegative integer.
Q
does not necessarily conform to standard Box and Jenkins
notation [1] because Q
captures the degrees of the nonseasonal and seasonal MA
polynomials (properties MA
and SMA
,
respectively). Explicitly, Q
= q +
qs. Q
conforms to Box
and Jenkins notation for models without a seasonal MA component
(SMA
= {}
).
Q
specifies the number of lagged innovations required to
initialize the MA components of the model.
Data Types: double
AR
— Nonseasonal AR polynomial coefficients ϕ
cell vector | empty cell vector {}
Nonseasonal AR polynomial coefficients ϕ for the error model
ut, specified as a cell vector. Cells
contain numeric scalars or NaN
values. A fully specified nonseasonal
AR polynomial must be stable.
Coefficient signs correspond to the model expressed in difference-equation notation.
For example, for the nonseasonal AR polynomial specify AR={0.5 –0.1}
.
If you do not set the ARLags
name-value argument,
AR{
is the coefficient of lag
j
}j
, j
= 1,…,p,
where p = numel(AR)
.
Otherwise, if ARLags
=
, with p =
arlags
max(
, the following conditions apply:arlags
)
The lengths of
AR
and
must be equal.arlags
AR{
is the coefficient of lagj
}
, for eacharlags
(j
)
.j
regARIMA
storesAR
as a length p cell vector. All cells that do not correspond to lags in
containarlags
0
.
The default value of AR
depends on other specifications:
If you use the shorthand syntax to specify
p
> 0,AR
is a lengthp
cell vector, where each cell contains aNaN
value.If you specify
ARLags
,AR
is a length p cell vector.AR{
=j
}NaN
for each lag
. All other cells containarlags
(j
)0
.Otherwise,
AR
is an empty cell vector{}
, meaning the model does not contain a nonseasonal AR polynomial.
The coefficients in AR
correspond to coefficients in an
underlying LagOp
lag operator polynomial, and they are
subject to a near-zero tolerance exclusion test. If a coefficient is
1e–12
or below, regARIMA
excludes that
coefficient and its corresponding lag in ARLags
from the
model.
Example: AR={0.8}
sets the only AR lag coefficient associated with
lag ARLags(1)
to 0.8
.
Example: regARIMA(AR={0.2 0 0.1})
sets the error model, in
difference-equation form, to .
Example: regARIMA(AR={NaN –0.1},ARLags=[4 8])
sets the AR lag
polynomial to , where ϕ4 is unknown and
estimable.
Data Types: cell
MA
— Nonseasonal MA polynomial coefficients θ
cell vector | empty cell vector {}
Nonseasonal MA polynomial coefficients θ for the error model
ut, specified as a cell vector. Cells
contain numeric scalars or NaN
values. A fully specified nonseasonal
MA polynomial must be invertible.
If you do not set the MALags
name-value pair argument,
MA{
is the coefficient of lag
j
}j
, j
= 1,…,q,
where q = numel(MA)
.
Otherwise, if MALags
=
, with q =
malags
max(MALags)
, the following conditions apply:
The lengths of
MA
and
must be equal.malags
MA{
is the coefficient of lagj
}
, for eachmalags
(j
)
.j
regARIMA
storesMA
as a length q cell vector. All cells that do not correspond to lags in
containmalags
0
.
The default value of MA
depends on other specifications:
If you use the shorthand syntax to specify
q
> 0,MA
is a lengthq
cell vector, where each cell contains aNaN
value.If you specify
MALags
,MA
is a length q cell vector.MA{
=j
}NaN
for each lag
. All other cells containmalags
(j
)0
.Otherwise,
MA
is an empty cell vector{}
, meaning the error model does not contain a nonseasonal MA polynomial.
The coefficients in MA
correspond to coefficients in an
underlying LagOp
lag operator polynomial, and they are
subject to a near-zero tolerance exclusion test. If a coefficient is
1e–12
or below, regARIMA
excludes that
coefficient and its corresponding lag in MALags
from the
model.
Example: MA=0.8
sets the only MA lag coefficient associated with
lag MALags(1)
to 0.8
.
Example: regARIMA(MA={0.2 0.1})
sets the error model to
Example: regARIMA(MA={NaN –0.1},MALags=[4 8])
sets the MA lag
polynomial to , where θ4 is unknown and
estimable.
Data Types: cell
SAR
— Seasonal AR polynomial coefficients Φ
cell vector | empty cell vector {}
Seasonal AR polynomial coefficients Φ for the error model
ut, specified as a cell vector. Cells
contain numeric scalars or NaN
values. A fully specified seasonal AR
polynomial must be stable.
Coefficient signs correspond to the model expressed in difference-equation notation.
For example, for the seasonal AR polynomial specify SAR={0.5 –0.1}
.
If you do not set the SARLags
name-value argument,
SAR{
is the coefficient of lag
j
}j
, j
=
1,…,ps, where
ps = numel(SAR)
.
Otherwise, if SARLags
=
, with
ps =
sarlags
max(
, the following conditions apply:sarlags
)
The lengths of
SAR
and
must be equal.sarlags
SAR{
is the coefficient of lagj
}
, for eachsarlags
(j
)
.j
regARIMA
storesSAR
as a length ps cell vector. All cells that do not correspond to lags in
containsarlags
0
.
The default value of SAR
depends on the value of
SARLags
:
If you specify
SARLags
,SAR
is a length ps cell vector.SAR{
=j
}NaN
for each lagSARLags(
. All other cells containj
)0
.Otherwise,
SAR
is an empty cell vector{}
, meaning the error model does not contain a seasonal AR polynomial.
The coefficients in SAR
correspond to coefficients in an
underlying LagOp
lag operator polynomial, and they are
subject to a near-zero tolerance exclusion test. If a coefficient is
1e–12
or below, regARIMA
excludes that
coefficient and its corresponding lag in SARLags
from the
model.
Example: SAR=0.8
sets the only SAR lag coefficient associated with
lag SARLags(1)
to 0.8
.
Example: regARIMA(SAR={0.2 0.1},Seasonality=4)
sets the error
model to .
Example: regARIMA(SAR={NaN –0.1},SARLags=[4 8],Seasonality=4)
sets
the SAR lag polynomial to , where Φ4 is unknown and
estimable.
Data Types: cell
SMA
— Seasonal MA polynomial coefficients
cell vector | empty cell vector {}
Seasonal MA polynomial coefficients for the error model, specified as a cell vector.
Cells contain numeric scalars or NaN
values. A fully specified
seasonal MA polynomial must be invertible.
If you do not set the SMALags
name-value argument,
SMA{
is the coefficient of lag
j
}j
, j
=
1,…,qs, where
qs = numel(SMA)
.
Otherwise, if SMALags
=
, with
qs =
smalags
max(
, the following conditions apply:smalags
)
The lengths of
SMA
andSMALags
must be equal.SMA{
is the coefficient of lagj
}
, for eachsmalags
(j
)
.j
regARIMA
storesSMA
as a length qs cell vector. All cells that do not correspond to lags in
containsmalags
0
.
The default value of SMA
depends on other specifications:
If you specify
SMALags
,MA
is a length q cell vector.MA{
=j
}NaN
for each lagMALags(
. All other cells containj
)0
.Otherwise,
SMA
is an empty cell vector{}
, meaning the error model does not contain a seasonal MA polynomial.
The coefficients in SMA
correspond to coefficients in an
underlying LagOp
lag operator polynomial, and they are
subject to a near-zero tolerance exclusion test. If a coefficient is
1e–12
or below, regARIMA
excludes that
coefficient and its corresponding lag in SMALags
from the
model.
Example: SMA=0.8
sets the only SMA lag coefficient associated with
lag SMALags(1)
to 0.8
.
Example: regARIMA(SMA{0.2 0.1},Seasonality=4)
specifies the error
model
Example: regARIMA(SMALags=[1 4],SMA={0.2 0.1},Seasonality = 4)
specifies the error model
Data Types: cell
D
— Degree of nonseasonal integration
0
(default) | nonnegative integer
Degree of nonseasonal integration, or the degree of the nonseasonal differencing polynomial, for the error model specified as a nonnegative integer.
If you use shorthand syntax to create Mdl
, the input
d
sets D
.
Example: D=1
Example: regARIMA(0,1,2)
sets D
to
1
.
Data Types: double
Seasonality
— Degree of seasonal differencing polynomial
0
(default) | nonnegative integer
Degree of the seasonal differencing polynomial s for the error model, specified as a nonnegative integer.
Example: Seasonality=12
specifies monthly
periodicity.
Data Types: double
Variance
— Variance σ2 of model innovations process εt
NaN
(default) | positive scalar
Variance σ2 of the model innovations process εt, specified as a positive scalar.
NaN
specifies an unknown and estimable variance, which
estimate
fits to data.
Example: Variance=1
Data Types: double
Other Properties
Description
— Model description
string scalar | character vector
Model description, specified as a string scalar or character vector. regARIMA
stores the value as a string scalar. The default value describes the parametric form of the model, for example, "Regression with ARMA(2,1) Error Model (Gaussian
Distribution)"
.
Example: "Model 1"
Data Types: string
| char
Distribution
— Conditional probability distribution of innovation process εt
"Gaussian"
(default) | "t"
| structure array
Conditional probability distribution of the innovation process
εt, specified as a string or structure
array. regARIMA
stores the value as a structure array.
Distribution | String | Structure Array |
---|---|---|
Gaussian | "Gaussian" | struct('Name',"Gaussian") |
Student’s t | "t" | struct('Name',"t",'DoF',DoF) |
The 'DoF'
field specifies the t distribution
degrees of freedom parameter.
DoF
> 2 orDoF
=NaN
.DoF
is estimable.If you specify
"t"
,DoF
isNaN
by default. You can change its value by using dot notation after you create the model. For example,Mdl.Distribution.DoF = 3
.If you supply a structure array to specify the Student's t distribution, then you must specify both the
'Name'
and the'DoF'
fields.
Example: Distribution=struct('Name',"t",'DoF',10)
SeriesName
— Response series name
"Y"
(default) | string scalar | character vector
Since R2023b
Response series name, specified as a string scalar or character vector. regARIMA
stores the value as a string scalar.
Example: "StockReturn"
Data Types: string
| char
Object Functions
estimate | Fit univariate regression model with ARIMA errors to data |
infer | Infer residuals of univariate regression model with ARIMA time series errors |
summarize | Display estimation results of regression model with ARIMA errors |
simulate | Monte Carlo simulation of univariate regression model with ARIMA time series 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 univariate regression model with ARIMA time series errors |
arima | Convert regression model with ARIMA errors to ARIMAX model |
Examples
Specify Regression Model with Nonseasonal ARIMA Errors
Specify the following regression model with ARIMA(2,1,3) errors:
Mdl = regARIMA(2,1,3)
Mdl = regARIMA with properties: Description: "ARIMA(2,1,3) Error Model (Gaussian Distribution)" SeriesName: "Y" Distribution: Name = "Gaussian" Intercept: NaN Beta: [1×0] P: 3 D: 1 Q: 3 AR: {NaN NaN} at lags [1 2] SAR: {} MA: {NaN NaN NaN} at lags [1 2 3] SMA: {} Variance: NaN
The output displays the values of the properties P
, D
, and Q
of Mdl
. The corresponding autoregressive and moving average coefficients (contained in AR
and MA
) are cell arrays containing the correct number of NaN
values. Because P
= p
+ D
= 3, you need three presample observations to initialize the model for estimation.
Modify Regression Model with ARIMA Errors
Define the regression model with ARIMA errors:
where is Gaussian with variance 0.5.
Mdl = regARIMA(Intercept=2,AR={0.2 0.3},MA={0.1}, ...
Variance=0.5,Beta=[1.5 0.2])
Mdl = regARIMA with properties: Description: "Regression with ARMA(2,1) Error Model (Gaussian Distribution)" SeriesName: "Y" Distribution: Name = "Gaussian" Intercept: 2 Beta: [1.5 0.2] P: 2 Q: 1 AR: {0.2 0.3} at lags [1 2] SAR: {} MA: {0.1} at lag [1] SMA: {} Variance: 0.5
Mdl
is fully specified to, for example, simulate a series of responses given the predictor data matrix, .
Modify the model to estimate the regression coefficient, the AR terms, and the variance of the innovations.
Mdl.Beta = [NaN NaN]; Mdl.AR = {NaN NaN}; Mdl.Variance = NaN;
Change the innovations distribution to a distribution with 15 degrees of freedom.
Mdl.Distribution = struct("Name","t","DoF",15)
Mdl = regARIMA with properties: Description: "Regression with ARMA(2,1) Error Model (t Distribution)" SeriesName: "Y" Distribution: Name = "t", DoF = 15 Intercept: 2 Beta: [NaN NaN] P: 2 Q: 1 AR: {NaN NaN} at lags [1 2] SAR: {} MA: {0.1} at lag [1] SMA: {} Variance: NaN
Specify Regression Model with SARIMA Errors
Specify the following model:
where is Gaussian with variance 1.
Mdl = regARIMA(Intercept=1,Beta=6,AR=0.2,MA=0.1,D=1, ... SAR={0.5,0.2},SARLags=[4, 8],SMA={0.05,0.01},SMALags=[4 8], ... Seasonality=4,Variance=1)
Mdl = regARIMA with properties: Description: "Regression with ARIMA(1,1,1) Error Model Seasonally Integrated with Seasonal AR(8) and MA(8) (Gaussian Distribution)" SeriesName: "Y" Distribution: Name = "Gaussian" Intercept: 1 Beta: [6] P: 14 D: 1 Q: 9 AR: {0.2} at lag [1] SAR: {0.5 0.2} at lags [4 8] MA: {0.1} at lag [1] SMA: {0.05 0.01} at lags [4 8] Seasonality: 4 Variance: 1
If you do not specify SARLags
or SMALags
, then the coefficients in SAR
and SMA
correspond to lags 1 and 2 by default.
Mdl = regARIMA(Intercept=1,Beta=6,AR=0.2,MA=0.1,D=1, ... SAR={0.5,0.2},SARLags=[4, 8], ... Seasonality=4,Variance=1)
Mdl = regARIMA with properties: Description: "Regression with ARIMA(1,1,1) Error Model Seasonally Integrated with Seasonal AR(8) (Gaussian Distribution)" SeriesName: "Y" Distribution: Name = "Gaussian" Intercept: 1 Beta: [6] P: 14 D: 1 Q: 1 AR: {0.2} at lag [1] SAR: {0.5 0.2} at lags [4 8] MA: {0.1} at lag [1] SMA: {} Seasonality: 4 Variance: 1
More About
Regression Model with ARIMA Time Series Errors
A regression model with ARIMA time series errors explains the behavior of a response series by applying linear regression with predictor data, though the errors have autocorrelation indicative of an ARIMA process.
The model has the form (in lag operator notation)
where:
t = 1,...,T.
yt is the response series.
Xt is row t of X, which is the matrix of concatenated predictor data vectors. That is, Xt is observation t of each predictor series.
c is the regression model intercept.
β is the regression coefficient.
ut is the disturbance series.
εt is the innovations series.
which is the degree p, nonseasonal autoregressive polynomial.
which is the degree ps, seasonal autoregressive polynomial.
which is the degree D, nonseasonal integration polynomial.
which is the degree s, seasonal integration polynomial.
which is the degree q, nonseasonal moving average polynomial.
which is the degree qs, seasonal moving average polynomial.
Regression models with ARIMA errors contain a hierarchy of error series. The unconditional disturbance, ut, or structural disturbance, is based on the structural regression component. The conditional error (one-step-ahead forecast or prediction error), εt is the innovation of ut.
Note
The degrees of the lag operators in the seasonal polynomials A(L) and B(L) do not conform to those defined by Box and Jenkins [1]. In other words, Econometrics Toolbox™ does not treat p1 = s, p2 = 2s,...,ps = cps nor q1 = s, q2 = 2s,...,qs = cqs, where cp and cq are positive integers. The software is flexible as it lets you specify the lag operator degrees. See Create Multiplicative ARIMA Models.
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.
Version History
Introduced in R2013bR2023b: Name the response series of a regression model with ARIMA errors
Name the response series of a regression model with ARIMA errors by setting the
SeriesName
property to a string scalar. When you supply input
response data to model object functions in a table or timetable, the functions choose the
variable with name SeriesName
as the response variable by default.
R2018a: Describe a response series of a regression model with ARIMA errors
Describe a response series of a regression model with ARIMA errors by setting the
Description
property to a string scalar.
R2018a: Use indices that are consistent with MATLAB cell array indexing
The indices of cell arrays of lag operator polynomial coefficients follow MATLAB® cell array indexing rules. Affected model properties are
AR
, MA
, SAR
, and
SMA
.
You cannot access any lag-zero coefficients by using an index of
0
. For example,Mdl.AR{0}
issues an error.Remove any instances of such zero indices from your code. The value of all lag-zero coefficients is
1
, except for the lag operator polynomial corresponding to theARCH
property, which has the value0
.You cannot index beyond the maximal lag in the polynomial. For example, if
Mdl.P
is 4, thenMdl.AR{p}
issues an error whenp
is greater than4
. For details on the maximal lags of the lag operator polynomials, see the corresponding property descriptions.Remove any instances of such indices beyond the maximal lag from your code. All coefficients beyond the maximal lag are
0
.
R2018a: Models store innovation distribution name as a string scalar
The Name
field of the Distribution
property of
regARIMA
model objects stores the innovation distribution name
as a string scalar, for example, "Gaussian"
for Gaussian innovations.
Before R2018a, MATLAB stored the innovation distribution name as a character vector, for example
'Gaussian'
for Gaussian innovations. Although most text-data
operations accept character vectors and string scalars for text-data input, the two data
types have some differences. For details, see Text in String and Character Arrays.
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