garch
GARCH conditional variance time series model
Description
Use garch
to specify a univariate GARCH (generalized autoregressive conditional heteroscedastic) model. The garch
function returns a garch
object specifying the functional form of a GARCH(P,Q) model, and stores its parameter values.
The key components of a garch
model include the:
GARCH polynomial, which is composed of lagged conditional variances. The degree is denoted by P.
ARCH polynomial, which is composed of the lagged squared innovations. The degree is denoted by Q.
P and Q are the maximum nonzero lags in the GARCH and ARCH polynomials, respectively. Other model components include an innovation mean model offset, a conditional variance model constant, and the innovations distribution.
All coefficients are unknown (NaN
values) and estimable unless you specify their values using name-value pair argument syntax. To estimate models containing all or partially unknown parameter values given data, use estimate
. For completely specified models (models in which all parameter values are known), simulate or forecast responses using simulate
or forecast
, respectively.
Creation
Description
returns a zero-degree conditional variance Mdl
= garchgarch
object.
creates a GARCH conditional variance model object (Mdl
= garch(P
,Q
)Mdl
) with a GARCH polynomial with a degree of P
and an ARCH polynomial with a degree of Q
. The GARCH and ARCH polynomials contain all consecutive lags from 1 through their degrees, and all coefficients are NaN
values.
This shorthand syntax enables you to create a template in which you specify the polynomial degrees explicitly. The model template is suited for unrestricted parameter estimation, that is, estimation without any parameter equality constraints. However, after you create a model, you can alter property values using dot notation.
sets properties or additional options using name-value pair arguments. Enclose each name in quotes. For example, Mdl
= garch(Name,Value
)'ARCHLags',[1 4],'ARCH',{0.2 0.3}
specifies the two ARCH coefficients in ARCH
at lags 1
and 4
.
This longhand syntax enables you to create more flexible models.
Input Arguments
The shorthand syntax provides an easy way for you to create model templates that are suitable for unrestricted parameter estimation. For example, to create a GARCH(1,2) model containing unknown parameter values, enter:
Mdl = garch(1,2);
P
— GARCH polynomial degree
nonnegative integer
GARCH polynomial degree, specified as a nonnegative integer. In the GARCH polynomial and at time t, MATLAB® includes all consecutive conditional variance terms from lag t – 1 through lag t – P
.
You can specify this argument using the
garch
(P,Q)
shorthand syntax only.
If P
> 0, then you must specify Q
as a positive integer.
Example: garch(1,1)
Data Types: double
Q
— ARCH polynomial degree
nonnegative integer
ARCH polynomial degree, specified as a nonnegative integer. In the ARCH polynomial and at time t, MATLAB includes all consecutive squared innovation terms from lag t – 1 through lag t – Q
.
You can specify this argument using the
garch
(P,Q)
shorthand syntax only.
If P
> 0, then you must specify Q
as a positive integer.
Example: garch(1,1)
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 models in which some or all coefficients are known. During estimation,
estimate
imposes equality constraints on any known parameters.
Example: 'ARCHLags',[1 4],'ARCH',{NaN NaN}
specifies a GARCH(0,4) model and unknown, but nonzero, ARCH coefficient matrices at lags 1
and 4
.
GARCHLags
— GARCH polynomial lags
1:P
(default) | numeric vector of unique positive integers
GARCH polynomial lags, specified as the comma-separated pair consisting of
'GARCHLags'
and a numeric vector of unique positive
integers.
GARCHLags(
is the lag corresponding to
the coefficient j
)GARCH{
. The lengths of
j
}GARCHLags
and GARCH
must be equal.
Assuming all GARCH coefficients (specified by the GARCH
property)
are positive or NaN
values, max(GARCHLags)
determines the value of the P
property.
Example: 'GARCHLags',[1 4]
Data Types: double
ARCHLags
— ARCH polynomial lags
1:Q
(default) | numeric vector of unique positive integers
ARCH polynomial lags, specified as the comma-separated pair consisting of 'ARCHLags'
and a numeric vector of unique positive integers.
ARCHLags(
is the lag corresponding to the coefficient j
)ARCH{
. The lengths of j
}ARCHLags
and ARCH
must be equal.
Assuming all ARCH coefficients (specified by the ARCH
property) are positive or NaN
values, max(ARCHLags)
determines the value of the Q
property.
Example: 'ARCHLags',[1 4]
Data Types: double
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 a GARCH(1,1) model with unknown coefficients, and then specify a t innovation distribution with unknown degrees of freedom, enter:
Mdl = garch('GARCHLags',1,'ARCHLags',1); Mdl.Distribution = "t";
P
— GARCH polynomial degree
nonnegative integer
This property is read-only.
GARCH polynomial degree, specified as a nonnegative integer. P
is
the maximum lag in the GARCH polynomial with a coefficient that is positive or
NaN
. Lags that are less than P
can have
coefficients equal to 0.
P
specifies the minimum number of presample conditional variances
required to initialize the model.
If you use name-value pair arguments to create the model, then MATLAB implements one of these alternatives (assuming the coefficient of the
largest lag is positive or NaN
):
If you specify
GARCHLags
, thenP
is the largest specified lag.If you specify
GARCH
, thenP
is the number of elements of the specified value. If you also specifyGARCHLags
, thengarch
usesGARCHLags
to determineP
instead.Otherwise,
P
is0
.
Data Types: double
Q
— ARCH polynomial degree
nonnegative integer
This property is read-only.
ARCH polynomial degree, specified as a nonnegative integer. Q
is the maximum lag in the ARCH polynomial with a coefficient that is positive or NaN
. Lags that are less than Q
can have coefficients equal to 0.
Q
specifies the minimum number of presample innovations required to initiate the model.
If you use name-value pair arguments to create the model, then MATLAB implements one of these alternatives (assuming the coefficient of the largest lag is positive or NaN
):
If you specify
ARCHLags
, thenQ
is the largest specified lag.If you specify
ARCH
, thenQ
is the number of elements of the specified value. If you also specifyARCHLags
, thengarch
uses its value to determineQ
instead.Otherwise,
Q
is0
.
Data Types: double
Constant
— Conditional variance model constant
NaN
(default) | positive scalar
Conditional variance model constant, specified as a positive scalar or NaN
value.
Data Types: double
GARCH
— GARCH polynomial coefficients
cell vector of positive scalars or NaN
values
GARCH polynomial coefficients, specified as a cell vector of positive scalars or NaN
values.
If you specify
GARCHLags
, then the following conditions apply.The lengths of
GARCH
andGARCHLags
are equal.GARCH{
is the coefficient of lagj
}GARCHLags(
.j
)By default,
GARCH
is anumel(GARCHLags)
-by-1 cell vector ofNaN
values.
Otherwise, the following conditions apply.
The length of
GARCH
isP
.GARCH{
is the coefficient of lagj
}j
.By default,
GARCH
is aP
-by-1 cell vector ofNaN
values.
The coefficients in GARCH
correspond to coefficients in an underlying LagOp
lag operator polynomial, and are subject to a near-zero tolerance exclusion test. If you set a coefficient to 1e–12
or below, garch
excludes that coefficient and its corresponding lag in GARCHLags
from the model.
Data Types: cell
ARCH
— ARCH polynomial coefficients
cell vector of positive scalars or NaN
values
ARCH polynomial coefficients, specified as a cell vector of positive scalars or NaN
values.
If you specify
ARCHLags
, then the following conditions apply.The lengths of
ARCH
andARCHLags
are equal.ARCH{
is the coefficient of lagj
}ARCHLags(
.j
)By default,
ARCH
is anumel(ARCHLags)
-by-1 cell vector ofNaN
values.
Otherwise, the following conditions apply.
The length of
ARCH
isQ
.ARCH{
is the coefficient of lagj
}j
.By default,
ARCH
is aQ
-by-1 cell vector ofNaN
values.
The coefficients in ARCH
correspond to coefficients in an underlying LagOp
lag operator polynomial, and are subject to a near-zero tolerance exclusion test. If you set a coefficient to 1e–12
or below, garch
excludes that coefficient and its corresponding lag in ARCHLags
from the model.
Data Types: cell
UnconditionalVariance
— Model unconditional variance
positive scalar
This property is read-only.
The model unconditional variance, specified as a positive scalar.
The unconditional variance is
κ is the conditional variance model constant (Constant
).
Data Types: double
Offset
— Innovation mean model offset
0
(default) | numeric scalar | NaN
Innovation mean model offset, or additive constant, specified as a numeric scalar or NaN
value.
Data Types: double
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. garch
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)
Description
— Model description
string scalar | character vector
Model description, specified as a string scalar or character vector. garch
stores the value as a string scalar. The default value describes the parametric form of the model, for example
"GARCH(1,1) Conditional Variance Model (Gaussian
Distribution)"
.
Example: 'Description','Model 1'
Data Types: string
| char
SeriesName
— Response series name
string scalar | character vector | "Y"
Since R2023a
Response series name, specified as a string scalar or character vector.
garch
stores the value as a string scalar.
Example: "StockReturn"
Data Types: string
| char
Note
All NaN
-valued model parameters, which
include coefficients and the t-innovation-distribution degrees of freedom (if
present), are estimable. When you pass the resulting garch
object and
data to estimate
, MATLAB estimates all NaN
-valued parameters. During estimation,
estimate
treats known parameters as equality constraints, that
is,estimate
holds any known parameters fixed at their values.
Object Functions
estimate | Fit conditional variance model to data |
filter | Filter disturbances through conditional variance model |
forecast | Forecast conditional variances from conditional variance models |
infer | Infer conditional variances of conditional variance models |
simulate | Monte Carlo simulation of conditional variance models |
summarize | Display estimation results of conditional variance model |
Examples
Create Default GARCH Model
Create a default garch
model object and specify its parameter values using dot notation.
Create a GARCH(0,0) model.
Mdl = garch
Mdl = garch with properties: Description: "GARCH(0,0) Conditional Variance Model (Gaussian Distribution)" SeriesName: "Y" Distribution: Name = "Gaussian" P: 0 Q: 0 Constant: NaN GARCH: {} ARCH: {} Offset: 0
Mdl
is a garch
model. It contains an unknown constant, its offset is 0
, and the innovation distribution is 'Gaussian'
. The model does not have a GARCH or ARCH polynomial.
Specify two unknown ARCH coefficients for lags one and two using dot notation.
Mdl.ARCH = {NaN NaN}
Mdl = garch with properties: Description: "GARCH(0,2) Conditional Variance Model (Gaussian Distribution)" SeriesName: "Y" Distribution: Name = "Gaussian" P: 0 Q: 2 Constant: NaN GARCH: {} ARCH: {NaN NaN} at lags [1 2] Offset: 0
The Q
and ARCH
properties are updated to 2
and {NaN NaN}
. The two ARCH coefficients are associated with lags 1 and 2.
Create GARCH Model Using Shorthand Syntax
Create a garch
model using the shorthand notation garch(P,Q)
, where P
is the degree of the GARCH polynomial and Q
is the degree of the ARCH polynomial.
Create a GARCH(3,2) model.
Mdl = garch(3,2)
Mdl = garch with properties: Description: "GARCH(3,2) Conditional Variance Model (Gaussian Distribution)" SeriesName: "Y" Distribution: Name = "Gaussian" P: 3 Q: 2 Constant: NaN GARCH: {NaN NaN NaN} at lags [1 2 3] ARCH: {NaN NaN} at lags [1 2] Offset: 0
Mdl
is a garch
model object. All properties of Mdl
, except P
, Q
, and Distribution
, are NaN
values. By default, the software:
Includes a conditional variance model constant
Excludes a conditional mean model offset (i.e., the offset is
0
)Includes all lag terms in the ARCH and GARCH lag-operator polynomials up to lags
Q
andP
, respectively
Mdl
specifies only the functional form of a GARCH model. Because it contains unknown parameter values, you can pass Mdl
and the time-series data to estimate
to estimate the parameters.
Create GARCH Model Using Longhand Syntax
Create a garch
model using name-value pair arguments.
Specify a GARCH(1,1) model. By default, the conditional mean model offset is zero. Specify that the offset is NaN
.
Mdl = garch('GARCHLags',1,'ARCHLags',1,'Offset',NaN)
Mdl = garch with properties: Description: "GARCH(1,1) Conditional Variance Model with Offset (Gaussian Distribution)" SeriesName: "Y" Distribution: Name = "Gaussian" P: 1 Q: 1 Constant: NaN GARCH: {NaN} at lag [1] ARCH: {NaN} at lag [1] Offset: NaN
Mdl
is a garch
model object. The software sets all parameters (the properties of the model object) to NaN
, except P
, Q
, and Distribution
.
Since Mdl
contains NaN
values, Mdl
is only appropriate for estimation only. Pass Mdl
and time-series data to estimate
.
Create GARCH Model with Known Coefficients
Create a GARCH(1,1) model with mean offset,
where
and is an independent and identically distributed standard Gaussian process.
Mdl = garch('Constant',0.0001,'GARCH',0.75,... 'ARCH',0.1,'Offset',0.5)
Mdl = garch with properties: Description: "GARCH(1,1) Conditional Variance Model with Offset (Gaussian Distribution)" SeriesName: "Y" Distribution: Name = "Gaussian" P: 1 Q: 1 Constant: 0.0001 GARCH: {0.75} at lag [1] ARCH: {0.1} at lag [1] Offset: 0.5
garch
assigns default values to any properties you do not specify with name-value pair arguments.
Access GARCH Model Properties
Access the properties of a garch
model object using dot notation.
Create a garch
model object.
Mdl = garch(3,2)
Mdl = garch with properties: Description: "GARCH(3,2) Conditional Variance Model (Gaussian Distribution)" SeriesName: "Y" Distribution: Name = "Gaussian" P: 3 Q: 2 Constant: NaN GARCH: {NaN NaN NaN} at lags [1 2 3] ARCH: {NaN NaN} at lags [1 2] Offset: 0
Remove the second GARCH term from the model. That is, specify that the GARCH coefficient of the second lagged conditional variance is 0
.
Mdl.GARCH{2} = 0
Mdl = garch with properties: Description: "GARCH(3,2) Conditional Variance Model (Gaussian Distribution)" SeriesName: "Y" Distribution: Name = "Gaussian" P: 3 Q: 2 Constant: NaN GARCH: {NaN NaN} at lags [1 3] ARCH: {NaN NaN} at lags [1 2] Offset: 0
The GARCH polynomial has two unknown parameters corresponding to lags 1 and 3.
Display the distribution of the disturbances.
Mdl.Distribution
ans = struct with fields:
Name: "Gaussian"
The disturbances are Gaussian with mean 0 and variance 1.
Specify that the underlying I.I.D. disturbances have a t distribution with five degrees of freedom.
Mdl.Distribution = struct('Name','t','DoF',5)
Mdl = garch with properties: Description: "GARCH(3,2) Conditional Variance Model (t Distribution)" SeriesName: "Y" Distribution: Name = "t", DoF = 5 P: 3 Q: 2 Constant: NaN GARCH: {NaN NaN} at lags [1 3] ARCH: {NaN NaN} at lags [1 2] Offset: 0
Specify that the ARCH coefficients are 0.2 for the first lag and 0.1 for the second lag.
Mdl.ARCH = {0.2 0.1}
Mdl = garch with properties: Description: "GARCH(3,2) Conditional Variance Model (t Distribution)" SeriesName: "Y" Distribution: Name = "t", DoF = 5 P: 3 Q: 2 Constant: NaN GARCH: {NaN NaN} at lags [1 3] ARCH: {0.2 0.1} at lags [1 2] Offset: 0
To estimate the remaining parameters, you can pass Mdl
and your data to estimate
and use the specified parameters as equality constraints. Or, you can specify the rest of the parameter values, and then simulate or forecast conditional variances from the GARCH model by passing the fully specified model to simulate
or forecast
, respectively.
Estimate GARCH Model
Fit a GARCH model to an annual time series of Danish nominal stock returns from 1922-1999.
Load the Data_Danish
data set. Plot the nominal returns (nr
).
load Data_Danish; nr = DataTable.RN; figure; plot(dates,nr); hold on; plot([dates(1) dates(end)],[0 0],'r:'); % Plot y = 0 hold off; title('Danish Nominal Stock Returns'); ylabel('Nominal return (%)'); xlabel('Year');
The nominal return series seems to have a nonzero conditional mean offset and seems to exhibit volatility clustering. That is, the variability is smaller for earlier years than it is for later years. For this example, assume that a GARCH(1,1) model is appropriate for this series.
Create a GARCH(1,1) model. The conditional mean offset is zero by default. To estimate the offset, specify that it is NaN
.
Mdl = garch('GARCHLags',1,'ARCHLags',1,'Offset',NaN);
Fit the GARCH(1,1) model to the data.
EstMdl = estimate(Mdl,nr);
GARCH(1,1) Conditional Variance Model with Offset (Gaussian Distribution): Value StandardError TStatistic PValue _________ _____________ __________ _________ Constant 0.0044476 0.007814 0.56918 0.56923 GARCH{1} 0.84932 0.26495 3.2056 0.0013477 ARCH{1} 0.07325 0.14953 0.48986 0.62423 Offset 0.11227 0.039214 2.8629 0.0041974
EstMdl
is a fully specified garch
model object. That is, it does not contain NaN
values. You can assess the adequacy of the model by generating residuals using infer
, and then analyzing them.
To simulate conditional variances or responses, pass EstMdl
to simulate
.
To forecast innovations, pass EstMdl
to forecast
.
Simulate GARCH Model Observations and Conditional Variances
Simulate conditional variance or response paths from a fully specified garch
model object. That is, simulate from an estimated garch
model or a known garch
model in which you specify all parameter values.
Load the Data_Danish
data set.
load Data_Danish;
nr = DataTable.RN;
Create a GARCH(1,1) model with an unknown conditional mean offset. Fit the model to the annual nominal return series.
Mdl = garch('GARCHLags',1,'ARCHLags',1,'Offset',NaN); EstMdl = estimate(Mdl,nr);
GARCH(1,1) Conditional Variance Model with Offset (Gaussian Distribution): Value StandardError TStatistic PValue _________ _____________ __________ _________ Constant 0.0044476 0.007814 0.56918 0.56923 GARCH{1} 0.84932 0.26495 3.2056 0.0013477 ARCH{1} 0.07325 0.14953 0.48986 0.62423 Offset 0.11227 0.039214 2.8629 0.0041974
Simulate 100 paths of conditional variances and responses for each period from the estimated GARCH model.
numObs = numel(nr); % Sample size (T) numPaths = 100; % Number of paths to simulate rng(1); % For reproducibility [VSim,YSim] = simulate(EstMdl,numObs,'NumPaths',numPaths);
VSim
and YSim
are T
-by- numPaths
matrices. Rows correspond to a sample period, and columns correspond to a simulated path.
Plot the average and the 97.5% and 2.5% percentiles of the simulated paths. Compare the simulation statistics to the original data.
VSimBar = mean(VSim,2); VSimCI = quantile(VSim,[0.025 0.975],2); YSimBar = mean(YSim,2); YSimCI = quantile(YSim,[0.025 0.975],2); figure; subplot(2,1,1); h1 = plot(dates,VSim,'Color',0.8*ones(1,3)); hold on; h2 = plot(dates,VSimBar,'k--','LineWidth',2); h3 = plot(dates,VSimCI,'r--','LineWidth',2); hold off; title('Simulated Conditional Variances'); ylabel('Cond. var.'); xlabel('Year'); subplot(2,1,2); h1 = plot(dates,YSim,'Color',0.8*ones(1,3)); hold on; h2 = plot(dates,YSimBar,'k--','LineWidth',2); h3 = plot(dates,YSimCI,'r--','LineWidth',2); hold off; title('Simulated Nominal Returns'); ylabel('Nominal return (%)'); xlabel('Year'); legend([h1(1) h2 h3(1)],{'Simulated path' 'Mean' 'Confidence bounds'},... 'FontSize',7,'Location','NorthWest');
Forecast GARCH Model Conditional Variances
Forecast conditional variances from a fully specified garch
model object. That is, forecast from an estimated garch
model or a known garch
model in which you specify all parameter values. The example follows from Estimate GARCH Model.
Load the Data_Danish
data set.
load Data_Danish;
nr = DataTable.RN;
Create a GARCH(1,1) model with an unknown conditional mean offset, and fit the model to the annual, nominal return series.
Mdl = garch('GARCHLags',1,'ARCHLags',1,'Offset',NaN); EstMdl = estimate(Mdl,nr);
GARCH(1,1) Conditional Variance Model with Offset (Gaussian Distribution): Value StandardError TStatistic PValue _________ _____________ __________ _________ Constant 0.0044476 0.007814 0.56918 0.56923 GARCH{1} 0.84932 0.26495 3.2056 0.0013477 ARCH{1} 0.07325 0.14953 0.48986 0.62423 Offset 0.11227 0.039214 2.8629 0.0041974
Forecast the conditional variance of the nominal return series 10 years into the future using the estimated GARCH model. Specify the entire returns series as presample observations. The software infers presample conditional variances using the presample observations and the model.
numPeriods = 10; vF = forecast(EstMdl,numPeriods,nr);
Plot the forecasted conditional variances of the nominal returns. Compare the forecasts to the observed conditional variances.
v = infer(EstMdl,nr); figure; plot(dates,v,'k:','LineWidth',2); hold on; plot(dates(end):dates(end) + 10,[v(end);vF],'r','LineWidth',2); title('Forecasted Conditional Variances of Nominal Returns'); ylabel('Conditional variances'); xlabel('Year'); legend({'Estimation sample cond. var.','Forecasted cond. var.'},... 'Location','Best');
More About
GARCH Model
A GARCH model is a dynamic model that addresses conditional heteroscedasticity, or volatility clustering, in an innovations process. Volatility clustering occurs when an innovations process does not exhibit significant autocorrelation, but the variance of the process changes with time.
A GARCH model posits that the current conditional variance is the sum of these linear processes, with coefficients for each term:
Past conditional variances (the GARCH component or polynomial)
Past squared innovations (the ARCH component or polynomial)
Constant offsets for the innovation mean and conditional variance models
Consider the time series
where The GARCH(P,Q) conditional variance process, , has the form
In lag operator notation, the model is
The table shows how the variables correspond to the properties of the garch
model object.
Variable | Description | Property |
---|---|---|
μ | Innovation mean model constant offset | 'Offset' |
κ > 0 | Conditional variance model constant | 'Constant' |
GARCH component coefficients | 'GARCH' | |
ARCH component coefficients | 'ARCH' | |
zt | Series of independent random variables with mean 0 and variance 1 | 'Distribution' |
For stationarity and positivity, GARCH models use these constraints:
Engle’s original ARCH(Q) model is equivalent to a GARCH(0,Q) specification.
GARCH models are appropriate when positive and negative shocks of equal magnitude contribute equally to volatility [1].
Tips
You can specify a garch
model as part of a composition of conditional mean and variance models. For details, see arima
.
References
[1] Tsay, R. S. Analysis of Financial Time Series. 3rd ed. Hoboken, NJ: John Wiley & Sons, Inc., 2010.
Version History
Introduced in R2012aR2023a: Name a GARCH model response series
You can name the response series of a GARCH model by setting the
SeriesName
property of the associated model 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 GARCH model
Describe a GARCH model 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 GARCH
and ARCH
properties.
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 indices of zero 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.ARCH{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
garch
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.
See Also
Objects
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