Option set for armax


opt = armaxOptions
opt = armaxOptions(Name,Value)


opt = armaxOptions creates the default options set for armax.

opt = armaxOptions(Name,Value) creates an option set with the options specified by one or more Name,Value pair arguments.

Input Arguments

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Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.


Specify how initial conditions are handled during estimation.

InitialCondition requires one of the following values:

  • 'zero' — The initial conditions are set to zero.

  • 'estimate' — The initial conditions are treated as independent estimation parameters.

  • 'backcast' — The initial conditions are estimated using the best least squares fit.

  • 'auto' — The software chooses the method to handle initial conditions based on the estimation data.


Defines how the errors e between the measured and the modeled outputs are weighed at specific frequencies during the minimization of the prediction error.

Higher weighting at specific frequencies emphasizes the requirement for a good fit at these frequencies.

Focus requires one of the following values:

  • 'simulation' — Estimates the model using the frequency weighting of the transfer function that is given by the input spectrum. Typically, this method favors the frequency range where the input spectrum has the most power.

    This method provides a stable model.

  • 'prediction' — Automatically calculates the weighting function as a product of the input spectrum and the inverse of the noise model. The weighting function minimizes the one-step-ahead prediction. This approach typically favors fitting small time intervals (higher frequency range). From a statistical-variance point of view, this weighting function is optimal. However, this method neglects the approximation aspects (bias) of the fit. Use 'stability' when you want to ensure a stable model.

  • 'stability' — Same as 'prediction', but with model stability enforced.

  • Passbands — Row vector or matrix containing frequency values that define desired passbands. For example:


    where wl and wh represent upper and lower limits of a passband. For a matrix with several rows defining frequency passbands, the algorithm uses union of frequency ranges to define the estimation passband.

  • SISO filter — Enter any SISO linear filter in any of the following ways:

    • A single-input-single-output (SISO) linear system

    • The {A,B,C,D} format, which specifies the state-space matrices of the filter

    • The {numerator, denominator} format, which specifies the numerator and denominator of the filter transfer function

      This option calculates the weighting function as a product of the filter and the input spectrum to estimate the transfer function. To obtain a good model fit for a specific frequency range, you must choose the filter with a passband in this range. You receive an estimation result that is the same as if you had first prefiltered using idfilt.

  • Weighting vector — For frequency-domain data only, enter a column vector of weights for 'Focus'. This vector must have the same length as the frequency vector of the data set, Data.Frequency. Each input and output response in the data is multiplied by the corresponding weight at that frequency.

'EstCovar' — Control whether to generate parameter covariance datatrue (default) | false

Controls whether parameter covariance data is generated, specified as true or false.

If EstCovar is true, then use getcov to fetch the covariance matrix from the estimated model.

'Display' — Specify whether to display the estimation progress'off' (default) | 'on'

Specify whether to display the estimation progress, specified as one of the following strings:

Display requires one of the following strings:

  • 'on' — Information on model structure and estimation results are displayed in a progress-viewer window

  • 'off' — No progress or results information is displayed

'InputOffset' — Remove offset from time-domain input data during estimation[] (default) | vector of positive integers

Removes offset from time-domain input data during estimation, specified as a vector of positive integers.

Specify as a column vector of length Nu, where Nu is the number of inputs.

Use [] to indicate no offset.

For multiexperiment data, specify InputOffset as a Nu-by-Ne matrix. Nu is the number of inputs, and Ne is the number of experiments.

Each entry specified by InputOffset is subtracted from the corresponding input data.

'OutputOffset' — Remove offset from time-domain output data during estimation[] (default) | vector

Removes offset from time domain output data during estimation, specified as a vector of positive integers or [].

Specify as a column vector of length Ny, where Ny is the number of outputs.

Use [] to indicate no offset.

For multiexperiment data, specify OutputOffset as a Ny-by-Ne matrix. Ny is the number of outputs, and Ne is the number of experiments.

Each entry specified by OutputOffset is subtracted from the corresponding output data.


Options for regularized estimation of model parameters. For more information on regularization, see Regularized Estimates of Model Parameters.

Structure with the following fields:

  • Lambda — Constant that determines the bias versus variance tradeoff.

    Specify a positive scalar to add the regularization term to the estimation cost.

    The default value of zero implies no regularization.

    Default: 0

  • R — Weighting matrix.

    Specify a vector of nonnegative numbers or a square positive semi-definite matrix. The length must be equal to the number of free parameters of the model.

    For black-box models, using the default value is recommended. For structured and grey-box models, you can also specify a vector of np positive numbers such that each entry denotes the confidence in the value of the associated parameter.

    The default value of 1 implies a value of eye(npfree), where npfree is the number of free parameters.

    Default: 1

  • Nominal — The nominal value towards which the free parameters are pulled during estimation.

    The default value of zero implies that the parameter values are pulled towards zero. If you are refining a model, you can set the value to 'model' to pull the parameters towards the parameter values of the initial model. The initial parameter values must be finite for this setting to work.

    Default: 0


Search method used for iterative parameter estimation.

SearchMethod requires one of the following values:

  • 'gn' — The subspace Gauss-Newton direction. Singular values of the Jacobian matrix less than GnPinvConst*eps*max(size(J))*norm(J) are discarded when computing the search direction. J is the Jacobian matrix. The Hessian matrix is approximated by JTJ. If there is no improvement in this direction, the function tries the gradient direction.

  • 'gna' — An adaptive version of subspace Gauss-Newton approach, suggested by Wills and Ninness [1]. Eigenvalues less than gamma*max(sv) of the Hessian are ignored, where sv are the singular values of the Hessian. The Gauss-Newton direction is computed in the remaining subspace. gamma has the initial value InitGnaTol (see Advanced for more information). This value is increased by the factor LMStep each time the search fails to find a lower value of the criterion in less than 5 bisections. This value is decreased by the factor 2*LMStep each time a search is successful without any bisections.

  • 'lm' — Uses the Levenberg-Marquardt method so that the next parameter value is -pinv(H+d*I)*grad from the previous one. H is the Hessian, I is the identity matrix, and grad is the gradient. d is a number that is increased until a lower value of the criterion is found.

  • 'lsqnonlin' — Uses lsqnonlin optimizer from Optimization Toolbox™ software. You must have Optimization Toolbox installed to use this option. This search method can handle only the Trace criterion.

  • 'grad' — The steepest descent gradient search method.

  • 'auto' — The algorithm chooses one of the preceding options. The descent direction is calculated using 'gn', 'gna', 'lm', and 'grad' successively at each iteration. The iterations continue until a sufficient reduction in error is achieved.


Options set for the search algorithm.

 SearchOption structure when SearchMethod is specified as 'gn', 'gna', 'lm', 'grad', or 'auto'

 SearchOption structure when SearchMethod is specified as ‘lsqnonlin'


Advanced is a structure with the following fields:

  • ErrorThreshold — Specifies when to adjust the weight of large errors from quadratic to linear.

    Errors larger than ErrorThreshold times the estimated standard deviation have a linear weight in the criteria. The standard deviation is estimated robustly as the median of the absolute deviations from the median and divided by 0.7. For more information on robust norm choices, see section 15.2 of [2].

    ErrorThreshold = 0 disables robustification and leads to a purely quadratic criterion. When estimating with frequency-domain data, the software sets ErrorThreshold to zero. For time-domain data that contains outliers, try setting ErrorThreshold to 1.6.

    Default: 0

  • MaxSize — Specifies the maximum number of elements in a segment when input-output data is split into segments.

    MaxSize must be a positive integer.

    Default: 250000

  • StabilityThreshold — Specifies thresholds for stability tests.

    StabilityThreshold is a structure with the following fields:

    • s — Specifies the location of the right-most pole to test the stability of continuous-time models. A model is considered stable when its right-most pole is to the left of s.

      Default: 0

    • z — Specifies the maximum distance of all poles from the origin to test stability of discrete-time models. A model is considered stable if all poles are within the distance z from the origin.

      Default: 1+sqrt(eps)

  • AutoInitThreshold — Specifies when to automatically estimate the initial condition.

    The initial condition is estimated when


    • ymeas is the measured output.

    • yp,z is the predicted output of a model estimated using zero initial conditions.

    • yp,e is the predicted output of a model estimated using estimated initial conditions.

    Applicable when InitialCondition is 'auto'.

    Default: 1.05

Output Arguments


Option set containing the specified options for armax.


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Specify Options for ARMAX Estimation

Create an options set for armax using the 'stability' for Focus. Set the Display to 'on'.

opt = armaxOptions('Focus','stability','Display','on');

Alternatively, use dot notation to set the values of opt.

opt = armaxOptions;
opt.Focus = 'stability';
opt.Display = 'on';


[1] Wills, Adrian, B. Ninness, and S. Gibson. "On Gradient-Based Search for Multivariable System Estimates". Proceedings of the 16th IFAC World Congress, Prague, Czech Republic, July 3–8, 2005. Oxford, UK: Elsevier Ltd., 2005.

[2] Ljung, L. System Identification: Theory for the User. Upper Saddle River, NJ: Prentice-Hall PTR, 1999.

See Also


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