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Estimate AR and ARMA Models

AR and ARMA models are autoregressive parametric models that have no measured inputs. These models operate on time series data.

  • The AR model contains a single polynomialA在测得的输出上运行。对于单输出信号y(t），AR模型由以下公式给出：

    A ( q ) y ( t ) = e ( t )

  • The ARMA model adds a second polynomialCthat calculates the moving average of the noise error. The ARMA model for a single-output time series is given by the following equation:

    A ( q ) y ( t ) = C ( q ) e ( t )

    ARMA结构减少到AR结构C(q）= 1。

AR和ARMA模型结构是更通用的ARX和ARMAX模型结构的特殊情况，确实为测量的输入提供了。您可以在命令行和应用中估算AR和ARMA模型。

For information about:

Estimate AR and ARMA Models at the Command Line

通过使用ar,arx,ivar, orarmaxwith estimation data that contains only output measurements. These functions return estimated models that are represented byiDpolymodel objects.

估计多项式AR和ARMA时间序列模型的选定命令

功能 描述
ar

Noniterative, least-squares method to estimate linear, discrete-time, single-output AR models. Provides algorithmic options including lattice-based approaches and the Yule-Walker covariance approach.

例子：sys = ar(y,na)estimates an AR modelsysof polynomial orderNAfrom the scalar time seriesy。
arx

用于估计线性AR模型的非词汇最小二乘法。万博1manbetx支持多个输出。假设白噪声。

例子：sys = arx（y，na）估计从多输出时间序列中的AR模型y。
ivar

用于估计单输出AR模型的非涉及仪器变量方法。对噪声颜色不敏感。

例子：sys = ivar(y,na)使用标量时间序列的仪器变量方法估算AR模型y。
armax

Iterative prediction-error method to estimate linear ARMA models.

例子：sys = armax(y,[na nc])估计多项式订单的ARMA模型NA和NCfrom the time seriesy。

有关这些功能可以估算的其他模型的信息，以及有关其他模型的信息，请参见ar,arx,ivar， 和armax。

估计应用中的AR和ARMA时间序列模型

在开始之前，请完成以下步骤：

Estimate AR and ARMA models using the System Identification app by following these steps.

  1. 在里面System Identification app, selectEstimate>多项式模型打开“多项式型号”对话框。

  2. 在里面结构list, select the polynomial model structure you want to estimate from the following options:

    • AR：[NA]

    • ARMA:[na nc]

    This action updates the options in the Polynomial Models dialog box to correspond with this model structure.

  3. 在里面Orders字段，指定模型订单。

    • For single-output models, enter the model orders according to the sequence displayed in the结构field.

    • For multiple-output ARX models, enter the model orders directly, as described inPolynomial Sizes and Orders of Multi-Output Polynomial Models。Alternatively, enter the name of the matrixNA在存储模型订单的MATLAB工作区浏览器中，纽约-经过-纽约。

    要使用订单编辑器对话框输入模型订单和延迟，请单击订单编辑器。

  4. (AR models only) Select the estimationMethodasARX或者iv（仪器变量方法）。有关这些方法的更多信息，请参见多项式模型估计算法。

  5. Select添加噪声集成如果您想在噪声源中包括一个集成器e(t）。This selection changes an AR model into an ARI model ( A y = e 1 − q − 1 ) and an ARMA model into an ARIMA model ( A y = C 1 − q − 1 e ( t ) ）。

  6. 在里面Namefield, edit the name of the model or keep the default. The name of the model must be unique in the Model Board.

  7. 在里面初始状态列表，指定您希望算法如何处理初始状态。有关可用选项的更多信息，请参阅Specifying Initial States for Iterative Estimation Algorithms。

    If you get an inaccurate fit, try setting a specific method for handling initial states rather than specifying automatic selection.

  8. 在里面Covariancelist, selectEstimateif you want the algorithm to compute parameter uncertainties. Effects of such uncertainties are displayed on plots as model confidence regions.

    If you do not want the algorithm to estimate uncertainty, select没有任何。Skipping uncertainty computation can reduce computation time for complex models and large data sets.

  9. ClickRegularizationto obtain regularized estimates of model parameters. Specify regularization constants in the Regularization Options dialog box. For more information, seeRegularized Estimates of Model Parameters。

  10. 要查看命令行的估计进度，请选择显示进度check box. During estimation, the following information is displayed for each iteration:

    • Loss function — Determinant of the estimated covariance matrix of the input noise.

    • 参数值 - 您指定的模型结构系数的值。

    • 搜索方向 - 从上一个迭代中的参数值更改。

    • Fit improvements — Actual versus expected improvements in the fit.

  11. ClickEstimate将此模型添加到系统标识应用程序中的模型板中。

  12. 对于预测错误方法，仅在当前迭代完成后停止搜索并保存结果，请单击Stop Iterations。要继续从当前模型进行迭代，请单击Continue iterbutton to assign current parameter values as initial guesses for the next search and start a new search. For the multi-output case, you can stop iterations for each output separately. Note that the software runs independent searches for each output.

  13. To plot the model, select the appropriate check box in the模型视图系统标识应用程序的区域。

You can export the model to the MATLAB workspace for further analysis by dragging it to the到工作区系统标识应用程序中的矩形。

See Also

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