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Create lag operator polynomial

Create a *p*-degree, *m*-dimensional lag operator polynomial *A*(*L*) = *A*_{0} + *A*_{1}*L*^{1} + *A*_{2}*L*^{2} +...+ *A*_{p}*L*^{p} by specifying the coefficient matrices *A*_{0},…,*A*_{p} and, optionally, the corresponding lags. *L* is the *lag* (or *backshift*) operator such that *L*^{j}*y*_{t} = *y*_{t–j}.

`LagOp`

object functions enable you to work with specified polynomials. For example, you can filter time series data through a polynomial, determine whether one is stable, or combine multiple polynomials by performing polynomial algebra including addition, subtraction, multiplication, and division.

To fit a dynamic model containing lag operator polynomials to data, create the appropriate model object, and then fit it to the data. For univariate models, see `arima`

and `estimate`

; for multivariate models, see `varm`

and `estimate`

. For further analysis, you can create a `LagOp`

object from the resulting estimated coefficients.

creates a lag operator polynomial `A`

= LagOp(`coefficients`

)`A`

with coefficients `coefficients`

, and sets the Coefficients property.

specifies additional options using one or more name-value pair arguments. For example, `A`

= LagOp(`coefficients`

,`Name,Value`

)`LagOp(coefficients,'Lags',[0 4 8],'Tolerance',1e-10)`

associates the coefficients to lags `0`

, `4`

, and `8`

, and sets the lag inclusion tolerance to `1e-10`

.

`filter` | Apply lag operator polynomial to filter time series |

`isEqLagOp` | Determine if two `LagOp` objects are same
mathematical polynomial |

`isNonZero` | Find lags associated with nonzero coefficients of `LagOp` objects |

`isStable` | Determine stability of lag operator polynomial |

`minus` | Lag operator polynomial subtraction |

`mldivide` | Lag operator polynomial left division |

`mrdivide` | Lag operator polynomial right division |

`mtimes` | Lag operator polynomial multiplication |

`plus` | Lag operator polynomial addition |

`reflect` | Reflect lag operator polynomial coefficients around lag zero |

`toCellArray` | Convert lag operator polynomial object to cell array |