This function computes the fitted residuals and fitted innovations from an AR(p>0) bent-cable regression.

1 | ```
cable.ar.p.resid(ar.p.fit)
``` |

`ar.p.fit` |
A |

Fitted residuals correspond to the detrended time series, where the fitted bent cable is subtracted from the data. They retain the autocorrelation structure of the response time series.

Fitted innovations are the *estimated* residual noise
after adjusting for the AR(p) structure, and should be
approximately independent if the AR(p) fit successfully
captures the actual autocorrelation in the data.

Both types of errors may be used for model diagnosis.

`resid ` |
A numeric vector of fitted residuals; it has the same length as the response data. |

`innov ` |
A numeric vector of fitted innovations; the first value in the vector corresponds to the (p+1)st time point. |

This function fails if `ar.p.fit`

is from a non-AR(p>0) fit.

The fitted innovations are only meaningful if `ar.p.fit`

is
associated with equidistant time points with unit increments.

This function is intended for internal use by `bentcable.ar`

.

Grace Chiu

See the `bentcableAR`

package references.

`cable.ar.p.diag`

1 2 3 4 5 | ```
data(sockeye)
fit.ar2 <- cable.ar.p.iter( c(13,.1,-.5,11,4,.5,-.5),
sockeye$logReturns, tol=1e-4 )
cable.ar.p.resid( fit.ar2 )
``` |

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