Compute localized autocovariance function for nonstationary
time series. Note: this function is borrowed from the `costat`

package, and modified to have linear smoothing, and when that package is complete, it will be removed
from this package.

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`x` |
The time series you wish to analyze |

`filter.number` |
Wavelet filter number you wish to use to
analyse the time series (to form the wavelet periodogram, etc)
See |

`family` |
Wavelet family to use, see |

`smooth.dev` |
Change variance estimate for smoothing. Note: |

`AutoReflect` |
If |

`lag.max` |
The maximum lag of acf required. If NULL then the
same default as in the regular |

`WPsmooth.type` |
The type of smoothing used to produce the
estimate. See |

`binwidth` |
If necessary, the |

`tol` |
Tolerance argument for |

`maxits` |
Maximum iterations argument for |

`ABBverbose` |
Verbosity of execution of |

`verbose` |
If |

`...` |
Other arguments for |

In essence, this routine is fairly simple. First, the EWS of the time series is computed. Then formula (14) from Nason, von Sachs and Kroisandr (2000) is applied to obtain the time-localized autocovariance from the spectral estimate.

An object of class `lacf`

which contains the
autocovariance. This object can be handled by functions
from the `costat`

package. The idea in this package
is that the function gets used internally and much of the
same functionality can be achieved by running
`Rvarlacf`

and `plot.lacfCI`

. However,
running `lacf`

on its own is much faster than
`Rvarlacf`

as the CI computation is intenstive.

Guy Nason.

Nason, G.P. (2013) A test for second-order stationarity and
approximate confidence intervals for localized autocovariances
for locally stationary time series. *J. R. Statist. Soc.* B,
**75**, 879-904.

Nason, G.P., von Sachs, R. and Kroisandt, G. (2000) Wavelet processes
and adaptive estimation of the evolutionary wavelet spectrum.
*J. R. Statist. Soc.* Ser B, **62**, 271-292.

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