# Compute localized autocovariance.

### Description

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.

### Usage

1 2 3 |

### Arguments

`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 |

### Details

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.

### Value

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.

### Author(s)

Guy Nason.

### References

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.

### See Also

`Rvarlacf`

### Examples

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