lmACF {fractal} | R Documentation

## ACF, PACF, and ACVF for various stochastic fractal time series models

### Description

Computes the autocovariance, autocorrelation or partial autocorrelation sequences for various stochastic fractal time series models.

### Usage

    lmACF(x, lag.max=32, type="correlation")

### Arguments

`x` | an object of class `"lmModel"`. Use the `lmModel` function to create this input.
`lag.max` | the maximum number of lags at which to compute the autocovariance, the autocorrelation or the partial autocorrelation. Default: `32`.
`type` | a character string defining the output type based on the following options: "covariance" autocovariance sequence "correlation" autocorrelation sequence "partial" partial autocorrelation sequence Default: `"correlation"`.

### Details

The autocovariance sequence is computed using Equation (2.10) of Beran (1994). The autocorrelation sequence is computed by dividing the autocovariance sequence by the variance of the process (i.e., the value of the autocovariance sequence at lag zero). The partial autocorrelation sequence is computed using the Levinson-Durbin recursions.

### Value

an object of class `signalSeries` containing the result.

### References

D. Percival and A. Walden (2000), Wavelet Methods for Time Series Analysis, Cambridge University Press, Chapter 7.

J. Beran (1994), Statistics for Long-Memory Processes, Chapman and Hall, Chapter 2.

D. Percival and A. Walden (1993), Spectral Analysis for Physical Applications, Cambridge University Press, 1993, Chapter 9.

### See Also

`lmModel`, `lmSDF`, `lmSimulate`, `ACVStoPACS`.

### Examples

    models <- c("ppl","fdp","fgn")
    lag <- 100
    z <- lapply(models, function(x, models, lag)
        { lmACF(lmModel(x), lag=lag)@data},
        models=models, lag=lag)
    names(z) <- paste(upperCase(models), "ACF")
    stackPlot(seq(0,lag), z, xlab="lag")
    title("Stochastic Fractal Model ACFs")

[Package fractal version 1.0-1 Index]