R: Autocorrelation Function Plots

acfPlot {fBasics} | R Documentation

## Autocorrelation Function Plots

### Description

Returns plots of autocorrelations including the autocorrelation function ACF, the partial ACF, the lagged ACF, and the Taylor effect plot.

The functions to display stylized facts are:

`acfPlot` | autocorrelation function plot,
`pacfPlot` | partial autocorrelation function plot,
`lacfPlot` | lagged autocorrelation function plot,
`teffectPlot` | Taylor effect plot.

### Usage

    acfPlot(x, labels = TRUE, ...)
    pacfPlot(x, labels = TRUE, ...)

    lacfPlot(x, n = 12, lag.max = 20, type = c("returns", "values"),
        labels = TRUE, ...)

    teffectPlot(x, deltas = seq(from = 0.2, to = 3, by = 0.2), lag.max = 10,
        ymax = NA, standardize = TRUE, labels = TRUE, ...)

### Arguments

`deltas` | the exponents, a numeric vector, by default ranging from 0.2 to 3.0 in steps of 0.2.
`labels` | a logical value. Whether or not x- and y-axes should be automatically labeled and a default main title should be added to the plot. By default `TRUE`.
`lag.max` | maximum lag for which the autocorrelation should be calculated, an integer.
`n` | an integer value, the number of lags.
`standardize` | a logical value. Should the vector `x` be standardized?
`type` | [lacf] - a character string which specifies the type of the input series, either "returns" or series "values". In the case of a return series as input, the required value series is computed by cumulating the financial returns: `exp(colCumsums(x))`
`x` | an uni- or multivariate return series of class `timeSeries` or any other object which can be transformed by the function `as.timeSeries()` into an object of class `timeSeries`.
`ymax` | maximum y-axis value on plot, `is.na(ymax)` TRUE, then the value is selected automatically.
`...` | arguments to be passed.

### Details

Autocorrelation Functions:
The functions `acfPlot` and `pacfPlot`, plot and estimate autocorrelation and partial autocorrelation function. The functions allow to get a first view on correlations within the time series. The functions are synonyme function calls for R's `acf` and `pacf` from the the `ts` package.

Taylor Effect:
The "Taylor Effect" describes the fact that absolute returns of speculative assets have significant serial correlation over long lags. Even more, autocorrelations of absolute returns are typically greater than those of squared returns. From these observations the Taylor effect states, that that the autocorrelations of absolute returns to the the power of `delta`, `abs(x-mean(x))^delta` reach their maximum at `delta=1`. The function `teffect` explores this behaviour. A plot is created which shows for each lag (from 1 to `max.lag`) the autocorrelations as a function of the exponent `delta`. In the case that the above formulated hypothesis is supported, all the curves should peak at the same value around `delta=1`.

### Value

`acfPlot`, `pacfplot`,
return an object of class `"acf"`, see `acf`.

`lacfPlot` returns a list with the following two elements: `Rho`, the autocorrelation function, `lagged`, the lagged correlations.

`teffectPlot`
returns a numeric matrix of order `deltas` by `max.lag` with the values of the autocorrelations.

### References

Taylor S.J. (1986); Modeling Financial Time Series, John Wiley and Sons, Chichester.

Ding Z., Granger C.W.J., Engle R.F. (1993); A long memory property of stock market returns and a new model, Journal of Empirical Finance 1, 83.

### Examples

    ## data -
       SPI <- LPP2005REC[, "SPI"]
       plot(SPI, type = "l", col = "steelblue", main = "SP500")
       abline(h = 0, col = "grey")

    ## teffectPlot -
       # Taylor Effect:
       teffectPlot(SPI)

[Package fBasics version 3042.89 Index]