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Last data update: 2014.03.03

R: Auto- and Cross- Covariance and -Correlation Function...

acf	R Documentation

Auto- and Cross- Covariance and -Correlation Function Estimation

Description

The function acf computes (and by default plots) estimates of the autocovariance or autocorrelation function. Function pacf is the function used for the partial autocorrelations. Function ccf computes the cross-correlation or cross-covariance of two univariate series.

Usage

acf(x, lag.max = NULL,
    type = c("correlation", "covariance", "partial"),
    plot = TRUE, na.action = na.fail, demean = TRUE, ...)

pacf(x, lag.max, plot, na.action, ...)

## Default S3 method:
pacf(x, lag.max = NULL, plot = TRUE, na.action = na.fail,
    ...)

ccf(x, y, lag.max = NULL, type = c("correlation", "covariance"),
    plot = TRUE, na.action = na.fail, ...)

## S3 method for class 'acf'
x[i, j]

Arguments

`x, y`	a univariate or multivariate (not `ccf`) numeric time series object or a numeric vector or matrix, or an `"acf"` object.
`lag.max`	maximum lag at which to calculate the acf. Default is 10log10(N/m)* where N is the number of observations and m the number of series. Will be automatically limited to one less than the number of observations in the series.
`type`	character string giving the type of acf to be computed. Allowed values are `"correlation"` (the default), `"covariance"` or `"partial"`. Will be partially matched.
`plot`	logical. If `TRUE` (the default) the acf is plotted.
`na.action`	function to be called to handle missing values. `na.pass` can be used.
`demean`	logical. Should the covariances be about the sample means?
`...`	further arguments to be passed to `plot.acf`.
`i`	a set of lags (time differences) to retain.
`j`	a set of series (names or numbers) to retain.

Details

For type = "correlation" and "covariance", the estimates are based on the sample covariance. (The lag 0 autocorrelation is fixed at 1 by convention.)

By default, no missing values are allowed. If the na.action function passes through missing values (as na.pass does), the covariances are computed from the complete cases. This means that the estimate computed may well not be a valid autocorrelation sequence, and may contain missing values. Missing values are not allowed when computing the PACF of a multivariate time series.

The partial correlation coefficient is estimated by fitting autoregressive models of successively higher orders up to lag.max.

The generic function plot has a method for objects of class "acf".

The lag is returned and plotted in units of time, and not numbers of observations.

There are print and subsetting methods for objects of class "acf".

Value

An object of class "acf", which is a list with the following elements:

`lag`	A three dimensional array containing the lags at which the acf is estimated.
`acf`	An array with the same dimensions as `lag` containing the estimated acf.
`type`	The type of correlation (same as the `type` argument).
`n.used`	The number of observations in the time series.
`series`	The name of the series `x`.
`snames`	The series names for a multivariate time series.

The lag k value returned by ccf(x, y) estimates the correlation between x[t+k] and y[t].

The result is returned invisibly if plot is TRUE.

Author(s)

Original: Paul Gilbert, Martyn Plummer. Extensive modifications and univariate case of pacf by B. D. Ripley.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth Edition. Springer-Verlag.

(This contains the exact definitions used.)

Examples

require(graphics)

## Examples from Venables & Ripley
acf(lh)
acf(lh, type = "covariance")
pacf(lh)

acf(ldeaths)
acf(ldeaths, ci.type = "ma")
acf(ts.union(mdeaths, fdeaths))
ccf(mdeaths, fdeaths, ylab = "cross-correlation")
# (just the cross-correlations)

presidents # contains missing values
acf(presidents, na.action = na.pass)
pacf(presidents, na.action = na.pass)

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(stats)
> png(filename="/home/ddbj/snapshot/RGM3/R_rel/result/stats/acf.Rd_%03d_medium.png", width=480, height=480)
> ### Name: acf
> ### Title: Auto- and Cross- Covariance and -Correlation Function Estimation
> ### Aliases: acf ccf pacf pacf.default [.acf
> ### Keywords: ts
> 
> ### ** Examples
> 
> require(graphics)
> 
> ## Examples from Venables & Ripley
> acf(lh)
> acf(lh, type = "covariance")
> pacf(lh)
> 
> acf(ldeaths)
> acf(ldeaths, ci.type = "ma")
> acf(ts.union(mdeaths, fdeaths))
> ccf(mdeaths, fdeaths, ylab = "cross-correlation")
> # (just the cross-correlations)
> 
> presidents # contains missing values
     Qtr1 Qtr2 Qtr3 Qtr4
1945   NA   87   82   75
1946   63   50   43   32
1947   35   60   54   55
1948   36   39   NA   NA
1949   69   57   57   51
1950   45   37   46   39
1951   36   24   32   23
1952   25   32   NA   32
1953   59   74   75   60
1954   71   61   71   57
1955   71   68   79   73
1956   76   71   67   75
1957   79   62   63   57
1958   60   49   48   52
1959   57   62   61   66
1960   71   62   61   57
1961   72   83   71   78
1962   79   71   62   74
1963   76   64   62   57
1964   80   73   69   69
1965   71   64   69   62
1966   63   46   56   44
1967   44   52   38   46
1968   36   49   35   44
1969   59   65   65   56
1970   66   53   61   52
1971   51   48   54   49
1972   49   61   NA   NA
1973   68   44   40   27
1974   28   25   24   24
> acf(presidents, na.action = na.pass)
> pacf(presidents, na.action = na.pass)
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>