R Graphical Manual

Browse All

Last data update: 2014.03.03

R: plot the theoretical ACF corresponding to an ARMA model

plotArmaTrueacf

R Documentation

plot the theoretical ACF corresponding to an ARMA model

Description

Compute the roots and theoretical ACF corresponding to an ARMA model

Usage

plotArmaTrueacf(object, lag.max=20, pacf=FALSE, plot=TRUE,
          xlab="lag", ylab=c("ACF", "PACF")[1+pacf],
          ylim=c(-1, 1)*max(ACF), type="h",
          complex.eps=1000*.Machine[["double.neg.eps"]], ...)

Arguments

`object`	either a numeric vector or a list with components 'ar' and 'ma'. If 'object' is numeric, it is interpreted as a model with no 'ma' part.
`lag.max`	the maximum number of lags for which to calculate the ACF or PACF
`pacf`	logical. Should the partial autocorrelations be returned?
`plot`	logical. Should the ACF (or PACF) be plotted?
`xlab, ylab, ylim, type`	arguments for 'plot'
`complex.eps`	a small positive number used to identify complex conjugates: Let 'roots' = the vector of p roots of the characteristic polynomial of the autoregressive part of 'object'. This is used by 'findConjugates': x[i] and x[j] are considered conjugate if their relative difference exceeds complex.eps but the relative difference of their conjugates is less than complex.eps. We use 'solve' in the 'polynom' package, because it was substially more accurate for cases we tested in R 2.6.0 than 'polyroot'.
`...`	optional arguments passed to 'plot'

Details

1. Compute and test stationarity. An ARMA process is stationary if all the roots of its AR component lie inside the unit circle (Box and Jenkins, 1970). If the process is not stationary, a warning is issued, and no plot is produced.

2. Compute and plot the theoretical ACF.

3. Analyze periodicity of any complex roots

Value

a list with the following components

`roots`	a complex vector of the roots sorted by modulus and sign of the immaginary part.
`acf, pacf`	a named numeric vector of the estimated ACF (or PACF of 'pacf = TRUE').
`periodicity`	a data.frame with one row for each complex conjugate pair of roots and columns 'damping' and 'period'.

Source

http://faculty.chicagogsb.edu/ruey.tsay/teaching/fts2

References

George E. P. Box and Gwilym M. Jenkins (1970) Time Series Analysis, Forecasting and Control (Holden-Day, sec. 3.4.1. Stationarity and invertibility properties of Mixed autoregressive-moving average processes)

Ruey Tsay (2005) Analysis of Financial Time Series, 2nd ed. (Wiley, ch. 2)

Examples

# Tsay, Figure 2.3
op <- par(mfcol=c(1, 2))
plotArmaTrueacf(.8, lag.max=8)
title("(a)")
plotArmaTrueacf(-.8, lag.max=8)
title("b")
par(op)

# Tsay, Figure 2.4
op <- par(mfrow=c(2,2))
plotArmaTrueacf(c(1.2, -.35))
title("(a)")
plotArmaTrueacf(c(.6, -.4))
title("(b)")
plotArmaTrueacf(c(.2, .35))
title("(c)")
plotArmaTrueacf(c(-.2, .35))
title("(d)")
par(op)

# Tsay, Example 2.1
data(q.gnp4791)
(fit.ar3 <- ar(q.gnp4791, aic=FALSE, order=3))
plotArmaTrueacf(fit.ar3)

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(FinTS)
Loading required package: zoo

Attaching package: 'zoo'

The following objects are masked from 'package:base':

    as.Date, as.Date.numeric

> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/FinTS/plotArmaTrueacf.Rd_%03d_medium.png", width=480, height=480)
> ### Name: plotArmaTrueacf
> ### Title: plot the theoretical ACF corresponding to an ARMA model
> ### Aliases: plotArmaTrueacf
> ### Keywords: hplot
> 
> ### ** Examples
> 
> # Tsay, Figure 2.3
> op <- par(mfcol=c(1, 2))
> plotArmaTrueacf(.8, lag.max=8)
$roots
[1] 0.8

$acf
        0         1         2         3         4         5         6         7 
1.0000000 0.8000000 0.6400000 0.5120000 0.4096000 0.3276800 0.2621440 0.2097152 
        8 
0.1677722 

$periodicity
[1] damping period 
<0 rows> (or 0-length row.names)

> title("(a)")
> plotArmaTrueacf(-.8, lag.max=8)
$roots
[1] -0.8

$acf
         0          1          2          3          4          5          6 
 1.0000000 -0.8000000  0.6400000 -0.5120000  0.4096000 -0.3276800  0.2621440 
         7          8 
-0.2097152  0.1677722 

$periodicity
[1] damping period 
<0 rows> (or 0-length row.names)

> title("b")
> par(op)
> 
> # Tsay, Figure 2.4
> op <- par(mfrow=c(2,2))
> plotArmaTrueacf(c(1.2, -.35))
$roots
[1] 0.7 0.5

$acf
          0           1           2           3           4           5 
1.000000000 0.888888889 0.716666667 0.548888889 0.407833333 0.297288889 
          6           7           8           9          10          11 
0.214005000 0.152754889 0.108404117 0.076620729 0.054003434 0.037986865 
         12          13          14          15          16          17 
0.026683037 0.018724241 0.013130027 0.009202547 0.006447548 0.004516166 
         18          19          20 
0.003162757 0.002214650 0.001550616 

$periodicity
[1] damping period 
<0 rows> (or 0-length row.names)

> title("(a)")
> plotArmaTrueacf(c(.6, -.4))
$roots
[1] 0.3+0.5567764i 0.3-0.5567764i

$acf
            0             1             2             3             4 
 1.000000e+00  4.285714e-01 -1.428571e-01 -2.571429e-01 -9.714286e-02 
            5             6             7             8             9 
 4.457143e-02  6.560000e-02  2.153143e-02 -1.332114e-02 -1.660526e-02 
           10            11            12            13            14 
-4.634697e-03  3.861285e-03  4.170650e-03  9.578759e-04 -1.093534e-03 
           15            16            17            18            19 
-1.039271e-03 -1.861489e-04  3.040191e-04  2.568710e-04  3.251496e-05 
           20 
-8.323941e-05 

$periodicity
    damping   period
1 0.6324555 5.836244

> title("(b)")
> plotArmaTrueacf(c(.2, .35))
$roots
[1] -0.5  0.7

$acf
           0            1            2            3            4            5 
1.0000000000 0.3076923077 0.4115384615 0.1900000000 0.1820384615 0.1029076923 
           6            7            8            9           10           11 
0.0842950000 0.0528766923 0.0400785885 0.0265225600 0.0193320180 0.0131492996 
          12           13           14           15           16           17 
0.0093960662 0.0064814681 0.0045849168 0.0031854972 0.0022418203 0.0015632881 
          18           19           20 
0.0010972947 0.0007666098 0.0005373751 

$periodicity
[1] damping period 
<0 rows> (or 0-length row.names)

> title("(c)")
> plotArmaTrueacf(c(-.2, .35))
$roots
[1] -0.7  0.5

$acf
            0             1             2             3             4 
 1.0000000000 -0.3076923077  0.4115384615 -0.1900000000  0.1820384615 
            5             6             7             8             9 
-0.1029076923  0.0842950000 -0.0528766923  0.0400785885 -0.0265225600 
           10            11            12            13            14 
 0.0193320180 -0.0131492996  0.0093960662 -0.0064814681  0.0045849168 
           15            16            17            18            19 
-0.0031854972  0.0022418203 -0.0015632881  0.0010972947 -0.0007666098 
           20 
 0.0005373751 

$periodicity
[1] damping period 
<0 rows> (or 0-length row.names)

> title("(d)")
> par(op)
> 
> # Tsay, Example 2.1
> data(q.gnp4791)
> (fit.ar3 <- ar(q.gnp4791, aic=FALSE, order=3))

Call:
ar(x = q.gnp4791, aic = FALSE, order.max = 3)

Coefficients:
      1        2        3  
 0.3463   0.1770  -0.1421  

Order selected 3  sigma^2 estimated as  9.676e-05
> plotArmaTrueacf(fit.ar3)
$roots
[1] -0.5198738+0.0000000i  0.4330640+0.2928575i  0.4330640-0.2928575i

$acf
            0             1             2             3             4 
 1.000000e+00  3.768704e-01  2.539120e-01  1.252511e-02 -4.277277e-03 
            5             6             7             8             9 
-3.534199e-02 -1.477390e-02 -1.076216e-02 -1.319312e-03 -2.621925e-04 
           10            11            12            13            14 
 1.204899e-03  5.582584e-04  4.437810e-04  8.125443e-05  2.734832e-05 
           15            16            17            18            19 
-3.920653e-05 -2.028084e-05 -1.784643e-05 -4.197719e-06 -1.730075e-06 
           20 
 1.193835e-06 

$periodicity
    damping   period
1 0.5227905 10.56699

> 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>