Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Library: times
See also: pacfplot acf acfplot fft invfft

Quantlet: pacf
Description: computes the (sample) partial autocorrelation function for the time series x. The output vector starts with the partial autocorrelation coefficient phi_1 at lag 1. The next entries are phi_2 ... phi_k.

Reference(s):

Usage: y = pacf(x {, maxlag})
Input:
x T x 1 vector of observed time series
maxlag (optional) integer; maximum lag length that will be calculated, default value is 30
Output:
y vector of sample partial autocorrelations with dimension 30 x 1 (default) or maxlag x 1.

Note:

Example:
library("times")           ; loads the quantlets from times library
dax    = read("dax.dat")   ; monthly DAX 1979:1-2000:10
return = tdiff(log(dax))   ; generates the monthly return
pac    = pacf(return,12)
pacsqr = pacf(return^2,12)
pac~pacsqr                 ; output matrix

Result:
Contents of _tmp
[ 1,]  0.036135    0.19351
[ 2,]  0.03197    -0.032352
[ 3,] -0.032397    0.071692
[ 4,]  0.014776    0.041088
[ 5,] -0.069044    0.030198
[ 6,] -0.045976   -0.053803
[ 7,] -0.011009   -0.030678
[ 8,] -0.017182    0.066633
[ 9,] -0.037066    0.027616
[10,]  0.13349     0.058726
[11,]  0.025715   -0.04407
[12,]  0.00055026 -0.049678
The sample partial autocorrelations with maximum lag length k = 12.
We have T = 261 observations and thus the confidence bands are
+/- 0.12. phi_10 of the DAX returns and phi_1 of the squared
DAX returns lie outside these bands.



Author: C. Hafner, R. Schulz, 20010419
(C) MD*TECH Method and Data Technologies, 05.02.2006