| Library: | times |
| See also: | acfplot pacf pacfplot fft invfft |
| Quantlet: | acf | |
| Description: | computes the (sample) autocorrelation function for the time series x. The output vector starts with the autocorrelation r_0 at lag length 0 (and thus is equal to 1). The next entries are r_1, r_2 ... r_k. |
| Usage: | y = acf(x) | |
| Input: | ||
| x | T x 1 vector of observed time series | |
| Output: | ||
| y | (T-1) x 1 vector of sample autocorrelations | |
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
ac = acf(return)
acsqr = acf(return^2)
ac[2:13]~acsqr[2:13] ; output matrix
Contents of _tmp [ 1,] 0.036135 0.19351 [ 2,] 0.033234 0.0063057 [ 3,] -0.030004 0.063934 [ 4,] 0.013575 0.065805 [ 5,] -0.069839 0.047433 [ 6,] -0.0488 -0.034815 [ 7,] -0.019639 -0.041839 [ 8,] -0.016576 0.058419 [ 9,] -0.038026 0.050764 [10,] 0.13247 0.060905 [11,] 0.039088 -0.020016 [12,] 0.017175 -0.052257 The sample autocorrelations with maximal lag length k = 12. We have T = 261 observations and thus the confidence bands are +/- 0.12. r_10 of the DAX returns and r_1 of the squared DAX returns lie outside these bands.