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

 Quantlet: boxpi Description: computes the autocorrelation function (acf) and the Box-Pierce statistics for autocorrelation in a time series. Additionally, the p-values for the statistic are computed.

 Usage: qbp = boxpi(x {, maxlag}) Input: x T x 1 vector, time series maxlag (optional) integer, maximum lag for which the above described values are calculated, default is maxlag = 30 Output: qbp maxlag x 3 matrix, gives the autocorrelation function in the first column, the Box-Pierce statistics in the second and the p-values for the statistic in the third column (see the notes).

Note:
Under the hypothesis that x is white noise, the Box-Pierce statistic is asymptotically distributed as Chi-Square with p degrees of freedom. Here, p is the respective lag for which the statistic is computed.

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
qbp    = boxpi(return,6) ; calculates the acf, lb-stat and p-values
qbp

```
Result:
```Generates a matrix with the autocorrelation
function, the Box-Pierce statistics and the
corresponding p-values for the returns of the
German stock index DAX

Contents of qbp
[1,]  0.036135  0.34081  0.55935
[2,]  0.033234  0.62907  0.73012
[3,] -0.030004  0.86403  0.83409
[4,]  0.013575  0.91213  0.92281
[5,] -0.069839   2.1852  0.82297
[6,]  -0.0488   2.8067  0.83268
```

Author: M. Fengler, 20030402 license MD*Tech
(C) MD*TECH Method and Data Technologies, 05.02.2006