NAG Library Manual, Mark 27.2
```/* nag_tsa_multi_corrmat_partlag (g13dnc) Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
*
* Mark 27.2, 2021.
*/

#include <math.h>
#include <nag.h>
#include <stdio.h>
#include <string.h>

static void zprint(Integer, Integer, Integer, Integer, double *, double *,
double *);

int main(void) {
/* Scalars */
Integer exit_status, i, j, k, m, maxlag, n, kmax;
/* Arrays */
double *parlag = 0, *pvalue = 0, *r0 = 0, *r = 0, *w = 0, *wmean = 0;
double *x = 0;
Nag_CovOrCorr matrix;
NagError fail;

#define W(I, J) w[(J - 1) * kmax + I - 1]

INIT_FAIL(fail);

exit_status = 0;

printf("nag_tsa_multi_corrmat_partlag (g13dnc) Example Program Results\n");

/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%*[^\n] ", &k, &n, &m);

if (k > 0 && n >= 1 && m >= 1) {
/* Allocate arrays */
if (!(parlag = NAG_ALLOC(k * k * m, double)) ||
!(pvalue = NAG_ALLOC(m, double)) || !(r0 = NAG_ALLOC(k * k, double)) ||
!(r = NAG_ALLOC(k * k * m, double)) ||
!(w = NAG_ALLOC(k * n, double)) || !(wmean = NAG_ALLOC(k, double)) ||
!(x = NAG_ALLOC(m, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

kmax = k;

for (i = 1; i <= k; ++i) {
for (j = 1; j <= n; ++j)
scanf("%lf", &W(i, j));
scanf("%*[^\n] ");
}

matrix = Nag_AutoCorr;

/* nag_tsa_multi_corrmat_cross (g13dmc).
* Multivariate time series, sample cross-correlation or
* cross-covariance matrices
*/
nag_tsa_multi_corrmat_cross(matrix, k, n, m, w, wmean, r0, r, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_tsa_multi_corrmat_cross (g13dmc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

/* nag_tsa_multi_corrmat_partlag (g13dnc).
* Multivariate time series, sample partial lag correlation
* matrices, chi^2 statistics and significance levels
*/
nag_tsa_multi_corrmat_partlag(k, n, m, r0, r, &maxlag, parlag, x, pvalue,
&fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_tsa_multi_corrmat_partlag (g13dnc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
zprint(k, n, m, k, parlag, x, pvalue);
}

END:
NAG_FREE(parlag);
NAG_FREE(pvalue);
NAG_FREE(r0);
NAG_FREE(r);
NAG_FREE(w);
NAG_FREE(wmean);
NAG_FREE(x);

return exit_status;
}

/* Print the partial lag correlation matrices. */
static void zprint(Integer k, Integer n, Integer m, Integer ik, double *parlag,
double *x, double *pvalue) {
/* Scalars */
double c1, c2, c3, c5, c6, c7, cnst, sum;
Integer i2, i, j, lf, llf, ii, jj;

/* Arrays */
char rec[7][80];

#define PARLAG(I, J, K) parlag[((K - 1) * ik + (J - 1)) * ik + I - 1]

cnst = 1.0 / sqrt((double)n);

printf("\n");
printf(" PARTIAL LAG CORRELATION MATRICES\n");
printf(" --------------------------------\n");

for (lf = 1; lf <= m; ++lf) {
printf("\n");
printf(" Lag = %2" NAG_IFMT "\n", lf);
for (ii = 1; ii <= k; ii++) {
for (jj = 1; jj <= k; jj++)
printf("%9.3f", PARLAG(ii, jj, lf));
printf("\n");
}
}

printf("\n");
printf(" Standard error = 1 / SQRT(N) = %5.3f\n", cnst);

/* Print indicator symbols to indicate significant elements. */
printf("\n");
printf(" TABLES OF INDICATOR SYMBOLS\n");
printf(" ---------------------------\n");
printf("\n");
printf(" For Lags 1 to %2" NAG_IFMT "\n", m);
printf("\n");

/* Set up the critical values */
c1 = cnst * 3.29;
c2 = cnst * 2.58;
c3 = cnst * 1.96;
c5 = -c3;
c6 = -c2;
c7 = -c1;

for (i = 1; i <= k; ++i) {
for (j = 1; j <= k; ++j) {
printf("\n");
printf("\n");
if (i == j) {
printf("Auto-correlation function for series %2" NAG_IFMT "\n", i);
printf("\n");
} else {
printf("Cross-correlation function for series %2" NAG_IFMT ""
" and series%2" NAG_IFMT "\n",
i, j);
printf("\n");
}

/* Clear the last plot with blanks */
sprintf(&rec[0][0], "              0.005  :");
sprintf(&rec[1][0], "        +     0.01   :");
sprintf(&rec[2][0], "              0.05   :");
sprintf(&rec[3][0], "   Sig. Level        : - - - - - - - - - -  Lags");
sprintf(&rec[4][0], "              0.05   :");
sprintf(&rec[5][0], "        -     0.01   :");
sprintf(&rec[6][0], "              0.005  :");
for (i2 = 0; i2 < 7; ++i2) {
for (ii = strlen(&rec[i2][0]); ii < 80; ii++)
rec[i2][ii] = ' ';
}

for (lf = 1; lf <= m; ++lf) {
llf = lf * 2 + 21;
sum = PARLAG(i, j, lf);
/* Check for significance */
if (sum > c1)
rec[0][llf] = '*';
if (sum > c2)
rec[1][llf] = '*';
if (sum > c3)
rec[2][llf] = '*';
if (sum < c5)
rec[4][llf] = '*';
if (sum < c6)
rec[5][llf] = '*';
if (sum < c7)
rec[6][llf] = '*';
}

/* Print */
for (i2 = 0; i2 < 7; ++i2) {
/* Terminate the string */
for (ii = 80; ii > 1 && rec[i2][ii - 1] == ' '; ii--)
;
rec[i2][ii] = '\0';
/* Print the string */
printf("%s\n", &rec[i2][0]);
}
}
}

/* Print the chi-square statistics and p-values. */
printf("\n");
printf(" Lag     Chi-square statistic     P-value\n");
printf(" ---     --------------------     -------\n");
printf("\n");

for (lf = 1; lf <= m; ++lf)
printf("%4" NAG_IFMT " %17.3f %18.4f\n", lf, x[lf - 1], pvalue[lf - 1]);

return;
}
```