/**
* @param y data
* @param k parameter giving the length 2 * k + 1 of the averaging interval
* @param l oder of the averaging polynomial
* @param p probability defining confidence limits
*/
public TimeSeries(double[] y, int k, int l, double p) {
this.y = y;
this.k = k;
this.l = l;
this.p = p;
n = y.length;
eta = new double[n + 2 * k];
coneta = new double[n + 2 * k];
// quantile of Student's distribution
pprime = 0.5 * (p + 1.);
nf = 2 * k - l;
talpha = StatFunct.quantileStudent(pprime, nf);
// compute matrices depending on k and l
k21 = 2 * k + 1;
l1 = l + 1;
a = new DatanMatrix(k21, l1);
for (int i = 0; i < k21; i++) {
for (int j = 0; j < l1; j++) {
if (j == 0) a.setElement(i, j, -1.);
else a.setElement(i, j, a.getElement(i, j - 1) * (double) (i - k));
}
}
ata1 = a.multiplyTransposedWith(a);
ata1.choleskyInversion();
ata1at = ata1.multiplyWithTransposed(a);
ata1at = ata1at.multiply(-1.);
// moving averages and confidence limits for inner part
ymat = new DatanMatrix(y);
for (int i = 2 * k; i < n; i++) {
ytmp = ymat.getSubmatrix(k21, 1, i - 2 * k, 0);
x = ata1at.multiply(ytmp);
eta[i] = x.getElement(0, 0);
etatmp = a.multiply(x);
etatmp = etatmp.add(ytmp);
sy2 = etatmp.multiplyTransposedWith(etatmp);
double s = sy2.getElement(0, 0) / (double) nf;
double a0 = Math.sqrt(Math.abs(ata1.getElement(0, 0)));
coneta[i] = a0 * Math.sqrt(s) * talpha;
// moving averages and confidence limits for end sections
if (i == 2 * k || i == n - 1) {
tt = new double[l + 1];
if (i == 2 * k) {
iadd = 2 * k;
is = -1;
} else {
iadd = n - 1;
is = 1;
}
for (int i1 = 1; i1 <= 2 * k; i1++) {
j = is * i1;
for (int i2 = 0; i2 < l + 1; i2++) {
for (int i3 = 0; i3 <= i2; i3++) {
if (i3 == 0) tt[i2] = 1.;
else tt[i2] = tt[i2] * (double) j;
}
}
tmat = new DatanMatrix(tt);
seta2 = tmat.multiplyTransposedWith(ata1.multiply(tmat));
double se2 = s * seta2.getElement(0, 0);
etai = tmat.multiplyTransposedWith(x);
eta[iadd + j] = etai.getElement(0, 0);
coneta[iadd + j] = Math.sqrt(Math.abs(se2)) * talpha;
}
}
}
}