You probably just need to adjust a couple of lines:
minPeriod = 0.1;
maxPeriod = 0.6;
minVal = 0;
maxVal = 10;
accum = accumPrev = 100;
t = tPrev = 0;
seedRandom(index,true);
while(t <= time){
tPrev = t;
accumPrev = accum;
accum -= random(minVal,maxVal);
t += random(minPeriod,maxPeriod);
}
linear(time,tPrev,t,accumPrev,accum)