I'm experimenting with a trading indicator based on the correlation of the closing price of a day and the simple moving average of P periods. When the correlation is above certain threshold, I need to determine at what closing price the correlation of this day will be go below that threshold.
Example:
y, is the simple moving average of 5 periods, starting at t4.
r, is calculated with previous 5 periods.
t0: x0=1, y0=(1)/1
t1: x1=2, y1=(1+2)/2
t2: x2=3, y2=(1+2+3)/3
t3: x3=4, y3=(1+2+3+4)/4
t4: x4=5, y4=(1+2+3+4+5)/5 ,r4=1
t5: x5=7, y5=(2+3+4+5+7)/5 ,r5= 0.9974
t6: x6=6, y6=(3+4+5+7+6)/5 ,r6=0.8826
t7: x7=8, y7=(4+5+7+6+8)/5 ,r7= 0.906
t8: x8=9, y8=(5+7+6+8+9)/5 ,r8= 0.917
Q: t9: x9=?, y9=(7+6+8+9+x9)/5, r9=0.9
How do I get x9 (nearest to x8) for r9=0.9.
I'd like to know if there's a general solution so that f(x) may not necessarily be the simple moving average but another linear function.
Thanks in advance.
Update:
In the previous example, y12 is calculated based on x12 and y11. So, in this case I just need to know x12 to calculate r12. But What I want is the value of x13 at which r13 crosses certain limit which is closer to x12 (I'm thinking that in this example that value should be higher than x12). For now I'm just using a loop to determine that value calculating r in each loop untill I get an approximated value that crosses the limit but I don't like it.