just getting started in Signal Processing - easy question I am reading Cycle Analytics for Traders by John Ehlers and need help.

in the first section "Transfer Response" he refers to:



so if I had $4$ prices say $8+8+8+8$ then average would be $8$ and output/input $= 8/32 = 1/4$

but not equal to $1/4 + 8/4 + 8/4 + 8/4$ so I think I've misunderstood?

I don't want to infringe copyright so all I can do is guide you to amazon where you can view this section.
The symbol $z^{-1}$ refers to a delay of one sample interval, no matter how long this interval actually is. It comes from the $\mathcal{Z}$-transform: if $X(z)$ is the $\mathcal{Z}$-transform of a data sequence $x[n]$, then $X(z)z^{-1}$ is the transform of the delayed sequence $x[n-1]$.

The transfer function (i.e. the quotient of the $\mathcal{Z}$-transforms of output and input sequences) is given by

$$H(z)=\frac14\left(1+z^{-1}+z^{-2}+z^{-3}\right)\tag{1}$$

which in the time (sample) domain means that the output sequence $y[n]$ and the input sequence $x[n]$ are related by

$$y[n]=\frac14\left(x[n]+x[n-1]+x[n-2]+x[n-3]\right)\tag{2}$$

This is of course the average of the current and the past three data samples. If, as in your example, all data samples have the value $8$, then the output is

$$y[n]=\frac14\left(8+8+8+8\right)=8$$