81 time points seem to be quite enough to solve Your problem. Your ACF looks like ACF of second order autoregressive process

X(t+1) = a1X(t) + a2X(t-1) + e(t+1) ,

where e(t) is the error of forecast made at time t.

So my advice is as follows.

1. Estimate coefficients a1 and a2 by minimizing the sum of squares (e(t))^2, t = 2, 3, … , 80. (Note that oscillation of Your ACF indicates that roots z1 , z2 of characteristic equation

1 - a1z + a2z^2 must be complex valued).

2. Made 79 forecasts using the proposed model and estimate spectrum of the errors.

3. The model is adequate if the spectral density of the errors is uniform. You can test the spectrum by means of Kolmogorov’s criterium.

Sorry, I lost sight of the fact that the amplitude of Your ACF decreases rather slow. This fact may indicate that process X(t) is not stationary. In this case it would be better to apply the proposed model to differences

Y(t) = X(t) – X(t - 1)

rather than to X(t). Than You will have 80 differences and 78 errors.

I would advice to try and compare both variants.

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Some kind of rule of thumb is n/3, which means that your 30 ACFs are about OK to draw meaningful conclusions.