Definition of a proxy in this context

An ARIMA model is a statistical model. I'm having problems to understand it.

The definition I found on Cambridge dictionary:

A situation, process, or activity to which another situation, etc. is compared, especially in order to calculate how successful or unsuccessful it is

The examples I found on internet don't seem help much in this context. Could you help me with other examples in this context?

If the ARIMA model isn't exactly equivalent to N, it can be a proxy for it in the sense of a stand-in, since the aim is to "get better information from our preliminary LFT model." The ARIMA model represents/does the job of/approximates N.

In other words, using the ARIMA model gives a more accurate evaluation than estimating as was done in (5.3.1).

proxy (n.)

3.a A person appointed or authorized to act on behalf of another; an attorney; a representative, an agent; a substitute.

b. figurative.
Leaving only lights of cities and fires to serve as ghostly proxies of the sites of human activity.

4. Chiefly Science and Economics. A variable that can be used as an indirect estimate of another variable with which it is correlated; (more generally) a property used as an estimate or indicator of another with which it is associated. Frequently attributive. OED

In this case ARIMA is proxy model for N.

Another common example of latent variables is when the quantity we can measure is a proxy for the variable we are interested in, such as the earlier example where we used TDR as a proxy for soil moisture (section 6.3). M. C. Dietze; Ecological Forecasting, p.109

The number of living children, which is a proxy for the variable representing household structure, is expected to capture the effect of informal familial support for their aged parent upon his/her participation. N. Ogawa et al.; Human Resources in Development Along the Asia-Pacific Rim, p.361

A proxy variable is a variable that is used to measure an unobservable quantity of interest. Although a proxy variable is not a direct measure of the desired quantity, a good proxy variable is strongly related to the unobserved variable of interest. M. Lewis-Beck et al.; The SAGE Encyclopedia of Social Science Research Methods, p.878