I’m currently completing my dissertation and need to compare forecasted wave height to the actual wave height. However I am unsure what statistical test to use.
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If I understand your question correctly, you're attempting to test whether your forecast is statistically different from an observed outcome.
If this is the case, then you want to use prediction intervals. Specifically, since your forecast is a random variable, you'll want to obtain the distribution of that r.v. and then perform a standard hypothesis test.
There are many ways to obtain a distribution for your forecast. The most general would be to utilize bootstrapping. Here is an example for an AR model.