I am currently completing my dissertation and I need to compare some wave data.
I have the forecast wave heights and the actual wave heights. I need to find how accurate the forecast wave heights were and therefore need the correct statistical test or multiple!
Thank you,
You are using a time series model to estimate Wave Height. Therefore, you need to run time series diagnostics as part of the overall goodness-of-fit diagnostics.

1] Diagnostics based on residuals: define Residual = Wave Height - Predicted Wave Height.

1.1] Estimate autocorrelation function (ACF) and partial autocorrelation function (PACF) of the residuals and see if they are statistically significant for any of the lags.

1.2] Run Ljung-Box test on the residuals to see if your model captures the serial correlation in the data overall (for all the lags).

1.3] Run Breusch-Pagan test on the residuals to see if there is any unaccounted heteroskedasticity in the data (stochastic volatility effects).

2] Diagnostics based on modeling extensions:

2.1] Whatever you model is, estimate [Your Model] + GARCH(1,1). If the GARCH coefficients are statistically significant, switch to the newly developed extension and improve it. Your original model does not capture heteroskedastic effects (stochastic volatility effects) well.

2.2] Try other modeling extensions and see if the "additions" are statistically significant. Have you considered all the possible predictors of Wave Height, those that are publicly observable?