In order to predict future observations of a noisedriven
system, we have to find a model that exactly or at
least approximately describes the behavior of the system so
that the current system state can be recovered from past
observations. However, sometimes it is very difficult to model
a system accurately, such as real ocean waves. It is therefore
particularly interesting to analyze ocean wave properties in
the time-domain using autoregressive moving average (ARMA)
models. Two ARMA/AR based models and their equivalent state
space representations will be used for predicting future ocean
wave elevations, where unknown parameters will be determined
using linear least squares and auto-covariance least squares
algorithms. Compared to existing wave prediction methods, in
this paper (i) an ARMA model is used to enhance the prediction
performance, (ii) noise covariances in the ARMA/AR model are
computed rather than guessed and (iii) we show that, in practice,
low pass filtering of historical wave data does not improve the
forecasting results.