Spectral analysis of wave sea: univariate models

Abstract

Spectral analysis is the technical process of a complex signal decomposition into simpler parts. Many physical processes are better described as a sum of many individual frequency components; alternatively a signal can be divided into short segments and the spectrum analysis can be applied to these individual segments. From the point of view of the study of Waves Sea, the spectrum plays a vital role and it is interpreted as the energy in the time series during the period. This study is based on analysis of the spectrum associated to data from the North Sea in the year of 1999, taken in North Alwyn platform, stored in the Heriot-Watt University in Edinburgh, separated in periods of 20 minutes. The total of the studied periods is 244. Thus, it was determined that there is information that does not add information to the problem, and it represents noise, which is the 3% of energy and it was not taken for the study. The spectrum was divided into 12 subintervals. Autoregressive models were fitted under the scheme Box-Jenskin and Reinsel. The model was studied until the best possible approximation for each subinterval was found by the statistical properties obtained by each model, together with the respective forecasts.

Keywords: Spectrum, spectral analysis, frequency domain, autoregressive, models.