The Southern Oscillation Index as a random walk

The Southern Oscillation Index (SOI) has been used as a predictor of variables associated with climatic data, such as rainfall and temperature, and is related to the El Nino and La Nina phenomena, also called the El Nino Southern Oscillation (ENSO). The present study aims to describe the characteristics of the SOI between 1876 and 2014 using statistical methods. The graph of the cumulative monthly SOI in the period 1876 - 2014 shows that the data can be divided into 4 periods. The first period, from 1876 to 1919, shows no trend. An increasing trend is apparent in the second period from 1920 until 1975, while a decreasing trend is apparent in the third period, 1976 to 1995. In the last period, between 1996 and 2014, the SOI appears fairly stable. In order to investigate those trends, the linear regression and autoregressive (AR) model have been fitted. For the linear regression model, the outcome, SOI, is regressed against boxcar function, where the functions model the trends of the SOI. An autoregressive process is used to account for serial correlation in the residuals. The conclusion is that the SOI is quite similar to a random noise process.