Accounting for Autocorrelation in the Linear Regression Problem by an Example of Analysis of the Atmospheric Column NO2 Content

Abstract

A method is proposed for accounting for serial correlation (autocorrelation) of data in the linear regression problem which enables accounting the autocorrelation on large scales. The residual series is represented as an autoregressive process of the order, k, that can be much greater than 1, and the autocorrelation function of the process is calculated by solving the system of the Yule-Walker equations. Given the autocorrelation function, the autocorrelation matrix is constructed that is included in formulas for estimates of regression coefficients and their standard errors. The efficiency of the method is demonstrated by the multiple regression analysis of data of 26-year measurements of the column NO₂ content at the Zvenigorod Research Station of the Institute of Atmospheric Physics. Estimates of regression coefficients and their errors depend on the order of autoregression, k. First, the error increases with increasing k. Then it reaches a maximum and next begins to decrease. In the case of NO₂, the maximum error is more than doubled compared to its initial value. The error decrease (after reaching the maximum) stops if k approaches the value at which the autoregressive process enables describing important features of the autocorrelation function of the residual series. Estimates of seasonally dependent NO₂ trends and effects on NO₂ of natural factors such as the 11-year solar cycle, the quasi-biennial oscillation, the North Atlantic Oscillation and others are obtained.