Accounting for long-term serial correlation in a linear regression problem

Turbulence, Atmosphere and Climate Dynamics

生态环境科学

Gruzdev, A.N.^1

A. M. Obukhov Institute of Atmospheric Physics, Pyzhevsky per. 3, Moscow

119017, Russia^1

关键词: Autoregressive process;    Ground based measurement;    Linear regression problems;    Multiple linear regression models;    Multiple regression analysis;    Quasi-biennial oscillation;    Regression coefficient;    Total ozone measurements;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/231/1/012020/pdf
DOI  :  10.1088/1755-1315/231/1/012020

学科分类：环境科学（综合）

来源: IOP

【 摘 要 】

The method is proposed for accounting for the long-term serial correlation (autocorrelation) of data in a linear regression problem. A serially correlated residual series is presented as an autoregressive (AR) process of an order, k, that can be much larger than 1, and the autocorrelation (AK) function of the processes is calculated by solving the system of the Yule-Walker equations. Given the AK function, the corresponding AK matrix is constructed which enters the formulas for estimates of regression coefficients and their errors. The efficiency of the method is demonstrated on the base of the multiple regression analysis of data of ground-based measurements of the column NO2 content at the Zvenigorod Research Station, Russia, and overpass satellite total ozone measurements over the station. Estimates of regression coefficients and their errors depend on the AR order, k. At first the error increases with increasing k. Then it can approach its maximum and thereafter begin to decrease. In the case of NO2 and O3 at Zvenigorod the errors more than double in their maxima compared to the beginning values. The decrease in the error stops at larger k if k approaches the value such that the AR process of this order is able to account for important features of the AK function of the residual series. The multiple linear regression model for NO2 and O3 observations includes the seasonally dependent linear trends and the effects of the solar cycle, the quasi-biennial oscillation, the North Atlantic and Southern Oscillations, and the Pinatubo volcanic eruption. Annual and seasonally dependent estimates of these effects in NO2 and O3 have been obtained taking into account the serial correlation as long as 50 months.