### Speaker

Dr
Aleksandr Gruzdev
(A.M. Obukhov Institute of Atmospheric Physics)

### Description

An autocorrelation, or serial correlation, affects values of regression coefficients and their confidence intervals estimated from a linear multiple-regression model. Usual way to account for the autocorrelation is the iterative Cochrane-Orcutt procedure that assumes that residuals (errors) are a 1-st order autoregressive process. Applying this procedure one assumes that it converges to a global minimum of the residual sum of squares. Another way is to solve directly matrix equations of a multivariate regression problem. If the serially correlated errors can be presented by an autoregressive process then the matrix exists which transforms correlated errors to uncorrelated errors. This matrix is related to the autocorrelation matrix of the autoregressive process. Given the autocorrelation matrix, regression coefficients and their errors can be calculated. One advantage of this procedure is that the order of autoregression accounting for autocorrelation of the residuals can take large values.
This report presents analysis of the residuals corresponding to multivariate regression to SBUV MOD 6 data after applying the two procedures. Autoregression order 1 is used in both cases. Spectral analysis of the residuals derived with the use of the Cochrane-Orcutt procedure shows that the residuals usually contain low-frequency variations. For example, the residuals corresponding to the lowest (32 hPa) level in the tropical belt (20S-20N) undergo variations with periods of about 20, 50, and 110 months. When one uses the second procedure to account for the autocorrelation, the long-period variations are absent in the residuals. It should be noted however that although the direct procedure has the advantage of more correct presentation of the “uncorrelated” errors, the estimates of the linear trends of ozone, at least for the data used, are close to each other for the two procedures.

### Primary author

Dr
Aleksandr Gruzdev
(A.M. Obukhov Institute of Atmospheric Physics)