Temporal disaggregation techniques of time series by related series : a comparison by a Monte Carlo experiment

This work presents a comparison of different techniques for disaggregating annual flow time series by a quarterly related indicator, based on a Monte Carlo experiment. A first goal of the study is related to the estimation of the autoregressive parameter implied by the solution proposed by Chow and Lin (1971), which is the most used technique by National Statistical Institutes (NSI). Three estimation approaches have been considered, being the more recurrent in the literature: the inversion of the relationship linking the first order aggregated autocorrelation and the autoregressive parameter at the highest frequency (Chow and Lin, 1971), the maximization of the log-likelihood (Bournay and Laroque, 1979), and the minimization of the sum of squared residual (Barbone, Bodo, and Visco, 1981). We evaluate the accuracy of the estimated autoregressive parameter from these approaches and compare the disaggregated series obtained with the simulated ones. Then, the comparison is extended to other regression-based techniques based on the proposals by Fernandez (1981), Litterman (1983), Santos Silva and Cardoso (2001) and Di Fonzo (2002). Nearly one hundred and fifty scenarios were designed, in order to detect the conditions that allow each technique to obtain the best dis- aggregation (in terms of in-sample and out-of-sample accuracy), verify whether a technique outperforms the other ones and evaluate the efficiency of the parameter estimates obtained maximizing the log-likelihood and minimizing the sum of squared residuals.