This paper considers an alternative method for fitting CARR models using combined estimating functions (CEF) by showing its usefulness in applications in economics and quantitative finance. The associated information matrix for corresponding new estimates is derived to calculate the standard errors. A simulation study is carried out to demonstrate its superiority relative to other two competitors: linear estimating functions (LEF) and the maximum likelihood (ML). Results show that CEF estimates are more efficient than LEF and ML estimates when the error distribution is mis-specified. Taking a real data set from financial economics, we illustrate the usefulness and applicability of the CEF method in practice and report reliable forecast values to minimize the risk in the decision making process.