| Random walk is often used to characterize the change of short-term interest rate,which is oftentimes the key component of a financial research problem.However,in many problems,the random walk is often too simple to describe the real-world change in short term interest rate.Therefore,more complicated econometrical model has been proposed to address this limitation of random walk.But the empirical estimation of the unknown paralmeters in such models in general is very difficult and requires sophisticated methods such as method of moment.The statistical inference based on random moments have broad applications in statistics and especially econometrics.When the number of moment conditions is greater than the number of unknown parameters,the estimating equation based on the moment conditions in general is insolvable.The generalized method of moments(GMM)can be used to overcome this difficulty via minimizing an objective loss function.In general,GMM estimator is more efficient than that based on estimating equation based on moment conditions.In other words,when the sample size is adequately large,the parameter estimator based on GMM is closer to the true parameter.Although there are many merits,the GMM is not broadly used in practice,the main difficulty is the numerical computation needed to minimize the objective function.Especially,when the objective is not differentiable,monotone or even discontinuous,the computational difficult is even more significant.This thesis proposed a series of new methods to overcome aforementioned difficulties in numerical computation as well as statistic inference in applying GMM in practice via a simple(may not be very accurate)initial estimator.Specifically,this thesis proposed to construct a simple consistent estimator for the parameter of interest and then use the moment conditions used in GMM to improve the efficiency of this initial estimator.The main step is constructing the efficiency augmented estimator by a linear combination of a simple initial estimator and estimating equations based on moment conditions.This construction of this new estimator doesn’t involve with complex minimization for an objective function and the resulting estimator can be more efficient than the GMM estimator.Next,in order to avoid additional variance caused by using too many moment conditions,this thesis proposed a matrix regularization-based method to empirically select the moment conditions in improving the efficiency of the initial estimator.Using moment conditions to improve the efficiency of the initial estimator has broad applications.In order to study it application in practice,this thesis generalized the commonly used econometric model for short term interest rate and use the model to study the history of short-term interest in USA and several other countries.The final fitted model may help to understand the policy and style of central bank in adjusting the short-term interest in different periods.At the end of thesis,the thesis has also discussed the limitations of the new methods and potential future research directions. |
