Uniform Experiment Design And Parameter Estimation Of DSGE Model

Uniform designs are widely used in various scientific investigations and industri-al applications.Constructing uniform designs,especially for the asymmetrical uniform design,is a complex task and can be computationally intractable,even for moderate number of runs,factors and levels.In this dissertation,an efficient method for construct-ing asymmetrical uniform generalized minimum aberration(GMA)designs and uniform minimum moment aberration(MMA)designs is proposed.Numerical results indicate that the designs obtained by our method have smaller discrepancies than the existing ones.Moreover,combining uniformity with sequential idea,a global optimal algorithm is proposed,namely,MSNTO algorithm.Finally,this algorithm is applied to parameter estimation of the dynamic stochastic general equilibrium(DSGE)model,which greatly enrich the economic model parameter estimation theory,and also lay the foundation for further integration of the experiment design method and economic model.The main conclusions and innovations are as follows:By considering level permutation of all the factors,the relationship between average centered L2-discrepancy and generalized wordlength pattern for asymmetrical designs is derived.We further extend the above results to any discrepancy defined by a reproducing kernel.And an analytic relationship between generalized wordlength pattern and any average discrepancy defined by a reproducing kernel is also obtained for asymmetrical designs,which is shown that the asymmetrical GMA design usually has low average discrepancy.Based on it,we proposed a general method for constructing asymmetrical uniform GMA designs with arbitrary number of levels.The above conclusions are further verified by numerical simulation in the case of the 18-run asymmetrical GMA designs which are chosen from the mixed-level orthogonal arrays(18,2136)and(18,6134).The conclusions of the GMA criterion are generalized to the MMA criterion.By considering level permutation of all the factors,an analytic relationship between power moments and any average discrepancy defined by a reproducing kernel is also obtained for symmetrical and asymmetrical designs.By considering level permutation,it is proved that symmetrical and asymmetrical minimum moment aberration designs often have low average discrepancies.The general method for constructing uniform MMA design and numerical examples are also given.Based on the relationship between the average L2-discrepancy and the generalized wordlength pattern,a new lower bound of the average L2-discrepancy is obtained for symmetrical and asymmetrical designs.It is can be used as a benchmark in helping to validate that the designs obtained by our method are in fact uniform(or optimal).The numerical results show that,for some designs,the lower bound of the average L2-discrepancy can be reached,which is shown that the method for constructing uniform design based on level permutation is good enough.Combining uniformity with sequential idea,a new global optimal algorithm is pro-posed,namely,MSNTO algorithm,and the theoretical proof of its convergence is given,including convergence criterion and estimation error.The algorithm is compared with other commonly used global algorithms,and numerical results show that our algorithm outperforms the other algorithms.Finally,the full information maximum likelihood method based on the MSNTO al-gorithm is applied to estimate a complex dynamic stochastic general equilibrium model,and the results is satisfied with economic reasoning.As compared with BFGS algorithm,it is found that MSNTO algorithm has the advantages of low qualification,strong appli-cability,and it is not easy to fall into the local optimal solution.And the application range of uniform experiment design can be extended to economic field.