Research On High-dimensional Non-linear Mixed Data Sampling Model With Applications

In the era of big data,innovations in information science and computer technology have made the collection and storage of large dataset possible.In multi-source information fusion modeling,one is often confronted with many time series that can be sampled or observed at different frequencies,which raises the problem of how to explore complex patterns among mixed frequency data and making an accurate forecast.As a typical regression model involves data sampled at the same frequency,the common solution in such cases is to turn mixed frequency data into the same frequency.In the process,a lot of high frequency information may be discarded.As an alternative,proposal of a mixed data sampling model(MIDAS)provides possibility for directly accommodate variables sampled at different frequencies.Furthermore,with increasing complexity of economic and financial research,there are a lot of unexplored mixed frequency data analysis problems,such as reverse,high-dimensional,and nonlinear patterns,which are unable to solve effectively by using the existing MIDAS-based methods.To effectively solve the technical problems arise in modeling process and extend the model of mixed data analysis,can be extremely helpful in promoting the application of mixed data and exploring complex patterns of economic management.It is of great importance for theoretical approaches and practical implications.To this end,this dissertation selects the subject of “research on high-dimensional nonlinear mixed data sampling model with applications”.Through integrating the discipline of statistics,economics,finance,and management,and combining the methods of theoretical analysis,numerical simulation and application research,this dissertation attempts to extend the obverse,low-dimensional,and linear mixed frequency data analysis methods to reverse,high-dimensional,and nonlinear cases,and then construct a reverse restricted mixed data sampling model,a group penalized mixed data sampling model,and an artificial neural network mixed data sampling model,respectively.Moreover,these models are applied to solve the problems of economic management.The detailed researches and main innovations of this dissertation are as follows:(1)Construct a novel reverse restricted mixed data sampling(RR-MIDAS)model,which allows us to forecast high frequency variables using low frequency information.The RR-MIDAS model is applicable to more general mixed frequency data without frequency mismatch limit.Firstly,borrowing the ideas from parameter restrictions in MIDAS and periodic structures in RU-MIDAS,we provide a procedure for RR-MIDAS regressions including frequency alignment,periodic processing,parameters estimation,and multi-step forecasting.Second,the efficacy of the RR-MIDAS model is illustrated through Monte Carlo simulations.We consider small,medium,and large values of frequency mismatches and compare the RR-MIDAS with several competing models including RU-MIDAS and HF model,the numerical results show that the performance of RR-MIDAS consistently outperform the other models,in terms of predictive ability.Finally,the decent performance of the RR-MIDAS model is demonstrated in a realworld application on forecasting China and US market interest rates,since it is able to explore the dynamic relationships among variables.(2)Construct a novel group penalized(reverse)unrestricted mixed data sampling(GP-(R)U-MIDAS)model,which allows us to identify important variables at block level in high dimensional mixed frequency data analysis,and take into account the grouping structures produced via the frequency alignment and multiple lag operation.The GP-(R)U-MIDAS model is able to solve the problems of mixed data analysis,dimension reduction,parameters estimation,and key variables identification.In addition,it can enhance the interpretability and prediction ability.Firstly,we introduce the group LASSO,group SCAD,and group MCP penalized function into the(R)UMIDAS regression framework,and propose the GP-(R)U-MIDAS model.Moreover,we provide detailed procedures for it with model setup,parameters estimation,group variables selection,and multi-step forecasting.Second,the efficacy of the GP-(R)UMIDAS model is illustrated through Monte Carlo simulations.We consider the different forms of variables and different values of frequency mismatches,and compare the GP-(R)U-MIDAS model with several competing models including P-(R)U-MIDAS,FC-(R)U-MIDAS,and(R)U-MIDAS,in terms of variables selection,goodness-of-fit,and prediction accuracy,the numerical results show that the performance of the GP-(R)UMIDAS model is significantly superior to the other models,when group effecting exist.Finally,the superiority of the GP-(R)U-MIDAS model is also illustrated in real-world applications on quarterly GDP growth forecast and asset pricing.The empirical results show that the GP-(R)U-MIDAS model outperforms the other competitive models,and is able to explore influencing mechanism and select crucial factors.(3)Construct a novel artificial neural network(unrestricted)mixed data sampling(ANN-(U-)MIDAS)model,which allows us to explore the potential nonlinear pattern hidden in raw mixed frequency data.The ANN-(U-)MIDAS model can make full use of high frequency effective information,and give full play to the data-driven and adaptive learning ability in machine learning.Firstly,we introduce the(U-)MIDAS approach into the ANNs framework,and propose the ANN-(U-)MIDAS model.Moreover,we provide detailed procedures for it including model setup,parameters estimation,and multi-step forecasting.Second,we conduct extensive Monte Carlo simulations to illustrate the efficacy of the ANN-(U-)MIDAS model,and then compare its decent performance with those of other competing models including ANN and(U-)MIDAS models in terms of goodness-of-fit and predictive ability.The numerical results show that the GP-(R)U-MIDAS model outperforms the other models.Finally,the decent performance of the ANN-(U-)MIDAS model,in terms of fitting and forecasting,is also demonstrated in a real-word application on monthly inflation forecasts by using both low frequency macroeconomic variables and high frequency financial market information.The results verify that ANN-(U-)MIDAS is an efficient tool to handle nonlinear mixed frequency data.In summary,consider the emerging problems of reverse,high-dimensional,and nonlinear mixed frequency data analysis in the filed of economic management,and based on previous research results,this dissertation further extend the classical(U-)MIDAS approach to develop a series of new mixed frequency data analysis models,which enrich the research content and application study of mixed frequency data.Moreover,this dissertation chooses the common problems in the filed of economic management,carry out the related subject research in the framework of mixed frequency data,and focus on promoting the interpretability and prediction accuracy.This will help policymakers and investors to keep abreast of changing development trends and deeper understanding of the market mechanism,and then improve the macroprudential regulatory ability and raise the investment decision-making and management level.