Modeling Theory,analysis Technology Of Mixed Frequency Data Model

At the moment of traditional econometric models analyzes the time series data variables.No matter in the construction of the model or specific application process,all implied an important assumption,namely must choose the same frequency variable s sample data,otherwise the model won't be able to identify.Traditional econometric models of command data with frequency requirements is not the same as basic data inconsistency of frequency which make the researchers in a dilemma,Especially in nowadays.the financial market is closely integrated with microeconomy,macroeconomic policymakers and researchers eagerly need models which is able to connect high frequency macroeconomic data,ultra high frequency financial data with low frequency macroeconomic data.Under the background of the traditional theory model application is limited and different frequency time series data is changed with each passing day.Mixing data econometric model analysis technique and the importance gradually emerged.In order to better introduce the development of analysis technology and domain of application level.This paper has deeply analyzed the internal structure of the mixing data regression MIDAS model and maked comparative analysis with the traditional distributed lag model.At the same time,pointed out the difference between the MIDAS model and the traditional regression model with contact.On that basis,combed the various forms of MIDAS model and variety of different forms of weighting function;gived the specific mechanism and deductive process of commonly used nonlinear least squares and maximum likelihood estimation method which are combined with numerical optimization algorithm methods,subsequent identification method based on traditional distributed lag model,combined with the Vandermonde matrix to derive a new class MIDAS model estimation method(OLS),and the parameters theoretical meaning of MIDAS models,the actual weighting function meaning,and MIDAS models applied in practical economic analysis.In the applications of MIDAS models,the selection of the weighting function is essential for MIDAS model,this paper full considers five different weighting functions to overcome the insufficient which only selects a single weighting function in the past research on MIDAS model,builds the MIDAS models and the limit of MIDAS models,studies a big controversy in the field of economy,which have different frequency index,at the same time,compared with the traditional econometric model to do analysis.It indudes the following several parts.First,according to the principle of mixing data prediction model which are initially proposed.and combined with the traditional time series regression model.we can deduce the basic form and the extended form of the mixed data regression.Mainly includes MIDAS model,M-MIDAS model.AR-M-MIDAS model,U-M-MIDAS model,FA-MIDAS model,ECM-MIDAS model,MS-MIDAS model.MF-VAR model and so on.It points out that the weighting function of design thought,teases out a variety of weighting function concrete form,and analyzes the nature of each of the weighting function and practical conditions.On this basis,designs a new weighting function according to Beta density function.Second:it describes the internal mechanism of MIDAS models commonly used estimation methods,and deduces theoretically a nonlinear least-squares method of MIDAS models,given initial value,deduces parameter estimation iterations export formula on the specific form of MIDAS model objective function,finds a converged solution by defined the termination condition,discusses mainly the objective function which is to the conditions of unconstrained minimization according to the nature of the objective function,discusses NLS binding numerical optimization algorithms,including Newton's method,Gauss-Newton method,quasi-Newton method,noting that the conditions of application,operational efficiency,the advantages and disadvantages of these methods,Using the above NLS estimation method,according to the time attribute of economic variables,it has constructed the multiple mixed-frequency data sampling model with 6 kinds of weighted function,analyzed the effect and the effect path that the high-frequency asset price impacts on the economic growth.The comparative analysis shows the Exp Almon-AR-M-MIDAS model is more accurate than other MIDAS models in the fitting effect and interpolation prediction,the model can extract more information about the daily data of the stock price.The empirical results also show that high-frequency asset price has significant effect on China's economic growth;it has positive and negative active infects on the economic growth and plays a preventive role in early warning.The effect of real estate price on economy is greater than that of the impact of stock price,the effecting-direction of stock price on the economy is uncertain.It analysizes mechanism and inflation forecasting results about stock price of the high-frequency variable,the results showed:rapid decline Beta-weighting function not only the effect but also forecasting precision has a comparative advantage,stock prices effect of the high-frequency asset price inflation is significant,as lag order increasing,influence degree of the stock price on inflation is rapidly downward trend,Beta-M-MIDAS has high accuracy and timeliness of the characteristics in terms of the real-time forecast of inflationin China,which forecast effect is superior to the same frequency of traditional econometric models and other mixed Sampling of regression models.Third:It gives maximum likelihood estimation method,identify principles and specific process of MIDAS model;combining traditional maximum likelihood estimation and specific forms of MIDAS system,we have derived MIDAS-ML estimator and its asymptotic distribution,gives variance-covariance matrix of MIDAS-ML estimator in a simplified form,It Studies transmission mechanism and effectiveness of monetary policy,effect and path of monetary policy on economic growth.The empirical results show that:the amount of money based on monetary policy affects economic growth significantly,in the short term,the expansionary monetary policy can stimulate economic growth.in the long term,especially 26 months until 37 months,monetary policy on economic growth once again plays a role in promoting the economic growth.Fourth:Combined with estimation method of the traditional distributed lag model'according to the internal mechanism of MIDAS model.It deduces the MIDAS Model.M-MIDAS Model.U-MIDAS Model,M-U-MIDAS Model.Ordinary least squares method and the MIDAS model OLS parameters identification conditions are given.At the same time,the MIDAS prediction model formally introduces the traditional distribution lag model parameters meaning,and then the theory basis of economic significance of the MIDAS model parameters is given.So the MIDAS model between different frequency variable structure analysis as possible.Fifth:Bias of the missing non-weight section about high frequency explanatory variables of the sample data has been proved,EQW model(traditional regression model by weighted average of the high frequency data)and the internal structure of MIDAS has been Analysed,parameter estimation bias of EQW model has been theoretically deduced,MIDAS model can separate into linear and nonlinear two-part which are pre-inspection of parameter estimation;on this basis,further discussion about constraints of the MIDAS models and the traditional linear regression model is equivalence,and conditions the estimator EQW model does not exist bias,the estimator's variances in the intrinsic link between EQW model and MIDAS models have explored.the determinants of MIDAS model and estimator's variances have discussed.estimator's asymptotic distribution of MIDAS models has developed,Through rigorous mathematical derivation.we found the EQW model which omissions and other non-weight high-frequency sample data of the explanatory variables will result in model bias and estimator's distortion;if before modeling the traditional econometric models have converted the high frequency data into low frequency simply by averaging.it has built five different weight's functions of MIDAS and unrestricted MIDAS,Combined the traditional estimation of autoregressive distributed lag model with MIDAS model.on this basis we have forecasted the quarterly GDP in China,and analysed the influence of high frequency explanatory lag order changes,low frequency variable and variations in lag length on GDP forecasting,according to the results of the six MIDAS models fitting and forecasting to further build the combined MIDAS model,investigating the prediction accuracy and prediction effect of combined MIDAS model.Research conclusions show that the unrestricted MIDAS model's prediction accuracy and fitting effect is higher than five different weights MIDAS models,the combined MIDAS which has used BIC was the optimal performance in Forecasting of China's Quarterly GDP.In short,the system analyzes the mixing regression modeling mechanism of MIDAS model,internal structure,model recognition method and parameters of the test method,and with the traditional frequency regression model of internal relations and in the specific application of the real economy.