Research On Model Misspecification Problem Based On RLS Process And Measure Transformatio

In recent years,significant and unpredictable events have occurred frequently,which have had a huge impact on the world economic and financial system.Research related to model misspecifications have brought much attention to scholars in such an uncertain environment.This thesis studies two important issues related to model misspecification: model instability and model ambiguity.Model instability refers to the problem that parameter values may change in different time periods,since the real data generating process may change over time.Model ambiguity refers to the problem that parameters may take different values even at the same time,i.e.the distorted beliefs on the real data generating process.We introduce random level shift parameters and changes of probability measure to deal with model instability and ambiguity respectively,and these two methods both try to solve the model misspecification problem by changing the model coefficients.We apply these methods in three applications.Our proposed model can fit the data better than traditional models and can reduce the biases caused by model misspecification effectively.First,we find that major economic events,financial crisis and major monetary policy intervention would have a significant impact on the term structure of interest rate.Potential model misspecifications may appear if ignoring those impact and continuing to use traditional models.Therefore,we develop a new model based on the classical dynamic Nelson-Siegel model by introducing random level shift(RLS)parameters.The built-in RLS can capture cyclical fluctuations in interest rates and structure breaks induced by technology progress,financial crisis,major monetary policy interventions,etc.In addition,the model can be used to forecast future structure breaks.We apply the model to fit and forecast daily U.S.Treasury yield curves and the model outperforms other widely used models.The empirical results show that the model not only has a better in-sample fit with residuals exhibiting less persistence but also has superior out-of-sample performance.Moreover,the model performs very well especially for short-term and long-term bonds,and the performance improves as the forecasting horizon increases.Second,we introduce RLS parameters to the diffusion index forecasting model to solve the problem of instability in macroeconomic forecasting process.Based on the frequency domain method,this paper uses common factors to predict macroeconomic variables and consider the unstable of model parameters.Forecasting is carried out in two-steps: first,the common factors are extracted from a dynamic factor model by principle component analysis;then these estimated factors are treated as observables in the predictive regression,where RLS parameters are introduced to capture parameter instability.Our model can be cast into a conditional linear Gaussian state space model,and can be estimated by mixture Kalman filter algorithm combined with Monte Carlo Expectation Maximization.Empirical results show that the predictive regressions with RLS parameters have better in-sample and out-of-sample performances than the constant parameter benchmark.We also compare with the full-split model.Our model shows comparative advantages in reducing forecast error when applied to different macroeconomic dataset at different frequencies.Our model performs especially well when economic situation is turbulent,for example during crisis.Finally,we introduce model ambiguity to investor’s optimal portfolio and consumption choice problem with/without sustainable spending constraint.We maximize investor’s total expected utility in the worst scenario,and obtain the optimal investment portfolio and consumption-wealth ratio.In the numerical analysis,we find that investors who take ambiguity into account will be more conservative and decrease the consumption-wealth ratio without constraint.However,under the constraint of sustainable consumption,the impact of ambiguity is two-fold.There exists a critical value of the risk-free rate.Investors are more conservative when the risk-free rate is higher than the critical value,and more radical in Reaching for Yield when the risk-free rate is lower than the critical value.This behavior will also accelerate the accumulation of risks in the entire economy.What’s more,sustainable consumption constraint will induce welfare losses for investors.A certain degree of ambiguity can reduce the welfare loss,but it will eventually increase with ambiguity beyond some threshold.Under sustainable consumption constraint,ambiguity erodes consumption and welfare,and negative interest rates will magnify the erosion.The welfare loss of investors under negative interest rates is greater than those under positive interest rates.Model uncertainty and instability constitute two aspects of the model misspecification problem under the impact of major unpredictable events.This thesis starts with these two perspectives and conducts research on different economic issues.Finally,we try to combine them and lay out some possible directions for our future research.