Locally Stationary Quantile Regression For Inflation and Interest Rates

Open Access
Author:
Xu, Zhuying
Graduate Program:
Statistics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
October 09, 2015
Committee Members:
  • Zhibiao Zhao, Dissertation Advisor
  • Runze Li, Committee Member
  • Bing Li, Committee Member
  • Fuqing Zhang, Committee Member
Keywords:
  • Locally stationary model; Nonparametric estimation; Quantile reg
Abstract:
There has been an extensive literature on understanding the role of interest rates and inflation in financial markets. Under some assumptions on the conditional expected real return, Fama's (1975) study about the predictability of the inflation from the interest rates has long attracted attention. However, as Fama focused on the conditional mean return but ignores the distribution of the return, two distributions with the same mean can have completely different shapes, focusing on the mean only may overlook other important aspects of the distribution. Moreover, Fama assumed that the relationship between inflation and interest rates is constant over time. Such stationarity can hardly be justified and the potential nonstationarity of interest rates could pose serious challenges in statistical inference. To overcome these limitations, we propose a time-varying locally stationary quantile regression (LSQR) model for the conditional quantile of inflation on the past inflation and interest rates, with the quantile-specific coefficients varying with time nonparametrically. The proposed model not only captures information about the distribution of the return but also exhibits time-varying dependence between the inflation and interest rates over long time span. We consider the LSQR model under both efficient market settings and non-efficient market settings. For each case, as the model is approximately stationary in short time period, we study nonparametric estimations for the time-varying and quantile-specific coefficients in the model and demonstrate their asymptotic behaviors under appropriate conditions. The proposed methodology is also demonstrated through both simulation data and an empirical analysis of the U.S. Treasury Bill.