Nonlinear Time Series Analysis in Financial Applications

  • Robin Miao

Student thesis: Doctoral ThesisPhD


The purpose of this thesis is to examine the nonlinear relationships betweenfinancial (and economic) variables within the field of financial econometrics. Thethesis comprises two reviews of literatures, one on nonlinear time series models andthe other one on term structure of interest rates, and four empirical essays on financialapplications using nonlinear modelling techniques.The first empirical essay compares different model specifications of a Markovswitching CIR model on the term structure of UK interest rates. We find the leastrestricted model provides the best in-sample estimation results. Although models with restrictive specifications may provide slightly better out-of-sample forecasts in directional movements of the yields, the economic gains seem to be small.In the second essay, we jointly model the nominal and real term structure ofthe UK interest rates using a three-factor essentially affine no-arbitrage term structure model. The model-implied expected inflation rates are then used in the subsequent analysis on its nonlinear relationship with the FTSE 100 index return premiums, utilizing a smooth transition vector autoregressive model. We find the model implied expected inflation rates remain below the actual inflation rates after the independence of the Bank of England in 1997, and the recent sharp decline of the expected inflation rates may lend support to the standing ground of the central bank for keeping interest rates low. The nonlinearity test on the relationship between the FTSE 100 index return premiums and the expected inflation rates shows that there exists a nonlinear adjustment on the impact from lagged expected inflation rates to current return premiums.The third essay provides us additional insight into the nature of the aggregatestock market volatilities and its relationship to the expected returns, in a Markovswitching model framework, using centuries-long aggregate stock market data from six countries (Australia, Canada, Sweden, Switzerland, UK and US). We find that the Markov switching model assuming both regime dependent mean and volatility with a 3-regime specification is capable to captures the extreme movements of the stock market which are short-lived. The volatility feedback effect that we studied on each of these six countries shows a positive sign on anticipating a high volatility regime of the current trading month. The investigation on the coherence in regimes over time for the six countries shows different results for different pairs of countries.In the last essay, we decompose the term premium of the North American CDX investment grade index into a permanent and a stationary component using aMarkov switching unobserved component model. We explain the evolution of the two components in relating them to monetary policy and stock market variables. We establish that the inversion of the CDX index term premium is induced by sudden changes in the unobserved stationary component, which represents the evolution of the fundamentals underpinning the risk neutral probability of default in the economy.We find strong evidence that the unprecedented monetary policy response from the Fed during the crisis period was effective in reducing market uncertainty and helped to steepen the term structure of the CDX index, thereby mitigating systemic risk concerns. The impact of stock market volatility on flattening the term premium was substantially more robust in the crisis period. We also show that equity returns make a significant contribution to the CDX term premium over the entire sample period.
Date of Award5 Jul 2012
Original languageEnglish
Awarding Institution
  • University of Bath
SupervisorChristos Ioannidis (Supervisor)


  • regime switching
  • term structure of interest rates
  • VSTR
  • CDX Term Premia

Cite this