Checking parameter stability of econometric models is a long-standing problem. Almost all existing structural change tests in econometrics are designed to detect abrupt breaks. Little attention has been paid to smooth structural changes, which may be more realistic in economics. We propose a consistent test for smooth structural changes as well as abrupt structural breaks with known or unknown change points. The idea is to estimate smooth time-varying parameters by local smoothing and compare the fitted values of the restricted constant parameter model and the unrestricted time-varying parameter model. The test is asymptotically pivotal and does not require prior information about the alternative. A simulation study highlights the merits of the proposed test relative to a variety of popular tests for structural changes. In an application, we strongly reject the stability of univariate and multivariate stock return prediction models in the postwar and post-oil-shocks periods.

This paper examines the predictability of corporate bond returns using the transaction-based index data for the period from October 1, 2002 to December 31, 2010. We find evidence of significant serial and cross-serial dependence in daily investment-grade and high-yield bond returns. The serial dependence exhibits a complex nonlinear structure. Both investment-grade and high-yield bond returns can be predicted by past stock market returns in-sample and out-of-sample, and the predictive relation is much stronger between stocks and high-yield bonds. By contrast, there is little evidence that stock returns can be predicted by past bond returns. These findings are robust to various model specifications and test methods, and provide important implications for modeling the term structure of defaultable bonds.