We provide the asymptotic theory for functionals of recurrent diffusions. Our asymptotics are completely general and applicable for all cases, including positive and null recurrent diffusions, and diffusions with and without the integrabil- ity conditions. They are established directly from the representation of diffusion as time-changed Brownian motion. Our approach provides a unified framework, and combines all existing theories of diffusion asymptotics with new results that appear to be particularly relevant in many practical applications. For an illustration of our asymptotics, we employ them to analyze a class of high frequency regressions that is commonly used in empirical economics and finance.
diffusion; positive and null recurrences; asymptotics; limit distri- bution; continuous time regression;
- C22: Time-Series Models • Dynamic Quantile Regressions • Dynamic Treatment Effect Models &bull Diffusion Processes
Jihyun Kim, and Joon Park, “Asymptotics for Recurrent Diffusions with Application to High Frequency Regression”, Journal of Econometrics, vol. 196, n. 1, January 2017, pp. 37–54.
Journal of Econometrics, vol. 196, n. 1, January 2017, pp. 37–54