Research Seminar Archive
Prof Ba Chu (Carleton University): On Weighted Convergence of Partial-Sum Processes for Time Series with Applications to Nonparametric Change-Point Tests
Abstract: This paper studies the weighted convergence of partial-sum processes for strictly stationary time series, effectively extending the existing results proved for sequences of i.i.d. random variables and moving-averages, by making use of a functional Hungarian construction for sums of independent random variables.
The present result is then employed to construct a new nonparametric [k-NN-based] test for change-points in volatility in time series models. The weighted convergence of this test statistic is established and shown to be free from the estimation effect arising from nonparametric estimation of unknown conditional expectation and volatility functions.