A0334
Title: A measure for the degree of distribution changes in locally stationary processes
Authors: Guy-Niklas Brunotte - Otto-Friedrich-Universitat Bamberg (Germany) [presenting]
Abstract: Non-stationary time series $\{X_{t,T}\}$ with $t=1,\dots,T$ and $T\in\mathbb{N}$ are considered in many applications. Thereby, it is often fundamental to know how much the distribution of $X_{t,T}$ depends on the concrete point in time $t$ because such an analysis contributes to answering how good estimators based on historical data forecast critical values concerning the future. For example, it is of interest whether the distributions of daily returns of a stock are more time-dependent after a crisis than before this event or even stay the same for all investigated points in time. This motivates the introduction of a characteristic function-based, well-interpretable measure which quantifies for a wide class of non-stationary processes $\{X_{t,T}\}$ how much the distribution of $X_{t,T}$ depends on $t$. Moreover, it is shown that this measure provides an asymptotic level alpha test which examines whether the distribution of $X_{t,T}$ changes over time. In addition, the present measure will be applied to several daily returns of stocks to investigate how much their distributions depend on time.
