Constructive Ensembles for Time Series Analysis Avoid Unit Root Testing

• Activity Number: 55
• Type: Contributed
• Date/Time: Sunday, August 3, 2003 : 4:00 PM to 5:50 PM
• Sponsor: Business & Economics Statistics Section
• Author(s): Hrishikesh D. Vinod*+
• Companies: Fordham University
• Keywords: Nonstationary ; Statistical Inference ; Finance ; Reduced Rank Regression ; Bootstrap ; Dependent data

Abstract

Since the ensemble is the notional "population" for the observed time series, I propose a new method of constructing it by using maximum entropy (ME) methods. The ME distribution satisfies the mean-preserving constraint. My seven-step algorithm is designed to satisfy the ergodic theorem and Doob's theorem, without assuming stationarity and without using asymptotics. My methods are suited for short nonstationary time series and simplify several inference problems. An example from reduced rank regression (RRR) for cointegration shows the power of the proposal in difficult inference problems avoiding all unit root type testing; (i) the constructed ensemble retains the basic shape and dependence structure of autocorrelation function and partial autocorrelation function of the original time series, (ii) one can avoid shape-destroying transformations (differencing) and the underlying need for achieving stationarity, and (iii) one can provide confidence intervals for coefficients of lagged dependent variables. A finance example shows confidence intervals for the value at risk.