Statistics Seminar（2015-13）

Title:Semiparametric Estimation of Interval-valued Time Series Using Extreme Value Approach

Speaker:Wei Lin, Capital University of Economics and Business

Time:Thursday, 24th September, 14:00-15:30

Location:Room 217, Guanghua Building 2

Abstract:Existing models in the current literature for interval-valued time series mainly focus on the regressions of minimum and maximum (or center and radius) of intervals on its lag terms with no or restrictive assumptions on the distribution of error terms. Such specification ignores the possible extreme nature of the lower and upper bounds of intervals under some circumstances. For example, in stock market, the low and high returns of an asset during a short time period can be regarded as the maximal and minimal observations within that time period. In this paper, we assume that there are some underlying stochastic processes that generate the interval-valued time series, and that the lower and upper bounds of the intervals are the realized extreme observations (minima and maxima) of the random draws according to conditional distributions of underlying stochastic process at each time period. Then the analysis of interval-valued time series is decomposed into two parts. The first part is the classical point-valued time series analysis for the underlying stochastic process, for which the returns calculated from close price are used as one realized sample path of the underlying stochastic process. The second part is to model the conditional mean of the maxima and minima nonparametrically, as the conditional mean of extreme value is often highly nonlinear and intractable. Correspondingly, we propose a two step procedure for the estimation of interval-valued time series: (i) specify and estimate parametric models for the point-valued time series which are the realized sample paths of underlying stochastic processes, and obtain the estimated conditional moments of it; and (ii) perform nonparametric regression of maxima and minima series with the estimated conditional moments as the parametrically generated regressors. Bases on the literature on nonparametric regression with generated regressors, the effect of parameter uncertainty in the second step is asymptotically negligible given some regularity conditions, and therefore, our two-step estimator has typical nonparametric convergence rate and asymptotic normality. The finite sample performances are investigated via Monte Carlo simulation exercises. In the empirical application, we compare our two-step estimator with its competing approaches using high frequency (5-minute time interval) financial data of Wells Fargo stock returns. The results show that our proposed two-step estimator is more accurate in the sense of delivering smaller losses than those from its competing models.