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on Econometric Time Series |
| By: | Tanaka, Katsuto |
| Abstract: | We discuss some computational problems associated with distributions of statistics arising from the fractional Brownian motion (fBm). In particular, we deal with (ratios of) its quadratic functionals. While it is easy in principle to deal with the standard Bm, the fBm is difficult to analyze because of its non-semimartingale nature. Here we suggest how to derive and compute the distributions of such functionals by using a martingale approximation. For this purpose we employ the Fredholm theory concerning the integral equations, illustrating how to compute the characteristic function via the Fredholm determinant. We also apply the present methodology to compute the fractional unit root distribution, and demonstrate some interesting moment properties. |
| Date: | 2011–06 |
| URL: | http://d.repec.org/n?u=RePEc:hit:econdp:2011-06&r=ets |
| By: | Tanaka, Katsuto |
| Abstract: | The work of Professor P.C.B. Phillips, even if it is focused on the area of linear nonstationary models, is enormous. So it is hard for me to explore the whole of his work in this paper. Therefore I have decided to take up only a few results of his work. The topics chosen here are applications of the martingale approximation and the problem of choosing between stochastic and deterministic trends, which I discuss and, hopefully extend. |
| Date: | 2011–04 |
| URL: | http://d.repec.org/n?u=RePEc:hit:econdp:2011-05&r=ets |
| By: | Tanaka, Katsuto |
| Abstract: | We discuss some inference problems associated with the fractional Ornstein-Uhlenbeck (fO-U) process driven by the fractional Brownian motion (fBm). In particular, we are concerned with the estimation of the drift parameter, assuming that the Hurst parameter H is known and is in [1/2, 1). Under this setting we compute the distributions of the maximum likelihood estimator (MLE) and the minimum contrast estimator (MCE) for the drift parameter, and explore their distributional properties by paying attention to the influence of H and the sampling span M. We shall also derive the asymptotic distributions of the two estimators as M becomes large. We further deal with the ordinary least squares estimator (OLSE) and examine the asymptotic relative efficiency. It is shown that the MCE is asymptotically efficient, while the OLSE is inefficient. We also consider the unit root testing problem in the fO-U process and compute the power of the tests based on the MLE and MCE. |
| Date: | 2011–08 |
| URL: | http://d.repec.org/n?u=RePEc:hit:econdp:2011-07&r=ets |
| By: | Barbara Rossi; Atsushi Inoue |
| Abstract: | This paper proposes new methodologies for evaluating out-of-sample forecasting performance that are robust to the choice of the estimation window size. The methodologies involve evaluating the predictive ability of forecasting models over a wide range of window sizes. The authors show that the tests proposed in the literature may lack the power to detect predictive ability and might be subject to data snooping across different window sizes if used repeatedly. An empirical application shows the usefulness of the methodologies for evaluating exchange rate models' forecasting ability. |
| Keywords: | Forecasting |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedpwp:11-31&r=ets |
| By: | A. Saichev; D. Sornette |
| Abstract: | We present a set of log-price integrated variance estimators, equal to the sum of open-high-low-close bridge estimators of spot variances within $n$ subsequent time-step intervals. The main characteristics of some of the introduced estimators is to take into account the information on the occurrence times of the high and low values. The use of the high's and low's of the bridge associated with the original process makes the estimators significantly more efficient that the standard realized variance estimators and its generalizations. Adding the information on the occurrence times of the high and low values improves further the efficiency of the estimators, much above those of the well-known realized variance estimator and those derived from the sum of Garman and Klass spot variance estimators. The exact analytical results are derived for the case where the underlying log-price process is an It\^o stochastic process. Our results suggests more efficient ways to record financial prices at intermediate frequencies. |
| Date: | 2011–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1108.2611&r=ets |