1. “Local Whittle Memory Parameter Estimation of Long Memory Process in the Presence of Low Frequency Contaminations,” (Job Market Paper) (Jie Hou and Pierre Perron), Journal of Econometrics 182 (2014) 309–328 Download
Abstract: We propose a modified local-Whittle estimator of the memory parameter of a long memory time series process which has good properties under an almost complete collection of contamination processes that have been discussed in the literature, mostly separately. These contaminations include processes whose spectral density functions dominate at low frequencies such as random level shifts, deterministic level shifts and deterministic trends. We show that our modified estimator has the usual asymptotic distribution applicable for the standard local Whittle estimator in the absence of such contaminations. We also show how the estimator can be modified to further account for additive noise and that our modification for low frequency contamination reduces the bias due to short-memory dynamics. Through extensive simulations, we show that the proposed estimator provides substantial efficiency gains compared to existing semiparametric estimators in the presence of contaminations, with little loss of efficiency when these are absent.
2. “Triangularization of a class of C1 unipotent maps,” Hou, Jie and Yang, Lijun, the Fifth International Conference on Information and Management Sciences, Chengdu, China, 2006 (ISTP Indexed).
1. “Robust Memory Parameter Estimates: A Re-examination of Daily and High-Frequency Asset Returns Volatility,” October 2013, Revised April 2014 Download
We apply the modified local-Whittle (LWLFC) estimator proposed in Hou and Perron (2013) to various volatilities series for stock indices and exchange rates to robustly estimate the long-memory parameter. We provide the first empirical approach for robustly estimating the memory parameters of data series that allows for coexistence of both the short-memory process and long-memory process, low frequency contaminations such as level shifts as well as additive noises. We provide a sufficient condition for the existence of long-memory and propose a mixed procedure that combines a modified Local-Whittle estimator and its perturbed and full-parametric variants to verify that sufficient condition in practice. Through our mixed procedure, we contribute to the literature by finding evidence of long-memory processes in most low frequency daily measures, suggesting a combination of a long-memory process, a noise, as well as a LFC in such data, with the relative magnitude of each of these components varying according to the specific series. We also perform extensive simulations to show the finite-sample properties of several modified LFC-robust LW estimators, including several perturbed and full-parametric estimators.
2. “Pivotal Inference for Structural Changes in a Joint Segmented Trend Model with Heterogeneous Innovations,” (Jie Hou and Pierre Perron), April 2014 Download
The issues addressed in this paper are related to testing for changes in the slope and variance of the noise in a linear time trend regression with changes in the slopes such that the series is joined at the break dates. We start with a single possible break in each and address the following issues: 1) testing for a change in trend with or without a change in variance; 2) testing for a change in variance with or without a change in trend. Asymptotically pivotal statistics are provided for each case. We then generalize some results to the case of multiple changes.
3. “On the Existence of a Pivotal Statistic for a Broad Range of “Searching for Missing Regressor” Problems,” April 2014, Draft Available upon Request
Using mathematical tools rarely employed in the field of Econometrics before, this paper gives a very general condition under which a pivotal statistic for coefficient break (e.g. trend break or mean shift) test is guaranteed to exist, under time-varying innovations. Since such statistic is derived from some maximized projections of a multi-dimensional standard normal variable and in its limit, Brownian motion, to a class of possible regressors, our results are also relevant to the literature of extreme value theory (EVT) in the sense that its key assumption, that the maximization has to be taken over a set of “strongly correlated” random variables, is exactly the opposite of the key assumption in EVT that the maximization is taken over a set of independent random variables. Moreover, we show that our result still holds if allowing for statistics without finite distribution before rescaling, hence includes EVT on normal variables as special case. We also point out that our results can be extended from scaling transformations to any invertible linear transformations.
To provide a proper framework for our result, we define a very general class of regression models, called “Searching for Missing Regressor” (SMR) models that incorporates all structural break models as its special cases. The innovation (idiosyncratic error) process is assumed to have a time-varying variance that covers almost all types of innovations that are not unit-root or fractionally integrated processes, which can also be included in our framework with a slight modification of argument. We argue that in SMR framework OLS in Perron and Zhu (2005) excels MLE in both estimation and testing. In the context of structural breaks, we briefly discuss the general results about consistency, rate of convergence and limit distribution of estimates of break fractions, coefficients and innovation parameters. Simulation results on a special case of “joint segmented trend break test under heterogeneous innovations” are also reported to illustrate the finite sample performance of the pivotal statistic.
Work in Progress
1.“Using Interactive Effects Factor Analysis to Improve the Berry, Levinsohn and Pakes (1995) model used in industrial organization”