Template-type: ReDIF-Article 1.0 Author-Name: Leeb, Hannes Author-Name: Pötscher, Benedikt M. Title: THE VARIANCE OF AN INTEGRATED PROCESS NEED NOT DIVERGE TO INFINITY, AND RELATED RESULTS ON PARTIAL SUMS OF STATIONARY PROCESSES Journal: Econometric Theory Pages: 671-685 Issue: 4 Volume: 17 Year: 2001 Month: August Abstract: For a process with stationary first differences a necessary and sufficient condition for the variance of the process to be unbounded is given. An example shows that the variance of an integrated process—although unbounded—need not diverge to infinity. Sufficient conditions for the variance of an integrated process to diverge to infinity are provided. File-URL: https://www.cambridge.org/core/product/identifier/S0266466601174013/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:17:y:2001:i:04:p:671-685_17 Template-type: ReDIF-Article 1.0 Author-Name: Deo, Rohit S. Author-Name: Hurvich, Clifford M. Title: ON THE LOG PERIODOGRAM REGRESSION ESTIMATOR OF THE MEMORY PARAMETER IN LONG MEMORY STOCHASTIC VOLATILITY MODELS Journal: Econometric Theory Pages: 686-710 Issue: 4 Volume: 17 Year: 2001 Month: August Abstract: We consider semiparametric estimation of the memory parameter in a long memory stochastic volatility model. We study the estimator based on a log periodogram regression as originally proposed by Geweke and Porter-Hudak (1983, Journal of Time Series Analysis 4, 221–238). Expressions for the asymptotic bias and variance of the estimator are obtained, and the asymptotic distribution is shown to be the same as that obtained in recent literature for a Gaussian long memory series. The theoretical result does not require omission of a block of frequencies near the origin. We show that this ability to use the lowest frequencies is particularly desirable in the context of the long memory stochastic volatility model. File-URL: https://www.cambridge.org/core/product/identifier/S0266466601174025/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:17:y:2001:i:04:p:686-710_17 Template-type: ReDIF-Article 1.0 Author-Name: Nabeya, Seiji Title: APPROXIMATION TO THE LIMITING DISTRIBUTION OF t- AND F-STATISTICS IN TESTING FOR SEASONAL UNIT ROOTS Journal: Econometric Theory Pages: 711-737 Issue: 4 Volume: 17 Year: 2001 Month: August Abstract: Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238), Beaulieu and Miron (1993, Journal of Econometrics 55, 305–328), Ghysels, Lee, and Noh (1994, Journal of Econometrics 62, 415–442), Smith and Taylor (1998, Journal of Econometrics 85, 269–288; 1999, Journal of Time Series Analysis 20, 453–476; 1999, Discussion paper 99-15 in economics, University of Birmingham), and Taylor (1998, Journal of Time Series Analysis 19, 349–368) have developed a method of testing for seasonal unit roots of zero and nonzero frequencies. They propose to use t- and F-statistics as criteria that are obtained from an auxiliary regression and find their limiting distributions as the number of observations becomes large. Their limiting distributions are expressed by means of Brownian motions. In this paper the moment generating functions associated with the limiting distributions are derived, and it is shown, as in Nabeya (2000, Econometric Theory 16, 200–230), that the limiting distribution of t is well approximated by a distribution given in Gram–Charlier series. The limiting distribution of F is also well approximated by another type of distribution. File-URL: https://www.cambridge.org/core/product/identifier/S0266466601174037/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:17:y:2001:i:04:p:711-737_17 Template-type: ReDIF-Article 1.0 Author-Name: Ling, Shiqing Author-Name: Li, W.K. Title: ASYMPTOTIC INFERENCE FOR NONSTATIONARY FRACTIONALLY INTEGRATED AUTOREGRESSIVE MOVING-AVERAGE MODELS Journal: Econometric Theory Pages: 738-764 Issue: 4 Volume: 17 Year: 2001 Month: August Abstract: This paper considers nonstationary fractional autoregressive integrated moving-average (p,d,q) models with the fractionally differencing parameter d ∈ (− 1/2,1/2) and the autoregression function with roots on or outside the unit circle. Asymptotic inference is based on the conditional sum of squares (CSS) estimation. Under some suitable conditions, it is shown that CSS estimators exist and are consistent. The asymptotic distributions of CSS estimators are expressed as functions of stochastic integrals of usual Brownian motions. Unlike results available in the literature, the limiting distributions of various unit roots are independent of the parameter d over the entire range d ∈ (− 1/2,1/2). This allows the unit roots and d to be estimated and tested separately without loss of efficiency. Our results are quite different from the current asymptotic theories on nonstationary long memory time series. The finite sample properties are examined for two special cases through simulations. File-URL: https://www.cambridge.org/core/product/identifier/S0266466601174049/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:17:y:2001:i:04:p:738-764_17 Template-type: ReDIF-Article 1.0 Author-Name: Zhao, Quanshui Title: ASYMPTOTICALLY EFFICIENT MEDIAN REGRESSION IN THE PRESENCE OF HETEROSKEDASTICITY OF UNKNOWN FORM Journal: Econometric Theory Pages: 765-784 Issue: 4 Volume: 17 Year: 2001 Month: August Abstract: We consider a linear model with heteroskedasticity of unknown form. Using Stone's (1977, Annals of Statistics 5, 595–645) k nearest neighbors (k-NN) estimation approach, the optimal weightings for efficient least absolute deviation regression are estimated consistently using residuals from preliminary estimation. The reweighted least absolute deviation or median regression estimator with the estimated weights is shown to be equivalent to the estimator using the true but unknown weights under mild conditions. Asymptotic normality of the estimators is also established. In the finite sample case, the proposed estimators are found to outperform the generalized least squares method of Robinson (1987, Econometrica 55, 875–891) and the one-step estimator of Newey and Powell (1990, Econometric Theory 6, 295–317) based on a Monte Carlo simulation experiment. File-URL: https://www.cambridge.org/core/product/identifier/S0266466601174050/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:17:y:2001:i:04:p:765-784_17 Template-type: ReDIF-Article 1.0 Author-Name: Pandher, Gurupdesh S. Title: ESTIMATION OF EXCESS RETURNS FROM DERIVATIVE PRICES AND TESTING FOR RISK NEUTRAL PRICING Journal: Econometric Theory Pages: 785-819 Issue: 4 Volume: 17 Year: 2001 Month: August Abstract: This paper develops an econometric framework for (i) estimating excess returns of the security process from high frequency derivative prices, (ii) testing for risk neutral pricing, and (iii) measuring premiums outside the no-arbitrage pricing model. The estimator is constructed by applying quasi-likelihood and Feynman–Kac theory to the risk neutral contingent claims pricing model to generate the optimal orthogonality restriction. The strong consistency and asymptotic normality of the estimator are established in the context of a nonstationary underlying state process. These results further imply that the estimator is robust to distributional assumptions on the underlying asset process. The proposed approach is applicable to any arbitrary derivative security, does not require estimation of the risk neutral probability measure, and has application to spot rate bond pricing models. A controlled diagnostic study based on generating the S&P500 index and calls verifies the ability of the estimators to correctly estimate security excess returns and test for risk neutral pricing. The estimator is invariant to call strikes, and larger samples constructed by cycling over shorter maturity options can be used to reduce its variance. File-URL: https://www.cambridge.org/core/product/identifier/S0266466601174062/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:17:y:2001:i:04:p:785-819_17 Template-type: ReDIF-Article 1.0 Author-Name: Rogers, Alan J. Title: LEAST ABSOLUTE DEVIATIONS REGRESSION UNDER NONSTANDARD CONDITIONS Journal: Econometric Theory Pages: 820-852 Issue: 4 Volume: 17 Year: 2001 Month: August Abstract: Most work on the asymptotic properties of least absolute deviations (LAD) estimators makes use of the assumption that the common distribution of the disturbances has a density that is both positive and finite at zero. We consider the implications of weakening this assumption in a number of regression settings, primarily with a time series orientation. These models include ones with deterministic and stochastic trends, and we pay particular attention to the case of a simple unit root model. The way in which the conventional assumption on the error distribution is modified is motivated in part by N.V. Smirnov's work on domains of attraction in the asymptotic theory of sample quantiles. The approach adopted usually allows for simple characterizations (often featuring a single parameter, γ), of both the shapes of the limiting distributions of the LAD estimators and their convergence rates. The present paper complements the closely related recent work of K. Knight. File-URL: https://www.cambridge.org/core/product/identifier/S0266466601174074/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:17:y:2001:i:04:p:820-852_17 Template-type: ReDIF-Article 1.0 Author-Name: , Title: CORRIGENDA Journal: Econometric Theory Pages: 859-859 Issue: 4 Volume: 17 Year: 2001 Month: August Abstract: In Econometric Theory, volume 17, number 1, an excellent solution to problem 00.1.3 also had been submitted by S. Puntanen, G.P.H. Styan, and H.J. Werner, and this fact was inadvertently omitted. In the same issue, in the restatement of problem 00.1.1, the phrase “skew symmetric” should read “real skew symmetric”; this modification was suggested by S. Puntanen, G.P.H. Styan, and H.J. Werner.A corrigendum to Problem 01.2.2 is also described. File-URL: https://www.cambridge.org/core/product/identifier/S0266466601174098/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:17:y:2001:i:4:p:859-859_9