Template-type: ReDIF-Article 1.0 Author-Name: Kazakevičius, Vytautas Author-Name: Leipus, Remigijus Title: ON STATIONARITY IN THE ARCH(∞) MODEL Journal: Econometric Theory Pages: 1-16 Issue: 1 Volume: 18 Year: 2002 Month: February Abstract: We continue investigation of the ARCH(∞) model begun in Giraitis, Kokoszka, and Leipus (2000, Econometric Theory 16, 3–22). Nonrestrictive conditions for the existence of a strictly stationary solution are established. The paper generalizes the results of Nelson (1990, Econometric Theory 6, 318–334) and Bougerol and Picard (1992, Journal of Econometrics 52, 115–127) to the ARCH(∞) model. File-URL: https://www.cambridge.org/core/product/identifier/S0266466602181011/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:18:y:2002:i:01:p:1-16_18 Template-type: ReDIF-Article 1.0 Author-Name: Carrasco, Marine Author-Name: Chen, Xiaohong Title: MIXING AND MOMENT PROPERTIES OF VARIOUS GARCH AND STOCHASTIC VOLATILITY MODELS Journal: Econometric Theory Pages: 17-39 Issue: 1 Volume: 18 Year: 2002 Month: February Abstract: This paper first provides some useful results on a generalized random coefficient autoregressive model and a generalized hidden Markov model. These results simultaneously imply strict stationarity, existence of higher order moments, geometric ergodicity, and β-mixing with exponential decay rates, which are important properties for statistical inference. As applications, we then provide easy-to-verify sufficient conditions to ensure β-mixing and finite higher order moments for various linear and nonlinear GARCH(1,1), linear and power GARCH(p,q), stochastic volatility, and autoregressive conditional duration models. For many of these models, our sufficient conditions for existence of second moments and exponential β-mixing are also necessary. For several GARCH(1,1) models, our sufficient conditions for existence of higher order moments again coincide with the necessary ones in He and Terasvirta (1999, Journal of Econometrics 92, 173–192). File-URL: https://www.cambridge.org/core/product/identifier/S0266466602181023/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:18:y:2002:i:01:p:17-39_18 Template-type: ReDIF-Article 1.0 Author-Name: Schafgans, Marcia M.A. Author-Name: Zinde-Walsh, Victoria Title: ON INTERCEPT ESTIMATION IN THE SAMPLE SELECTION MODEL Journal: Econometric Theory Pages: 40-50 Issue: 1 Volume: 18 Year: 2002 Month: February Abstract: We provide a proof of the consistency and asymptotic normality of the estimator suggested by Heckman (1990, American Economic Review 80, 313–318) for the intercept of a semiparametrically estimated sample selection model. The estimator is based on “identification at infinity,” which leads to nonstandard convergence rate. File-URL: https://www.cambridge.org/core/product/identifier/S0266466602181035/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:18:y:2002:i:01:p:40-50_18 Template-type: ReDIF-Article 1.0 Author-Name: Chung, Ching-Fan Title: SAMPLE MEANS, SAMPLE AUTOCOVARIANCES, AND LINEAR REGRESSION OF STATIONARY MULTIVARIATE LONG MEMORY PROCESSES Journal: Econometric Theory Pages: 51-78 Issue: 1 Volume: 18 Year: 2002 Month: February Abstract: We develop an asymptotic theory for the first two sample moments of a stationary multivariate long memory process under fairly general conditions. In this theory the convergence rates and the limits (the fractional Brownian motion, the Rosenblatt process, etc.) all depend intrinsically on the degree of long memory in the process. The theory of the sample moments is then applied to the multiple linear regression model. An interesting finding is that, even though all the regressors and the disturbance are stationary and ergodic, the joint long memory in one single regressor and in the disturbance can invalidate the usual asymptotic theory for the ordinary least squares (OLS) estimation. Specifically, the convergence rates of the OLS estimators become slower, the limits are not normal, and the standard t- and F-tests all collapse. File-URL: https://www.cambridge.org/core/product/identifier/S0266466602181047/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:18:y:2002:i:01:p:51-78_18 Template-type: ReDIF-Article 1.0 Author-Name: Lahiri, S.N. Title: ON THE JACKKNIFE-AFTER-BOOTSTRAP METHOD FOR DEPENDENT DATA AND ITS CONSISTENCY PROPERTIES Journal: Econometric Theory Pages: 79-98 Issue: 1 Volume: 18 Year: 2002 Month: February Abstract: Motivated by Efron (1992, Journal of the Royal Statistical Society, Series B 54, 83–111), this paper proposes a version of the moving block jackknife as a method of estimating standard errors of block-bootstrap estimators under dependence. As in the case of independent and identically distributed (i.i.d.) observations, the proposed method merely regroups the values of a statistic from different bootstrap replicates to produce an estimate of its standard error. Consistency of the resulting jackknife standard error estimator is proved for block-bootstrap estimators of the bias and the variance of a large class of statistics. Consistency of Efron's method is also established in similar problems for i.i.d. data. File-URL: https://www.cambridge.org/core/product/identifier/S0266466602181059/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:18:y:2002:i:01:p:79-98_18 Template-type: ReDIF-Article 1.0 Author-Name: Nicolau, João Title: STATIONARY PROCESSES THAT LOOK LIKE RANDOM WALKS— THE BOUNDED RANDOM WALK PROCESS IN DISCRETE AND CONTINUOUS TIME Journal: Econometric Theory Pages: 99-118 Issue: 1 Volume: 18 Year: 2002 Month: February Abstract: Several economic and financial time series are bounded by an upper and lower finite limit (e.g., interest rates). It is not possible to say that these time series are random walks because random walks are limitless with probability one (as time goes to infinity). Yet, some of these time series behave just like random walks. In this paper we propose a new approach that takes into account these ideas. We propose a discrete-time and a continuous-time process (diffusion process) that generate bounded random walks. These paths are almost indistinguishable from random walks, although they are stochastically bounded by an upper and lower finite limit. We derive for both cases the ergodic conditions, and for the diffusion process we present a closed expression for the stationary distribution. This approach suggests that many time series with random walk behavior can in fact be stationarity processes. File-URL: https://www.cambridge.org/core/product/identifier/S0266466602181060/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:18:y:2002:i:01:p:99-118_18 Template-type: ReDIF-Article 1.0 Author-Name: Wang, Qiying Author-Name: Lin, Yan-Xia Author-Name: Gulati, Chandra M. Title: THE INVARIANCE PRINCIPLE FOR LINEAR PROCESSES WITH APPLICATIONS Journal: Econometric Theory Pages: 119-139 Issue: 1 Volume: 18 Year: 2002 Month: February Abstract: Let Xt be a linear process defined by Xt = [sum ]k=0∞ ψkεt−k, where {ψk, k ≥ 0} is a sequence of real numbers and {εk, k = 0,±1,±2,...} is a sequence of random variables. Two basic results, on the invariance principle of the partial sum process of the Xt converging to a standard Wiener process on [0,1], are presented in this paper. In the first result, we assume that the innovations εk are independent and identically distributed random variables but do not restrict [sum ]k=0∞ |ψk| < ∞. We note that, for the partial sum process of the Xt converging to a standard Wiener process, the condition [sum ]k=0∞ |ψk| < ∞ or stronger conditions are commonly used in previous research. The second result is for the situation where the innovations εk form a martingale difference sequence. For this result, the commonly used assumption of equal variance of the innovations εk is weakened. We apply these general results to unit root testing. It turns out that the limit distributions of the Dickey–Fuller test statistic and Kwiatkowski, Phillips, Schmidt, and Shin (KPSS) test statistic still hold for the more general models under very weak conditions. File-URL: https://www.cambridge.org/core/product/identifier/S0266466602181072/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:18:y:2002:i:01:p:119-139_18 Template-type: ReDIF-Article 1.0 Author-Name: Hahn, Jinyong Title: OPTIMAL INFERENCE WITH MANY INSTRUMENTS Journal: Econometric Theory Pages: 140-168 Issue: 1 Volume: 18 Year: 2002 Month: February Abstract: In this paper, I derive the efficiency bound of the structural parameter in a linear simultaneous equations model with many instruments. The bound is derived by applying a convolution theorem to Bekker's (1994, Econometrica 62, 657–681) asymptotic approximation, where the number of instruments grows to infinity at the same rate as the sample size. Usual instrumental variables estimators with a small number of instruments are heuristically argued to be efficient estimators in the sense that their asymptotic distribution is minimal. Bayesian estimators based on parameter orthogonalization are heuristically argued to be inefficient. File-URL: https://www.cambridge.org/core/product/identifier/S0266466602181084/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:18:y:2002:i:01:p:140-168_18 Template-type: ReDIF-Article 1.0 Author-Name: Cai, Zongwu Title: REGRESSION QUANTILES FOR TIME SERIES Journal: Econometric Theory Pages: 169-192 Issue: 1 Volume: 18 Year: 2002 Month: February Abstract: In this paper we study nonparametric estimation of regression quantiles for time series data by inverting a weighted Nadaraya–Watson (WNW) estimator of conditional distribution function, which was first used by Hall, Wolff, and Yao (1999, Journal of the American Statistical Association 94, 154–163). First, under some regularity conditions, we establish the asymptotic normality and weak consistency of the WNW conditional distribution estimator for α-mixing time series at both boundary and interior points, and we show that the WNW conditional distribution estimator not only preserves the bias, variance, and, more important, automatic good boundary behavior properties of local linear “double-kernel” estimators introduced by Yu and Jones (1998, Journal of the American Statistical Association 93, 228–237), but also has the additional advantage of always being a distribution itself. Second, it is shown that under some regularity conditions, the WNW conditional quantile estimator is weakly consistent and normally distributed and that it inherits all good properties from the WNW conditional distribution estimator. A small simulation study is carried out to illustrate the performance of the estimates, and a real example is also used to demonstrate the methodology. File-URL: https://www.cambridge.org/core/product/identifier/S0266466602181096/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:18:y:2002:i:01:p:169-192_18 Template-type: ReDIF-Article 1.0 Author-Name: , Title: PROBLEMS AND SOLUTIONS Journal: Econometric Theory Pages: 193-194 Issue: 1 Volume: 18 Year: 2002 Month: February Abstract: File-URL: https://www.cambridge.org/core/product/identifier/S026646660200110X/type/journal_article File-Function: link to article abstract page File-Format: text/html Handle: RePEc:cup:etheor:v:18:y:2002:i:1:p:193-194_10