Assessment of annihilation anxiety from projective tests

This report details procedures to measure annihilation anxiety, a concept derived from Freud's 1926 formulation of traumatic anxiety. A 25-item pencil-and-paper inventory administered to patient and to nonpatient samples is described, along with a brief summary of earlier findings. The delineation of nine interrelated experiential components of annihilation anxiety provides the background for the construction of Rorschach and TAT measures of the concept. Findings comparing the pencil-and-paper inventory and the projective test measures are presented as well as examples of responses judged to reflect annihilation anxiety from Rorschach and TAT protocols.     

The averaged periodogram estimator for a power law in coherency

We prove the consistency of the averaged periodogram estimator (APE) in two new cases. First, we prove that the APE is consistent for negative memory parameters, after suitable tapering. Second, we prove that the APE is consistent for a power law in the cross‐spectrum and therefore for a power law in the coherency, provided that sufficiently many frequencies are used in estimation. Simulation evidence suggests that the lower bound on the number of frequencies is a necessary condition for consistency. For a Taylor series approximation to the estimator of the power law in the cross‐spectrum, we consider the rate of convergence and obtain a central limit theorem under suitable regularity conditions.     

The mean squared error of Geweke and Porter-Hudak's estimator of the memory parameter of a long-memory time series

We establish some asymptotic properties of a log-periodogram regression estimator for the memory parameter of a long-memory time series. We consider the estimator originally proposed by Geweke and Porter-Hudak (The estimation and application of long memory time series models. Journal of Time Ser. Anal. 4 (1983), 221–37). In particular, we do not omit any of the low frequency periodogram ordinates from the regression. We derive expressions for the estimator's asymptotic bias, variance and mean squared error as functions of the number of periodogram ordinates, m , used in the regression. Consistency of the estimator is obtained as long as m ←∞ and n ←∞ with ( m log m )/ n ← 0, where n is the sample size. Under these and the additional conditions assumed in this paper, the optimal m , minimizing the mean squared error, is of order O( n ^4/5). We also establish the asymptotic normality of the estimator. In a simulation study, we assess the accuracy of our asymptotic theory on mean squared error for finite sample sizes. One finding is that the choice m = n ^1/2, originally suggested by Geweke and Porter-Hudak (1983), can lead to performance which is markedly inferior to that of the optimal choice, even in reasonably small samples.     

Plug-in Selection of the Number of Frequencies in Regression Estimates of the Memory Parameter of a Long-memory Time Series

We consider the problem of selecting the number of frequencies, m , in a log-periodogram regression estimator of the memory parameter d of a Gaussian long-memory time series. It is known that under certain conditions the optimal m , minimizing the mean squared error of the corresponding estimator of d , is given by m ^(opt)= Cn ^4/5, where n is the sample size and C is a constant. In practice, C would be unknown since it depends on the properties of the spectral density near zero frequency. In this paper, we propose an estimator of C based again on a log-periodogram regression and derive its consistency. We also derive an asymptotically valid confidence interval for d when the number of frequencies used in the regression is deterministic and proportional to n ^4/5. In this case, squared bias cannot be neglected since it is of the same order as the variance. In a Monte Carlo study, we examine the performance of the plug-in estimator of d , in which m is obtained by using the estimator of C in the formula for m ^(opt) above. We also study the performance of a bias-corrected version of the plug-in estimator of d . Comparisons with the choice m = n ^1/2 frequencies, as originally suggested by Geweke and Porter-Hudak (The estimation and application of long memory time series models. Journal of Time Ser. Anal. 4 (1983), 221–37), are provided.     

CROSS-VALIDATORY CHOICE OF A SPECTRUM ESTIMATE AND ITS CONNECTIONS WITH AIC

Abstract. This paper concerns the use of a generalized version of the cross-validated log likelihood criterion (CVLL) for selecting a spectrum estimator from an arbitrary class of candidate estimators. It is shown that CVLL is asymptotically equivalent to the expected Kullback-Leibler information of the candidate estimator. The Akaike information criterion (AIC) is also asymptotically equivalent to Kullback-Leibler information, but the applicability of AIC is limited to parametric estimators. Thus CVLL can be viewed as a cross-validatory generalization of AIC. Monte Carlo results show that CVLL is able to provide an effective choice from a class of candidates which simultaneously includes autoregressive and classical smoothed periodogram estimators. To save computation time, CVLL can be evaluated only for the classical estimators while the computationally more efficient AIC is evaluated for the parametric estimators. The criterion values are all directly comparable in this case. As an additional computation-saving device, a non-cross-validatory version of CVLL for classical estimators is proposed and studied.     

Nightmares and annihilation anxiety.

Evaluated the relation between self-reported frequency of nightmares, a number of saliency measures of the nightmare experience, and a self-report measure of annihilation anxiety (appended) for 1,357 undergraduates from 2 independent populations. A significant positive relation was found between nightmare frequency and salience and annihilation anxiety. Findings were cross-validated across both samples. Results are discussed within the context of object relations and ego psychology theory utilizing an ego boundary model and are consistent with previous research (e.g., E. Hartmann, 1991) demonstrating boundary impairment in Ss with self-reported frequent nightmares. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The Slow Convergence of Ordinary Least Squares Estimators of α, β and Portfolio Weights under Long‐Memory Stochastic Volatility

We consider inference for the market model coefficients based on simple linear regression under a long memory stochastic volatility generating mechanism for the returns. We obtain limit theorems for the ordinary least squares (OLS) estimators of α and β in this framework. These theorems imply that the convergence rate of the OLS estimators is typically slower than if both the regressor and the predictor have long memory in volatility, where T is the sample size. The traditional standard errors of the OLS‐estimated intercept () and slope (), which disregard long memory in volatility, are typically too optimistic, and therefore the traditional t‐statistic for testing, say, α = 0 or β = 1, will diverge under the null hypothesis. We also obtain limit theorems (which imply slow convergence) for the estimated weights of the minimum variance portfolio and the optimal portfolio in the same framework. In addition, we propose and study the performance of a subsampling‐based approach to hypothesis testing for α and β. We conclude by noting that analogous results hold under more general conditions on long‐memory volatility models and state these general conditions which cover certain fractionally integrated exponential generalized autoregressive conditional heteroskedasticity (EGARCH) models.     

Linear Trend with Fractionally Integrated Errors

We consider the estimation of linear trend for a time series in the presence of additive long-memory noise with memory parameter d ∈[0, 1.5). Although no parametric model is assumed for the noise, our assumptions include as special cases the random walk with drift as well as linear trend with stationary invertible autoregressive moving-average errors. Moreover, our assumptions include a wide variety of trend-stationary and difference-stationary situations. We consider three different trend estimators: the ordinary least squares estimator based on the original series, the sample mean of the first differences and a class of weighted (tapered) means of the first differences. We present expressions for the asymptotic variances of these estimators in the form of one-dimensional integrals. We also establish the asymptotic normality of the tapered means for d ∈[0, 1.5) −{0.5} and of the ordinary least squares estimator for d ∈ (0.5, 1.5). We point out connections with existing theory and present applications of the methodology.     

An Efficient Taper for Potentially Overdifferenced Long-memory Time Series

We propose a new complex-valued taper and derive the properties of a tapered Gaussian semiparametric estimator of the long-memory parameter d ε (−0.5, 1.5). The estimator and its accompanying theory can be applied to generalized unit root testing. In the proposed method, the data are differenced once before the taper is applied. This guarantees that the tapered estimator is invariant with respect to deterministic linear trends in the original series. Any detrimental leakage effects due to the potential noninvertibility of the differenced series are strongly mitigated by the taper. The proposed estimator is shown to be more efficient than existing invariant tapered estimators. Invariance to k th order polynomial trends can be attained by differencing the data k times and then applying a stronger taper, which is given by the k th power of the proposed taper. We show that this new family of tapers enjoys strong efficiency gains over comparable existing tapers. Analysis of both simulated and actual data highlights potential advantages of the tapered estimator of d compared with the nontapered estimator.     

Computationally efficient methods for two multivariate fractionally integrated models

Abstract.  We discuss two distinct multivariate time-series models that extend the univariate ARFIMA (autoregressive fractionally integrated moving average) model. We discuss the different implications of the two models and describe an extension to fractional cointegration. We describe algorithms for computing the covariances of each model, for computing the quadratic form and approximating the determinant for maximum likelihood estimation and for simulating from each model. We compare the speed and accuracy of each algorithm with existing methods individually. Then, we measure the performance of the maximum likelihood estimator and of existing methods in a Monte Carlo. These algorithms are much more computationally efficient than the existing algorithms and are equally accurate, making it feasible to model multivariate long memory time series and to simulate from these models. We use maximum likelihood to fit models to data on goods and services inflation in the United States.