Serial Correlation Pattern Research Articles

Bivariate INAR Processes with Application to Mutual Fund Share Purchase/Redemption Counts

We propose a new bivariate nonnegative integer-autoregressive (BINAR) model for count process data. We first generalize the existing BINAR(1) model by allowing for dependence between different thinning operators. The extended family allows for intuitive interpretation, as well as tractable properties in terms of aggregation and stationarity. Then we also introduce higher order BINAR(p) and BINAR(∞) dynamics allowing for more flexible serial correlation pattern. So far, the literature has considered the standard BINAR(1) model and its potential extensions to be rather computationally intractable. Our biggest contribution is to show that the proposed extended BINAR family allows for (quasi-)closed-form predictive densities, which significantly facilitates non-linear forecasting and likelihood based estimation. Finally, a BINAR(∞) model with memory persistence is applied to mutual fund purchase/redemption order counts.

Multilevel Models for Intensive Longitudinal Data with Heterogeneous Autoregressive Errors: The Effect of Misspecification and Correction with Cholesky Transformation.

Intensive longitudinal studies, such as ecological momentary assessment studies using electronic diaries, are gaining popularity across many areas of psychology. Multilevel models (MLMs) are most widely used analytical tools for intensive longitudinal data (ILD). Although ILD often have individually distinct patterns of serial correlation of measures over time, inferences of the fixed effects, and random components in MLMs are made under the assumption that all variance and autocovariance components are homogenous across individuals. In the present study, we introduced a multilevel model with Cholesky transformation to model ILD with individually heterogeneous covariance structure. In addition, the performance of the transformation method and the effects of misspecification of heterogeneous covariance structure were investigated through a Monte Carlo simulation. We found that, if individually heterogeneous covariances are incorrectly assumed as homogenous independent or homogenous autoregressive, MLMs produce highly biased estimates of the variance of random intercepts and the standard errors of the fixed intercept and the fixed effect of a level 2 covariate when the average autocorrelation is high. For intensive longitudinal data with individual specific residual covariance, the suggested transformation method showed lower bias in those estimates than the misspecified models when the number of repeated observations within individuals is 50 or more.

Motor Imagery May Incorporate Trial-to-Trial Error

ABSTRACT The authors tested for 1/f noise in motor imagery (MI). Participants pointed and imagined pointing to a single target (Experiment 1), to targets of varied size (Experiment 2), and switched between pointing and grasping (Experiment 3). Experiment 1 showed comparable patterns of serial correlation in actual and imagined movement. Experiment 2 suggested increased correlation for MI and performance with increased task difficulty, perhaps reflecting adaptation to a more complex environment. Experiment 3 suggested a parallel decrease in correlation with task switching, perhaps reflecting discontinuity of mental set. Although present results do not conclusively reveal 1/f fluctuation, the emergent patterns suggest that MI could incorporate trial-to-trial error across a range of constraints.

Predictability in Financial Analyst Forecast Errors: Learning or Irrationality?

ABSTRACTIn this paper, we propose a rational learning‐based explanation for the predictability in financial analysts' earnings forecast errors documented in prior literature. In particular, we argue that the serial correlation pattern in analysts' quarterly earnings forecast errors is consistent with an environment in which analysts face parameter uncertainty and learn rationally about the parameters over time. Using simulations and real data, we show that the predictability evidence is more consistent with rational learning than with irrationality (fixation on a seasonal random walk model or some other dogmatic belief).

Serial correlation in lateralized choices of hand and target

We investigated how lateralized choices of hand and target are influenced by previous behavior. Three monkeys retrieved food pellets following cues indicating the location of available food pellet targets, and the hand that could be used to acquire a target. In pseudo-randomized trials, the monkeys could retrieve food pellet targets only on their right side, only on their left side, or their choice of either right or left side, using only their right hand, only their left hand, or their choice of either hand. We examined separately the patterns of serial correlation in target choices and hand choices. Although individual monkeys showed overall laterality preferences, instead of repeatedly using the preferred hand, we found that the monkeys tended to switch hands in successive trials. This serial correlation in hand choice was stronger and more robust than serial correlation in target choice. Furthermore, the pattern of serial correlation for target choice closely resembled that of serial correlation for hand choice when the animal was allowed to choose both target and hand, but only when the target cue was presented before the hand cue. These results suggest that when cued to choose a hand first, the monkeys tended to make a separate decision as to whether to switch their target choices or not, whereas their decisions to switch hands and targets were linked more tightly if the animal was cued to choose a target first.

Predictability in Financial Analyst Forecast Errors: Learning or Irrationality?

In this paper, we propose a rational learning-based explanation for the predictability in financial analysts' earnings forecast errors documented in prior literature. In particular, we argue that the serial correlation pattern in analysts' quarterly earnings forecast errors is consistent with an environment in which analysts face parameter uncertainty and learn rationally about the parameters over time. Using simulations and real data, we show that the predictability evidence is more consistent with rational learning than with irrationality (fixation on a seasonal random walk model or some other dogmatic belief).

BOOMS AND SLUMPS IN A GAME OF SEQUENTIAL INVESTMENT WITH THE CHANGING FUNDAMENTALS

Many less developed countries have experienced prolonged periods of expansions and reversals in foreign investment inflows. This paper presents a simple game-theoretic model that can explain hysteretic patterns of serial correlation in investment behavior. We develop a sequential move game of coordinated investment played by short-run players under the changing economic environment and demonstrate that in a unique equilibrium of the game, the economy fluctuates over multiple static equilibria, generating hysteresis.

Semiparametric-efficient estimation of AR(1) panel data models

This study focuses on the semiparametric-efficient estimation of random effect panel models containing AR(1) disturbances. We also consider such estimators when the effects and regressors are correlated (Hausman and Taylor, 1981). We introduce two semiparametric-efficient estimators that make minimal assumptions on the distribution of the random errors, effects, and the regressors and that provide semiparametric-efficient estimates of the slope parameters and of the effects. Our estimators extend the previous work of Park and Simar (J. Amer. Statist. Assoc. 89 (1994) 929), Park et al. (J. Econometrics 84 (1998) 273), and Adams et al. (J. Business Econom. Statist. 17 (1999) 349). Theoretical derivations are supplemented by Monte Carlo simulations. We also provide an empirical illustration by estimating relative efficiencies from a stochastic distance function for the U.S. banking industry over the 1980s and 1990s. In markets where regulatory constraints have been lessened or done away with, the deregulatory dynamic market shocks may not be adjusted to immediately and may induce a serial correlation pattern in firm's use of best-practice banking technologies. Our semiparametric estimators have an important role in providing robust point estimates and inferences of the productivity and efficiency gains due to such economic reforms.

The role of measurement error on the interpretation of otolith increment width in the study of growth in larval fish

Patterns in increment widths and the associated measurement error were studied in the otoliths of radiated shanny (Ulvaria subbifurcata) larvae sampled from the field. Mean increment widths increased with larval age, whereas the relative measurement error decreased. Furthermore, the level of serial correlation in increment widths showed a clear increase with age. When measurement error was taken into consideration, the pattern of serial correlation indicates that an individual's growth increments did not show the effect of changes in local environmental conditions for at least 3 days, independent of age. Only after that period can we hope to detect the effect of environmental influences on increment widths (and by inference growth rates). The patterns of measurement error and serial correlation will have direct impacts on our ability to find the influence of environmental conditions on growth rates of individual larvae and determine patterns of selective loss in a population of larval fish.

Fitting a Serial Correlation Pattern to Repeated Observations

When repeated observations are taken at equal time intervals, a simple form of a stationary time series structure may be fitted to the observations. Wallenstein and Fleiss (1979) have shown that the degrees-of-freedom correction factor for time effects has a higher lowerbound for data with a serial correlation pattern (or a simplex pattern) than for data without such a structure. The reanalysis of the example data found in Hearne, Clark, and Hatch (1983) indicated that the correction factor from a patterned matrix could be smaller than the counterpart without fitting a simplex pattern. First, an example from education was used to illustrate the computational steps in obtaining these two correction factors. Second, a simulation study was conducted to determine the conditions under which fitting a simplex pattern would be advantageous over not assuming such a pattern. Fitting a serial correlation pattern did not always produce more powerful tests of time effects than not assuming such a pattern. This was particularly true when correlations were high (ρ > .50). Furthermore, it inflated Type I error rates when the simplex shypothesis was not warranted. Indiscriminately fitting a serial correlation pattern should be discouraged.

Fitting a Serial Correlation Pattern to Repeated Observations

Fitting a Serial Correlation Pattern to Repeated Observations

N = 1 Designs: The Failure of ANOVA-Based Tests

Several methods have been proposed for the analysis of data from single-subject research settings. This research focuses on the modifications of ANOVA-based tests proposed by Shine and Bower, a procedure that precedes the ANOVA F test by preliminary testing of within-phase lag one serial correlation and the one-way ANOVA as presented by Gentile, Roden and Klein. Monte Carlo simulation is used to investigate these tests with respect to robustness and power. Each test was analyzed under various patterns of serial correlation, various patterns of phase and trial means, normal and exponential distributions, and equal and unequal phase variances. The findings indicate that the probability of a Type I error for these ANOVA-based tests is seriously inflated by nonzero serial correlation. These tests, therefore, cannot be recommended for use with data that have nonzero serial correlation.

A Test for Serial Correlation in Univariate Repeated-Measures Analysis

A popular design in biostatistics and psychometrics is the time-factor experiment involving one grouping factor, e.g. treatment or drug, and one repeated-measures factor, e.g. time or visit. If F tests involving the repeated-measures factor are to be valid, univariate analytic procedures require special assumptions for covariance matrices across groups. The robustness of these univariate procedures is investigated when the covariance matrices do not satisfy these assumptions but have a frequently occurring form, namely the serial correlation or simplex pattern. A table is presented which shows that, for some matrices that fit the pattern, the main-effect repeated-measures estimated actual probability level is more than three times the .05 nominal level. A likelihood ratio test for the serial correlation pattern is presented, along with an example from the field of biostatistics.

A method of testing for serial correlation in univariate repeated-measures analyses of variance

Many behavioral experiments utilize a two-factor split-plot design having one between-subjects grouping factor and one within-subjects repeated-measures factor. Subjects are assigned at random to the various levels of the grouping factor, but all subjects are exposed to all levels of the repeated-measures factor. Very often, the repeated-measures factor represents levels of a temporal variable (e.g., laboratory sessions or experimental trials). There are two assumptions concerning the variance-covariance matrices that must be met for a valid univariate test of the trials effect or the Trials by Groups interaction effect. First, the variance-covariance matrices for a set of orthonormal variables corresponding to the effect of the repeated factor must be equal across groups. The Box M test may be used to test this assumption (Huynh & Mandeville, 1979). Second, the common covariance matrix must be spherical. An approximate test for this assumption appears in Huynh and Feldt (1970).1 When these assumptions are not met, the use of a multivariate test or reducing the degrees of freedom on repeated-measures factors (Geisser & Greenhouse, 1958) to yield a conservative but more robust univariate F test are recommended. The purpose of this discussion is to comment briefly on a particular covariance matrix structure that is not spherical and to introduce a method with which to further explore the covariance matrix structure when violations of the sphericity assumption occur. When the repeated-measures factor is time, observations made closer together tend to be more highly correlated than those made further apart. One such pattern is the serial correlation pattern, and it can be a common cause of sphericity assumption violations in behavioral research. We recently examined the effects of the serial correlation pattern on conventional alpha levels (Hearne, Clark, & Hatch, in press) and found that in extreme cases of the pattern (correlation of trial levels one step apart =.8) actual alpha levels were more than three times the nominal level. Thus, certain types of covariance matrix structure that violate the sphericity