Convergence of Discount Time Series Dynamic Linear Models

This article studies the limiting behavior of multiple discount time series dynamic linear models (TSDLMs). It is shown that, under mild conditions, all discount TSDLMs converge to the constant (time-invariant) TSDLM. In particular, the limiting posterior precision matrix of the superposition of multiple discount TSDLMs is explored. For non seasonal models, the elements of the limiting posterior precision of the states are given in a recurrence relationship, while for seasonal models the solution of a linear system provides the elements of the respective limiting precision matrix. The proposed methodology uses canonical Jordan forms and it is illustrated with a detailed example of simulated data featuring both trend and seasonal time series.     

Smoothing Time Series with Local Polynomial Regression on Time

Time series smoothers estimate the level of a time series at time t as its conditional expectation given present, past and future observations, with the smoothed value depending on the estimated time series model. Alternatively, local polynomial regressions on time can be used to estimate the level, with the implied smoothed value depending on the weight function and the bandwidth in the local linear least squares fit. In this article we compare the two smoothing approaches and describe their similarities. Through simulations, we assess the increase in the mean square error that results when approximating the estimated optimal time series smoother with the local regression estimate of the level.     

Nonparametric Trend Estimation for Periodic Autoregressive Time Series

A periodically stationary time series has seasonal variances. A local linear trend estimation is proposed to accommodate unequal variances. A comparison of this proposed estimator with the estimator commonly used for a stationary time series is provided. The optimal bandwidth selection for this new trend estimator is discussed.     

On the total sojourn time of particles in semi-markov compartmental system with branching particles

We consider a semi-Markov compartroental system with branching particles, Me study the total sojourn time of all the particles and obtain the asymptotic behaviour of its mean. We also discuss some special systems.     

Bhattacharyya distance based linear discriminant function for stationary time series

The problem of classifying a covariance stationary normal time series is considered. Under certain regularity conditions, a compact form of the linear discriminant function in the sense of maximizing the Bhattacharyya distance is obtained.     

Unobserved-Components Models for Seasonal Adjustment Filters

Time series models are presented, for which the seasonal-component estimates delivered by linear least squares signal extraction closely approximate those of the standard option of the widely-used Census X-11 program. Earlier work is extended by consideration of a broader class of models and by examination of asymmetric filters, in addition to the symmetric filter implicit in the adjustment of historical data. Various criteria that guide the specification of unobserved- components models are discussed, and a new preferred model is presented. Some nonstandard options in X-11 are considered in the Appendix.     

Inference for Time Series Regression Models With Weakly Dependent and Heteroscedastic Errors

Motivated by the need to assess the significance of the trend in some macroeconomic series, this article considers inference of a parameter in parametric trend functions when the errors exhibit certain degrees of nonstationarity with changing unconditional variances. We adopt the recently developed self-normalized approach to avoid the difficulty involved in the estimation of the asymptotic variance of the ordinary least-square estimator. The limiting distribution of the self-normalized quantity is nonpivotal but can be consistently approximated by using the wild bootstrap, which is not consistent in general without studentization. Numerical simulation demonstrates favorable coverage properties of the proposed method in comparison with alternative ones. The U.S. nominal wages series is analyzed to illustrate the finite sample performance. Some technical details are included in the online supplemental material.     

How Employed Mothers in Australia Find Time for Both Market Work and Childcare

Time use studies find that employed mothers reduce their parental childcare time by much less than an hour for every hour they spend in market work. This paper uses data from the Australian Bureau of Statistics Time Use Survey 1997 (4,059 randomly selected households) to investigate how employed mothers manage to avoid a one-for-one trade-off between work and childcare. It compares the time allocation of employed fathers, employed mothers and non-employed mothers and finds that parents use non-parental childcare to reschedule as well as to replace their own childcare, that employed mothers reschedule activities from weekdays to weekends or to earlier or later in the day, and spend less time than other mothers in housework, childfree leisure and personal care.

Educational assortative mating and time use in the home

This study examines the association between individuals' educational assortative mating and time spent on child care and housework. Focus is put on hypogamous couples, or couples in which wives have more education than their husbands. Relative resources and gender revolution frameworks are considered as contexts to explain why hypogamous couples may share their time differently than other couples. A series of ordinary least squares regressions with population and sampling weights are employed using American Time Use Survey data from 2003 to 2018. Three, separate analyses using relative education, gender, and all educational pairings as the independent variables of interest are presented with child care and housework as the dependent variables. The current findings show that men in hypogamous marriages perform about 10 min more of child care per day on average than their peers in hypergamous and homogamous marriages, and that this comes primarily from basic care activities. This accounts for approximately 43% of the difference between men and women in the average amount of time spent on child care. No clear pattern of significance is apparent comparing individuals’ time spent on housework by relative education, suggesting that housework and child care have evolved differently in the context of gendered domestic responsibilities. Men in hypogamous marriages are more egalitarian in their sharing of child care. However, this is only true for couples in which men have at least a high school diploma and women are highly educated.