A methodology for population projections: an application to Spain

This paper looks at projections for the Spanish population by sex and age for the period of 2005 to 2050. These were carried out using forecasts for birth and mortality rates, and migration. These rates are calculated using two main sources of information. First, a multivariate time series model was applied for the series of variables from the 1970 to 2001 period. Second a model was estimated for life expectancy and for a synthetic fertility index. Both sources of information were combined to obtain the forecasts for the rates. Immigration rates are predicted by assuming three possible scenarios based on the maximum proportion that immigrants will represent in the Spanish population. With these variables a structure of ages and sex for the Spanish population is estimated using a cohort component model

INTRODUCING MODEL UNCERTAINTY IN TIME SERIES BOOTSTRAP

It is common in parametric bootstrap to select the model from the data, and then treat it as it were the true model. Kilian (1998) have shown that ignoring the model uncertainty may seriously undermine the coverage accuracy of bootstrap confidence intervals for impulse response estimates which are closely related with multi-step-ahead prediction intervals. In this paper, we propose different ways of introducing the model selection step in the resampling algorithm. We present a Monte Carlo study comparing the finite sample properties of the proposed method with those of alternative methods in the case of prediction intervals.

A methodology for population projections: an application to Spain

This paper looks at projections for the Spanish population by sex and age for the period of 2005 to 2050. These were carried out using forecasts for birth and mortality rates, and migration. These rates are calculated using two main sources of information. First, a multivariate time series model was applied for the series of variables from the 1970 to 2001 period. Second a model was estimated for life expectancy and for a synthetic fertility index. Both sources of information were combined to obtain the forecasts for the rates. Immigration rates are predicted by assuming three possible scenarios based on the maximum proportion that immigrants will represent in the Spanish population. With these variables a structure of ages and sex for the Spanish population is estimated using a cohort component model.Population projections, Time series, Factorial model, Bootstrap

Clustering time series by linear dependency

We present a new way to find clusters in large vectors of time series by using a measure of similarity between two time series, the generalized cross correlation. This measure compares the determinant of the correlation matrix until some lag k of the bivariate vector with those of the two univariate time series. A matrix of similarities among the series based on this measure is used as input of a clustering algorithm. The procedure is automatic, can be applied to large data sets and it is useful to find groups in dynamic factor models. The cluster method is illustrated with some Monte Carlo experiments and a real data example

Forecasting time series with sieve bootstrap

In this paper we consider bootstrap methods for constructing nonparametric prediction intervals for a general class of linear processes. Our approach uses the sieve bootstrap procedure of Biihlmann (1997) based on residual resampling from an autoregressive approximation to the given process. We show that the sieve bootstrap provides consistent estimators of the conditional distribution of future values given the observed data, assuming that the order of the autoregressive approximation increases with the sample size at a suitable rate and some restrictions about polynomial decay of the coefficients ~ j t:o of the process MA(oo) representation. We present a Monte Carlo study comparing the finite sample properties of the sieve bootstrap with those of alternative methods. Finally, we illustrate the performance of the proposed method with real data examples

Resampling time series by missing values techniques

For strongly dependent data, deleting blocks of observations is expected to produce bias as in the moving block jackknife of KOnsch (1989) and Liu and Singh (1992). We propose an alternative technique which considers the blocks of deleted observations in the blockwise jackknife as missing data which are replaced by missing values estimates incorporating the observations dependence structure. Thus, the variance estimator is a weighted sample variance of the statistic evaluated in a "complete" series. We establish consistency for the variance and distribution of the sample mean. Also we extent this missing values approach to the blockwise bootstrap by assuming some missing observations among two consecutive blocks. We present the results of an extensive Monte Carlo study to evaluate the performance of the proposed methods in finite sample sizes in which it is shown that our proposal produces estimates of the variance of several time series statistics with smaller mean squared error than previous procedures

Forecasting time series with sieve bootstrap.

In this paper we propose bootstrap methods for constructing nonparametric prediction intervals for a general class of linear processes. Our approach uses the AR(∞)-sieve bootstrap procedure based on residual resampling from an autoregressive approximation to the given process. We present a Monte Carlo study comparing the finite sample properties of the sieve bootstrap with those of alternative methods. Finally, we illustrate the performance of the proposed method with a real data example.We would like to thank Mike Wiper, two referees and the coordinating editor for carefully reading that greatly improved the paper. This research was partially supported by the Dirección General de Educación Superior project DGES PB96-0111 and Cátedra de Calidad BBVA.Publicad

Análisis antracológico del yacimiento arqueológico de Peña Parda

Se presenta el estudio antracológico de los carbones recuperados en el abrigo de Peña Parda (Laguardia, Álava). El Nivel DI, de cronología calcolítica, es el de mayor fiabilidad estratigráfíca ya que el Nivel I incluye con bastante probabilidad restos vegetales de cronología reciente. En el Nivel III la madera más abundante es el boj (42%), seguido del tejo (33%). Otros taxones menores, presentes en porcentajes inferiores al 5% son: enebro, pino, gayuba/madroño, cornejo, fresno, hiedra, leguminosas, pomoidea, cerezo, roble/quejigo, grosellero y morrionera. Sugerimos que en el momento de ocupación del yacimiento las formaciones de bojedo debieron ser importantes en el entorno. La presencia del tejo debe responder a su capacidad de colonizar suelos delgados y rocosos

Una revisión de los métodos de remuestreo en series temporales.

Desde Efron y Tibshirani (1986), se han propuesto varios métodos de remuestreo para datos temporales. En este artículo, presentamos los principales métodos de remuestreo desarrollados para series temporales, centrándonos en el jackknife por bloques móviles, el bootstrap por bloques móviles, y en el bootstrap para modelos autorregresivos, y proponemos nuevas alternativas para los métodos de remuestreo basados en bloques de observaciones.Publicad

On sieve bootstrap prediction intervals.

In this paper we consider a sieve bootstrap method for constructing nonparametric prediction intervals for a general class of linear processes. We show that the sieve bootstrap provides consistent estimators of the conditional distribution of future values given the observed data.We would like to thank Mike Wiper for his careful reading which greatly improved the paper. This research was partially supported by the CYCIT project BEC 2000-0167 and by the Cátedra de Calidad BBVA.Publicad