A note on influence diagnostics in AR(1) time series models

The purpose of this paper is to develop influence diagnostics for AR(1) models under the innovative and the data perturbation schemes. There are four main contributions. First, we derive analytical expressions for the slope and curvature statistics. Second, we establish a relationship between the slope and curvature showing that the standardised slope and standardised curvature are equal for the innovative perturbation scheme, and these vectors are nearly identical for several values of the autoregressive parameter, for the data perturbation scheme. Third, we present a connection between the influence statistics and the tests for outlier detection. Fourth, for the innovative perturbation scheme, we derive the asymptotic distribution of a new influence statistic, whereas for the data perturbation scheme, the distribution of the influence statistics is obtained via Monte Carlo simulation. We additionally discuss practical guidelines for the use of local influence statistics, which are illustrated on a chemical process data set.     

It Takes Two to Tango: Couples’ Happiness and Childbearing

The existing literature has so far considered the role of the individual’s subjective well-being on fertility, neglecting the importance of the partner’s well-being. Using data from the British Household Panel Survey (BHPS) and event history models estimated separately by parity, we find that in a couple, women’s happiness matters more than that of the male partner in terms of having the first child. Specifically, we observe that couples in which either partner is happier than usual are more at risk of having the first child, but the effect is stronger with higher happiness of the woman. For the transition to the second child, we find that couples in which the woman declares to be happier or less happy than usual have a lower risk of childbirth. We, moreover, find support for a multiplicative effect of partners’ SWB on the decision to have a first child. Our results show that failing to acknowledge that the subjective well-being of both partners matters for the inherently joint decision making of childbearing can lead to an incomplete view of how subjective well-being affects fertility.     

The choice of time interval in seasonal adjustment: A heuristic approach

A typical problem of the seasonal adjustment procedures arises when the series to be adjusted is subject to structural breaks. In fact, using the full span of the series can result in a biased estimation of the “true” seasonally adjusted series, with unclear evidence showed by the usual diagnostic tests. In these cases the researcher has to decide where to cut-off the observed series to obtain a homogeneous span; this is generally performed by a simple visual inspection of the graph of the series and/or using a-priori information about the occurrence of the break. In this paper we propose a statistical criterion based on a distance measure between filters, evaluating its performance with Monte Carlo experiments. The first results of this work have been presented at the XL scientific meeting of the Italian statistical society, Florence, 26–28 April 2000, benefiting of the discussion arisen there; a preliminary version of this paper circulated as ISAE working paper No. 21/2001 with the title “The Choice of Time Interval in Seasonal Adjustment: Characterization and Tools”. We thank an anonymous referee for precious suggestions. The authors are solely responsible of any remaining error.     

A spatiotemporal model for Mexico City ozone levels

Summary.  We consider hourly readings of concentrations of ozone over Mexico City and propose a model for spatial as well as temporal interpolation and prediction. The model is based on a time-varying regression of the observed readings on air temperature. Such a regression requires interpolated values of temperature at locations and times where readings are not available. These are obtained from a time-varying spatiotemporal model that is coupled to the model for the ozone readings. Two location-dependent harmonic components are added to account for the main periodicities that ozone presents during a given day and that are not explained through the covariate. The model incorporates spatial covariance structure for the observations and the parameters that define the harmonic components. Using the dynamic linear model framework, we show how to compute smoothed means and predictive values for ozone. We illustrate the methodology on data from September 1997.     

Bayesian deconvolution of oil well test data using Gaussian processes

We use Bayesian methods to infer an unobserved function that is convolved with a known kernel. Our method is based on the assumption that the function of interest is a Gaussian process and, assuming a particular correlation structure, the resulting convolution is also a Gaussian process. This fact is used to obtain inferences regarding the unobserved process, effectively providing a deconvolution method. We apply the methodology to the problem of estimating the parameters of an oil reservoir from well-test pressure data. Here, the unknown process describes the structure of the well. Applications to data from Mexican oil wells show very accurate results.     

New Results for Computing Blaker’s Exact Confidence Interval for One Parameter Discrete Distributions

The authors state new general results for computing Blaker’s exact confidence interval limits for usual one-parameter discrete distributions. Specific results for implementing an accurate and fast algorithm are made explicit for the binomial, negative binomial, Poisson and hypergeometric model.     

Goodness-of-fit for regime-switching copula models with application to option pricing

We consider several time series, and for each of them, we fit an appropriate dynamic parametric model. This produces serially independent error terms for each time series. The dependence between these error terms is then modelled by a regime-switching copula. The EM algorithm is used for estimating the parameters and a sequential goodness-of-fit procedure based on Cramér–von Mises statistics is proposed to select the appropriate number of regimes. Numerical experiments are performed to assess the validity of the proposed methodology. As an example of application, we evaluate a European put-on-max option on the returns of two assets. To facilitate the use of our methodology, we have built a R package HMMcopula available on CRAN. The Canadian Journal of Statistics 48: 79–96; 2020 © 2020 Statistical Society of Canada     

Remember the curse of dimensionality: the case of goodness-of-fit testing in arbitrary dimension

Despite a substantial literature on nonparametric two-sample goodness-of-fit testing in arbitrary dimensions, there is no mention there of any curse of dimensionality. In fact, in some publications, a parametric rate is derived. As we discuss below, this is because a directional alternative is considered. Indeed, even in dimension one, Ingster, Y. I. [(1987). Minimax testing of nonparametric hypotheses on a distribution density in the l_p metrics. Theory of Probability & Its Applications, 31(2), 333–337] has shown that the minimax rate is not parametric. In this paper, we extend his results to arbitrary dimension and confirm that the minimax rate is not only nonparametric, exhibits but also a prototypical curse of dimensionality. We further extend Ingster's work to show that the chi-squared test achieves the minimax rate. Moreover, we show that the test adapts to the intrinsic dimensionality of the data. Finally, in the spirit of Ingster, Y. I. [(2000). Adaptive chi-square tests. Journal of Mathematical Sciences, 99(2), 1110–1119], we consider a multiscale version of the chi-square test, showing that one can adapt to unknown smoothness without much loss in power.