Time series models with asymmetric Laplace innovations

We propose autoregressive moving average (ARMA) and generalized autoregressive conditional heteroscedastic (GARCH) models driven by asymmetric Laplace (AL) noise. The AL distribution plays, in the geometric-stable class, the analogous role played by the normal in the alpha-stable class, and has shown promise in the modelling of certain types of financial and engineering data. In the case of an ARMA model we derive the marginal distribution of the process, as well as its bivariate distribution when separated by a finite number of lags. The calculation of exact confidence bands for minimum mean-squared error linear predictors is shown to be straightforward. Conditional maximum likelihood-based inference is advocated, and corresponding asymptotic results are discussed. The models are particularly suited for processes that are skewed, peaked, and leptokurtic, but which appear to have some higher order moments. A case study of a fund of real estate returns reveals that AL noise models tend to deliver a superior fit with substantially less parameters than normal noise counterparts, and provide both a competitive fit and a greater degree of numerical stability with respect to other skewed distributions.     

Quantile Regression for Location‐Scale Time Series Models with Conditional Heteroscedasticity

This paper considers quantile regression for a wide class of time series models including autoregressive and moving average (ARMA) models with asymmetric generalized autoregressive conditional heteroscedasticity errors. The classical mean‐variance models are reinterpreted as conditional location‐scale models so that the quantile regression method can be naturally geared into the considered models. The consistency and asymptotic normality of the quantile regression estimator is established in location‐scale time series models under mild conditions. In the application of this result to ARMA‐generalized autoregressive conditional heteroscedasticity models, more primitive conditions are deduced to obtain the asymptotic properties. For illustration, a simulation study and a real data analysis are provided.     

The information matrix test in the linear regression with ARMA errors

Summary The paper shows that the informaton matrix test presented by White (1982) decomposes into the sum of quadratic forms in the case of a linear model with ARMA errors. By extending previous results, which analysed the information matrix test in the presence of serial correlation, the test allows detection of additional sources of misspecification.     

巨灾风险对非寿险总产出核算影响的研究

 随着中国保险业的迅猛发展，保险核算在一国经济中变得越来越重要。越来越频繁发生的自然灾害、恐怖袭击等造成的巨大损失对联合国国民账户体系(93SNA)推荐的非寿险服务产出核算产生重大冲击，严格按照93SNA算法计算保险服务价值会导致荒谬的结果。首先本文介绍了国际上几种主要的改进方法，对每种方法的优缺点进行了深入分析。这些方法对我国改善保险核算，尤其是非寿险服务产出核算具有重要的启示意义。其次运用广东省（不含深圳）保险业的数据和期望法对06、07年的总产出进行计算，构建预测模型，并比较分析计算的结果。最后，本文提出对改进我国保险核算的建议。     

Identification of arma models with non-gaussian innovations

The problem of modelling time series driven by non-Gaussian innovation has been considered recently by Li and McLeod (1988). In this paper we have discussed the problem of identification of ARMA models with non-Gaussian innovations. Simulation experiments are used to study the applicability of theoretical results.     

基于时间序列分析方法的连续性抽样调查研究

针对连续性抽样调查中如何利用过去各期的调查信息来提高现期抽样估计精度的问题，引入时间序列分析方法，分别考虑连续性抽样调查中重复样本和重叠样本等不同情况，建立了不同情况下的时间序列模型，利用成熟的时间序列分析方法给出了总体特征的线性组合估计量。由于时间序列分析方法能够充分利用以往各期的调查信息，从而能够给出精度更高的估计量。     

The effects of correlation among observations on the consistency property of sample variance

It is well known that even when the sample observations are correlated and not normal the sample variance, S² converges in probability to E(S²). But the required sample size for S² to be a consistent estimator of E(S²) is an open question. Some light is shed on this question in this paper. In particular the relation between the rate of convergence and the correlation property of the observations is explored. It is shown that the retardation to the rate of convergence is not appreciable if the correlation is moderate but it can be severe for extreme correlations.     

Identification of composite (∑+II) arma models by relatively simpler models

In the real world situations, many time series are aggregates of two or more time series. An aggregation may take place due to an addition or the product or both of two or more time series. We are often interested in the study of the properties of aggregates which are, in turn, dependent on the properties of the constituent series. Motivated by this problem, the authors study in this paper the properties of models generated by the operator (Σ+II) on autoregressive-moving-average (ARMA) processes of orders (p_i,q_i), i = l→n . A few practical examples where such models have been used are given in the introduction and an illustrative numerical example is discussed at the end of the paper.     

Analysis and modelling of wind speed in New York

In this paper we propose an ARMA time-series model for the wind speed at a single spatial location, and estimate it on in-sample data recorded in three different wind farm regions in New York state. The data have a three-hour granularity, but based on applications to financial wind derivatives contracts, we also consider daily average wind speeds. We demonstrate that there are large discrepancies in the behaviour of daily average and three-hourly wind speed records. The validation procedure based on out-of-sample observations reflects that the proposed model is reliable and can be used for various practical applications, like, for instance, weather prediction, pricing of financial wind contracts, wind generated power, etc. Furthermore, we discuss some striking resemblances with temperature dynamics.     

Transformed generalized linear models

The estimation of data transformation is very useful to yield response variables satisfying closely a normal linear model. Generalized linear models enable the fitting of models to a wide range of data types. These models are based on exponential dispersion models. We propose a new class of transformed generalized linear models to extend the Box and Cox models and the generalized linear models. We use the generalized linear model framework to fit these models and discuss maximum likelihood estimation and inference. We give a simple formula to estimate the parameter that index the transformation of the response variable for a subclass of models. We also give a simple formula to estimate the r$r$th moment of the original dependent variable. We explore the possibility of using these models to time series data to extend the generalized autoregressive moving average models discussed by Benjamin et al. [Generalized autoregressive moving average models. J. Amer. Statist. Assoc. 98, 214–223]. The usefulness of these models is illustrated in a simulation study and in applications to three real data sets.