Spline-backfitted kernel forecasting for functional-coefficient autoregressive models

Oracally Efficient Estimation of Functional-Coefficient Autoregressive Models

Nonlinear autoregressive models are very useful for modeling many natural processes, however, the size of the class of these models is large. Functional-coefficient autoregressive models (FCAR) are useful structures for reducing the size of the class of these models. Although this structure reduces the class of nonlinear models, it is broad enough to include some common time series models as specific cases. A recent development in estimating nonlinear time series data is the spline backfitted kernel (SBK) method. This method combines the computational speed of splines with the asymptotic prope…

具有Laplacian-P-splines的分布式滞后非线性模型用于空间结构时间序列分析

Distributed lag non-linear models with Laplacian-P-splines for analysis of spatially structured time series

本文提出了一种结合Laplacian-P-splines的贝叶斯DLNM方法，用于分析空间结构时间序列中的非线性滞后关系，通过条件自回归先验引入空间依赖性，提高计算效率。

多重时间序列的泊松自回归模型估计

Estimation of Poisson Autoregressive Model for Multiple Time Series

本文将泊松自回归（PAR）模型视为加性模型，采用三次平滑样条与极大似然估计的混合方法进行参数估计，并将其推广至多重计数时间序列，发现该方法在计数值较大时优于状态空间方法且对结构变化具有稳健性。

A Tutorial on Estimating Time-Varying Vector Autoregressive Models

Time series of individual subjects have become a common data type in psychological research. These data allow one to estimate models of within-subject dynamics, and thereby avoid the notorious problem of making within-subjects inferences from between-subjects data, and naturally address heterogeneity between subjects. A popular model for these data is the Vector Autoregressive (VAR) model, in which each variable is predicted as a linear function of all variables at previous time points. A key assumption of this model is that its parameters are constant (or stationary) across time. However, in …

Bayesian semi-parametric forecasting of ultrafine particle number concentration with penalised splines and autoregressive errors

Observational time series data often exhibit both cyclic temporal trends and autocorrelation and may also depend on covariates. As such, there is a need for flexible regression models that are able to capture these trends and model any residual autocorrelation simultaneously. Modelling the autocorrelation in the residuals leads to more realistic forecasts than an assumption of independence. In this paper we propose a method which combines spline-based semi-parametric regression modelling with the modelling of auto-regressive errors. The method is applied to a simulated data set in order to sho…

Spatial Correlation in Weather Forecast Accuracy: A Functional Time Series Approach

A functional time series approach is proposed for investigating spatial correlation in daily maximum temperature forecast errors for 111 cities spread across the U.S. The modelling of spatial correlation is most fruitful for longer forecast horizons, and becomes less relevant as the forecast horizon shrinks towards zero. For 6-day-ahead forecasts, the functional approach uncovers interpretable regional spatial effects, and captures the higher variance observed in inland cities versus coastal cities, as well as the higher variance observed in mountain and midwest states. The functional approach…