Related papers: Nonparametric Vector Quantile Autoregression
Quantile regression has become a valuable tool to analyze heterogeneous covaraite-response associations that are often encountered in practice. The development of quantile regression methodology for high-dimensional covariates primarily…
Multivariate network time series are ubiquitous in modern systems, yet existing network autoregressive models typically treat nodes as scalar processes, ignoring cross-variable spillovers. To capture these complex interactions without the…
Autoregressive models are a class of generative model that probabilistically predict the next output of a sequence based on previous inputs. The autoregressive sequence is by definition one-dimensional (1D), which is natural for language…
Regression models that go beyond the mean, alongside coherent risk measures, have been important tools in modern data analysis. This paper introduces the innovative concept of Average Quantile Regression (AQR), which is smooth at the…
Quantile regression, that is the prediction of conditional quantiles, has steadily gained importance in statistical modeling and financial applications. The authors introduce a new semiparametric quantile regression method based on…
We propose Multivariate Quantile Function Forecaster (MQF$^2$), a global probabilistic forecasting method constructed using a multivariate quantile function and investigate its application to multi-horizon forecasting. Prior approaches are…
This paper considers a class of nonparametric autoregressive models with nonstationarity. We propose a nonparametric kernel test for the conditional mean and then establish an asymptotic distribution of the proposed test. Both the setting…
Timely characterizations of risks in economic and financial systems play an essential role in both economic policy and private sector decisions. However, the informational content of low-frequency variables and the results from conditional…
Forecasting in probabilistic time series is a complex endeavor that extends beyond predicting future values to also quantifying the uncertainty inherent in these predictions. Gaussian process regression stands out as a Bayesian machine…
Crossing of fitted conditional quantiles is a prevalent problem for quantile regression models. We propose a new Bayesian modelling framework that penalises multiple quantile regression functions toward the desired non-crossing space. We…
In this article, we present a novel approach to multivariate probabilistic forecasting. Our approach is based on an extension of single-output quantile regression (QR) to multivariate-targets, called quantile surfaces (QS). QS uses a simple…
The time series with periodic behavior, such as the periodic autoregressive (PAR) models belonging to the class of the periodically correlated processes, are present in various real applications. In the literature, such processes were…
Forecasting time series data is a critical area of research with applications spanning from stock prices to early epidemic prediction. While numerous statistical and machine learning methods have been proposed, real-life prediction problems…
The standard quantile regression model assumes a linear relationship at the quantile of interest and that all variables are observed. We relax these assumptions by considering a partial linear model while allowing for missing linear…
In this paper, we discuss a family of robust, high-dimensional regression models for quantile and composite quantile regression, both with and without an adaptive lasso penalty for variable selection. We reformulate these quantile…
In this paper, we propose two important measures, quantile correlation (QCOR) and quantile partial correlation (QPCOR). We then apply them to quantile autoregressive (QAR) models, and introduce two valuable quantities, the quantile…
We consider nonparametric estimation of a regression curve when the data are observed with multiplicative distortion which depends on an observed confounding variable. We suggest several estimators, ranging from a relatively simple one that…
The quantile spectrum was introduced in Li (2012; 2014) as an alternative tool for spectral analysis of time series. It has the capability of providing a richer view of time series data than that offered by the ordinary spectrum especially…
In this work, we propose \texttt{TimeGrad}, an autoregressive model for multivariate probabilistic time series forecasting which samples from the data distribution at each time step by estimating its gradient. To this end, we use diffusion…
This paper deals with improvement of linear quantile regression, when there are a few distinct values of the covariates but many replicates. On can improve asymptotic efficiency of the estimated regression coefficients by using suitable…