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用混合转移分布模型描述时间序列的平坦段、突发与离群值AI 解读

The class of mixture transition distribution (MTD) time series models is extended to general non-Gaussian time series. In these models the conditional distribution of the current observation given the past is a mixture of conditional distributions given each one of the last p observations. They can capture non-Gaussian and nonlinear features such as flat stretches, bursts of activity, outliers changepoints in a single unified model class. They can also represent time series…

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存在加性异常值的自回归过程的稳健贝叶斯模型选择AI 解读

Autoregressive (AR) models of order k are often used for forecasting and control of time series, as well as for the estimation of functionals such as the spectrum. Here we propose a method that consists of calculating the posterior probabilities of the competing AR(k) models in a way that is robust to outliers, and then obtaining the predictive distributions of quantities of interest, such as future observations and the spectrum, as a weighted average of the predictive…

含加性异常值的自回归过程稳健贝叶斯模型选择AI 解读

Autoregressive (AR) models of order k are often used for forecasting and control of time series, as well as for the estimation of functionals such as the spectrum. Here we propose a method that consists of calculating the posterior probabilities of the competing AR(k) models in a way that is robust to outliers, and then obtaining the predictive distributions of quantities of interest, such as future observations and the spectrum, as a weighted average of the predictive…

效率约束下的位置参数偏差稳健估计AI 解读

In 1964, P. Huber established the following minimax bias robustness result for estimating the location $\mu$ in the $\varepsilon$-contamination family $F(x)=(1-\varepsilon)\phi[(x-\mu)/s]+\varepsilon H(x)$, where $\phi$ is the standard normal distribution and H is an arbitrary distribution function: The median minimizes the maximum asymptotic bias among all translation equivariant estimates of location. However, the median efficiency of $2/\pi$ at the Gaussian model may be…

时间序列的留 K 个观测诊断AI 解读

Andrew G. Bruce, R. Douglas Martin; Leave-K-Out Diagnostics for Time Series, Journal of the Royal Statistical Society Series B: Statistical Methodology, Vo

时间序列的留 K 法诊断AI 解读

SUMMARY We propose diagnostics for autoregressive integrated moving average (ARIMA) model fitting for time series formed by deleting observations from the data and measuring the change in the estimates of the parameters. The use of leave-one-out diagnostics is a well-established tool in regression analysis. We demonstrate the efficacy of observation-deletion-based diagnostics for ARIMA models, addressing issues special to the time series setting. It is shown that the…

正值随机变量尺度的渐近极小极大偏差稳健 M 估计AI 解读

Asymptotically min—max bias robust M-estimates of scale are obtained for positive random variables with ε-contaminated distributions, using any one of a broad class of loss functions of positive and negative bias. Any such estimate is a scaled order statistic, with the order statistic and scaling constant determined by ε, the nominal distribution, and the loss function. Some calculations for specific cases show that for a large range of ε the min—max order statistic solution…

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时间序列的影响泛函AI 解读

A definition is given for influence functionals of parameter estimates in time-series models. The definition involves the use of a contaminated observations process of the form $y^\gamma_t=(1-z^\gamma_t){x_t+z^\gamma_tw_t}$, $p=1,2,...,0\leq\gamma\leq1$ where $x_t$ is a core process (usually Gaussian), $w_t$ is a contaminating process, and $z^\gamma_t"$ is a zero-one process with $P(z^\gamma_t=1)={\gamma+0(\gamma)}$. This form is sufficiently general to model such diverse…

自回归移动平均模型的普通与似然型位置M估计AI 解读

Proper location M-estimates for a model with non-Gaussian autoregressive-moving average type errors are genuine maximum likelihood type estimates, whereas ordinary location M-estimates are those introduced by P. Huber for independent and identically distributed errors. The relative behaviour of ordinary location M-estimates and proper location M-estimates is studied for situations with dependent errors of purely autoregress ive and purely moving average type. It is shown…

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自回归模型的 Cramér–Rao 下界与稳健 M 估计AI 解读

A Cramér-Rao lower bound is computed for estimates of the location, innovations scale and autoregressive parameters for a finite-variance pth-order autoregression. The implication of the bound is that the usual least-squares estimates of all of these parameters have asymptotically the same lack of efficieney robustness toward heavy-tailed innovations distributions as does the sample mean for estimating location. On the other hand, autoregression analogues of Huber's…

一阶自回归参数的稳健估计AI 解读

Outliers in time series can adversely affect both the least squares estimates and ordinary M-estimates of autoregressive parameters. Attention is focused here on obtaining robust estimates of the parameter for a first-order autoregressive time series xk The observations are y k = z k + v k, and two models are considered: Model IO, with v k ≡ 0, x k possibly non-Gaussian, and Model AO, with v k nonzero and possibly quite large a small fraction of the time, and x k Gaussian. A…