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状态空间模型的分块相关伪边际采样器AI 解读

Pseudo Marginal Metropolis-Hastings (PMMH) is a general approach to Bayesian inference when the likelihood is intractable, but can be estimated unbiasedly.Our article develops an efficient PMMH method that scales up better to higher dimensional state vectors than previous approaches.The improvement is achieved by the following innovations.First, a novel block version of PMMH that works with multiple particle filters is proposed.Second, the trimmed mean of the unbiased…

非线性结构时间序列模型的贝叶斯推断AI 解读

We consider efficient methods for likelihood inference applied to structural models. In particular, we introduce a particle filter method which concentrates upon disturbances in the Markov state of the approximating solution to the structural model. A particular feature of such models is that the conditional distribution of interest for the disturbances is often multimodal. We provide a fast and effective method for approximating such distributions. We estimate a…

多重变点与混合创新模型的高效贝叶斯推断AI 解读

Time series subject to parameter shifts of random magnitude and timing are commonly modeled with a change-point approach using Chib's algorithm to draw the break dates. We outline some advantages of an alternative approach in which breaks come through mixture distributions in state innovations, and for which the sampler of Gerlach, Carter, and Kohn allows reliable and efficient inference. We show how the same sampler can be used to model shifts in variance that occur…

动态混合模型的高效贝叶斯推断AI 解读

A Bayesian approach is presented for estimating a mixture of linear Gaussian state-space models. Such models are used to model interventions in time series and nonparametric regression. Markov chain Monte Carlo sampling is usually necessary to obtain the posterior distributions of such mixture models, because it is difficult to obtain them analytically. The methodological contribution of the article is to derive a set of recursions for dynamic mixture models that efficiently…

自相关误差下的加性非参数回归AI 解读

Summary A Bayesian approach is presented for nonparametric estimation of an additive regression model with autocorrelated errors. Each of the potentially non-linear components is modelled as a regression spline using many knots, while the errors are modelled by a high order stationary autoregressive process parameterized in terms of its autocorrelations. The distribution of significant knots and partial autocorrelations is accounted for using subset selection. Our approach…

非参数二元回归的贝叶斯方法AI 解读

This article outlines a general Bayesian approach to estimating a bivariate regression function in a nonparametric manner. It models the function using a bivariate regression spline basis with many terms. Binary indicator variables corresponding to these terms are introduced to explicitly model the uncertainty of whether or not the terms provide a significant contribution to the regression. The regression function is estimated using an estimate of its posterior mean,…

具有自回归移动平均误差的非参数样条回归AI 解读

We estimate by spline nonparametric regression an unknown function observed with autocorrelated errors when the errors are modelled by an autoregressive moving average model. Unknown parameters are estimated by either maximum likelihood, cross-validation or generalized cross-validation. By expressing the problem in state space form we obtain O(n) algorithms to estimate the function and its derivatives and evaluate the marginal likelihood and cross-validation functions. The…

具有 ARMA 误差的非参数样条回归AI 解读

We estimate by spline nonparametric regression an unknown function observed with autocorrelated errors when the errors are modelled by an autoregressive moving average model. Unknown parameters are estimated by either maximum likelihood, cross-validation or generalized cross-validation. By expressing the problem in state space form we obtain O(n) algorithms to estimate the function and its derivatives and evaluate the marginal likelihood and cross-validation functions. The…

处理组与对照组曲线估计的信号提取方法AI 解读

Suppose that the response of a group of subjects, which we call the control group, is monitored over time. At a given time after the start of the experiment, the experimenter intervenes and applies a treatment to a subset of the group. We propose a signal extraction approach to the simultaneous estimation of the treatment and control mean response curves, and their rates of change, imposing a smooth transition constraint between the two curves at the time of intervention. By…

时间序列回归中 Durbin–Watson 等不变检验统计量分布的快速计算AI 解读

A method is given for evaluating p values in O(n) operations for a general class of invariant test statistics that can be expressed as the ratio of quadratic forms in time series regression residuals. The best known of these is the Durbin-Watson statistic, although several others have been discussed in the literature. The method is numerically exact in the sense that the user specifies the error tolerance at the outset. As with existing exact methods, the problem is…

状态空间模型中信号提取、影响分析与交叉验证的快速算法AI 解读

A fast algorithm is developed for computing the conditional mean and variance of the signal given the observations in a signal plus noise model. The resulting recursions can be applied immediately to provide new and efficient formulae for smoothing part or all of the state vector. The ideas of studentized residuals and leverage from regression analysis are generalized to state space models, and the new algorithm is used to compute the various measures. The results are also…

状态空间模型中信号提取、影响诊断与交叉验证的快速算法AI 解读

A fast algorithm is developed for computing the conditional mean and variance of the signal given the observations in a signal plus noise model. The resulting recursions can be applied immediately to provide new and efficient formulae for smoothing part or all of the state vector. The ideas of studentized residuals and leverage from regression analysis are generalized to state space models, and the new algorithm is used to compute the various measures. The results are also…

有限观测下非平稳时间序列的信号提取AI 解读

For a signal plus noise model, where both signal and noise are generated by nonstation ary ARIMA, autoregressive integrated moving average, models, we use the transformation approach of Ansley & Kohn (1985) to construct an estimate of the signal and obtain its mean squared error given a finite number of observations. A method for efficient computation of the signal estimate and its mean squared error is also presented.

状态空间模型的高效广义交叉验证AI 解读

For a signal plus noise model with a state space representation, an efficient procedure is given for obtaining the trace of the influence matrix, where the influence matrix expresses the estimated signal vector as a linear combination of the observed data. This allows an O(n) evaluation of the generalized cross-validation criterion function. Our approach is very efficient, requiring the addition of only one equation to the ordinary Kalman filter, and extends to models with…

状态空间模型的高效广义交叉验证AI 解读

For a signal plus noise model with a state space representation, an efficient procedure is given for obtaining the trace of the influence matrix, where the influence matrix expresses the estimated signal vector as a linear combination of the observed data. This allows an O(n) evaluation of the generalized cross-validation criterion function. Our approach is very efficient, requiring the addition of only one equation to the ordinary Kalman filter, and extends to models with…

含缺失观测的 ARIMA 模型：估计、预测与插值AI 解读

We show how to define and then compute efficiently the marginal likelihood of an ARIMA model with missing observations. The computation is carried out by using the univariate version of the modified Kalman filter introduced by Ansley and Kohn (1985a), which allows a partially diffuse initial state vector. We also show how to predict and interpolate missing observations and obtain the mean squared error of the estimate.

季节性移动平均模型的快速滤波AI 解读

Pearlman (1980) gives a fast filtering algorithm for an ARMA, i.e. autoregressive-moving average, model. When the algorithm is applied to a seasonal moving average model significant computational savings can be obtained by taking advantage of the structural zeros noted by Kohn & Ansley (1984) and Melard (1984). In this paper we identify a second set of structural zeros which leads to further significant computational savings. Our results can be applied to produce a fast…

参数经估计的状态空间模型预测均方误差AI 解读

We obtain a conditional prediction mean squared error for a state space model with estimated parameters. An important application of our results is the derivation of conditional forecast and interpolation mean squared errors for autoregressive-moving average models with estimated parameters. We also obtain the conditional mean squared error for filtered and smoothed estimates of the state vector.

季节性移动平均模型的快速滤波AI 解读

Pearlman (1980) gives a fast filtering algorithm for an ARMA, i.e. autoregressive-moving average, model. When the algorithm is applied to a seasonal moving average model significant computational savings can be obtained by taking advantage of the structural zeros noted by Kohn & Ansley (1984) and Melard (1984). In this paper we identify a second set of structural zeros which leads to further significant computational savings. Our results can be applied to produce a fast…

初始条件未完全指定的状态空间模型：估计、滤波与平滑AI 解读

The likelihood is defined for a state space model with incompletely specified initial conditions by transforming the data to eliminate the dependence on the unspecified conditions. This approach is extended to obtain estimates of the state vectors and predictors and interpolators for missing observations. It is then shown that this method is equivalent to placing a diffuse prior distribution on the unspecified part of the initial state vector, and modified versions of the…

时间序列回归模型的高效估计与预测AI 解读

For a time series regression model with correlated residuals we show how to compute efficiently the likelihood, predict future values and interpolate missing values. As an illustration we consider a regression model with autoregressive moving average residuals.

移动平均过程新息表示的收敛速度AI 解读

A moving average process of order q can be written as a linear combination of the (q+1) most recent innovations. We show that if the moving average polynomial has roots on the unit circle, then the coefficients of the innovations tend to the true moving average coefficients, the difference between the two being O (1/t), where t is the number of observations we consider. The results are extended to mixed autoregressive moving average models and multivariate models.

时间序列回归模型中的高效估计与预测AI 解读

For a time series regression model with correlated residuals we show how to compute efficiently the likelihood, predict future values and interpolate missing values. As an illustration we consider a regression model with autoregressive moving average residuals.

移动平均过程创新表示的收敛速度AI 解读

SUMMARY A moving average process of order q can be written as a linear combination of the (q+ 1) most recent innovations. We show that if the moving average polynomial has roots on the unit circle, then the coefficients of the innovations tend to the true moving average coefficients, the difference between the two being O(l/t), where t is the number of observations we consider. The results are extended to mixed autoregressive moving average models and multivariate models.