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都市工资率的单因子多元时间序列模型AI 解读

The paper formulates and estimates a single-factor multivariate time series model. The model is a dynamic generalization of the multiple indicator (or factor analysis) model. It is shown to be a special case of the general state space model and can be estimated by maximum likelihood methods using the Kalman filter algorithm. The model is used to obtain estimates of the unobserved metropolitan wage rate for Los Angeles, based on observations of sectoral wages within the…

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计量经济模型中事后预测方差的一则札记AI 解读

IT IS WELL KNOWN that in an econometric model, under general assumptions, the ex-post forecast error (conditional on predetermined variables) can be decomposed into the sum of two independent terms; the former is the component due to error in estimated coefficients, while the latter depends on the random error terms. The asymptotic covariance matrix of the first component can be analytically derived through intermediate computation of the covariance matrix of restricted…

论贝叶斯稳态预测模型AI 解读

Summary A recent criterion of Smith (1979) seeks to generalize the steady forecasting model of Harrison and Stevens (1976) to take account of non-normality in the observation and system variables. In this note, predictive distributions and forecasts corresponding to quadratic and step loss functions are examined when the observation variable has a distribution belonging to the exponential family. It is shown that Smith's generalized model does not always yield forecasts…

未知自回归阶数对预测均方误差的影响（一）AI 解读

Given a realization of T consecutive observations of an autoregressive process, x, of unknown order m, a process of an arbitrary order p is assumed to be fitted for predicting the future values of another process [xtilde](t), where [xtilde](t) is independent of xt but otherwise has identical probabilistic structure. The mean squared error of prediction when the autoregressive coefficients are estimated by least squares is obtained to terms of order T -1. The bias in…

大量时间序列的预测AI 解读

Principles for constructing estimators of the Stein type (shrinkage estimators) are discussed in general terms, with emphasis on underlying assumptions. The problem of parameter estimation and prediction for multiple time series is examined with these principles in mind, particularly for the case in which the number of time series is large and the number of observations from each series is small. Our results are applied to the problem of demand estimation in an inventory…

预测均方误差估计中的偏差AI 解读

We examine the forecasting problem for a finite series of observations from either a nonseasonal or a seasonal autoregressive-moving average process. Four sources of bias in the usual estimator of forecast mean squared error are identified and analyzed for particular models using maximum likelihood and least squares parameter estimates. The usual estimator is found to be biased downwards, especially near the boundary of a stationary or invertible region, and the bias is…

预测均方误差估计中的偏差AI 解读

We examine the forecasting problem for a finite series of observations from either a nonseasonal or a seasonal autoregressive-moving average process. Four sources of bias in the usual estimator of forecast mean squared error are identified and analyzed for particular models using maximum likelihood and least squares parameter estimates. The usual estimator is found to be biased downwards, especially near the boundary of a stationary or invertible region, and the bias is…

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向量自回归误差下动态联立方程模型的预测AI 解读

The asymptotic distribution of prediction is derived for the general simultaneous equation model with lagged endogenous variables and vector autoregressive errors. The results turn out to be particularly simple when no lagged endogenous variables are present. errors. It seems worthwhile to extend Schmidt's results, since the estimation of dynamic simultaneous equation models with autoregressive errors is now fairly commonplace in the literature. Also, as noted by Schmidt…

多元自回归移动平均模型的预测AI 解读

A simple formula for multiperiod perdietions of mulativariate autoregressive-moving average models is derived. The formula is explicitly given as a function of suitably defined parameter matrices and an observation vectors, and includes simple models as its special cases. The asymptotic prediction mean squared error is also derived for perdictions with estimated parameters.

双线性时间序列模型理论AI 解读

SUMMARY The theory of bilinear time series models is considered in this paper. The sufficient conditions for asymptotic stationarity of the bilinear time series models are derived, and the expressions for the variance and covariance are obtained. The conditions for the invertibility of the model are also included. The estimation of the parameters of the scalar bilinear time series model is considered. The bilinear models are fitted to sunspot numbers and also to a P-wave of…

多变量自回归移动平均模型的预测AI 解读

A simple formula for multiperiod perdietions of mulativariate autoregressive-moving average models is derived. The formula is explicitly given as a function of suitably defined parameter matrices and an observation vectors, and includes simple models as its special cases. The asymptotic prediction mean squared error is also derived for perdictions with estimated parameters.

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基于 Kalman 滤波的多项式投影预测模型的结构表示AI 解读

Summary Harrison and Stevens (1976) give a general class of dynamic linear models which incorporates a stochastic structure for describing model components and which utilizes the Kalman filter algorithm to update the system. This paper derives conditions for the dynamic linear models to yield polynomial-projecting predictors which do not have limiting constraints imposed upon them. Some examples of structurally simple models which satisfy these conditions are given, and the…

使用估计参数的多元自回归模型预测误差之渐近性质AI 解读

Summary In this paper we consider the asymptotic properties of the prediction errors for the multivariate autoregressive model when estimated coefficient parameters are used. Formulae for the asymptotic covariance matrix of the prediction errors for arbitrary lead times using estimated parameters are derived.

广告与总消费：Granger 因果关系分析AI 解读

This paper is concerned with testing for causation, using the Granger definition, in a bivariate time-series context. It is argued that a sound and natural approach to such tests must rely primarily on the out-of-sample forecasting performance of models relating the original (non-prewhitened) series of interest. A specific technique of this sort is presented and employed to investigate the relation between aggregate advertising and aggregate consumption spending. The null…

改进多项式滞后对任意分布滞后结构的逼近：扩展AI 解读

Since a uniform approximation of distributed lag models by representatives of some subfamily of the family of all possible lag structures guarantees neither a reasonable standard error of forecast in large samples nor a good approximation of the true long-run response and mean lag, it is shown that the modified polynomial lags fulfill a stronger approximation property. A possible simplification of the estimation procedure for these models is mentioned.

经济事件的可预测性AI 解读

Events by Grunberg and Modigliani [3]. Economic forecasts are made to be used, and decisions based on them may affect their ultimate realization. Grunberg and Modigliani explored this problem in a model in which future aggregate supply was influenced by current decisions based on the predicted future price. They applied the Brouwer fixed point theorem to show that if the future equilibrium price is a bounded continuous function of its currently predicted value, a exists. In…

正态与非正态扰动下联立方程估计量的小样本蒙特卡洛比较AI 解读

In this paper we consider four alternative forms of two-parameter normal and nonnormal error distributions and report on a Monte Carlo study of the small-sample properties of least squares, two-stage least squares, three-stage least squares and full information maximum likelihood estimators. On the basis of 1,000 replications of sample size 20 in two experiments on an overidentified model, we found that the small-sample rankings of econometric estimators of both structural…

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摘要暂缺

线性过程参数估计中模型阶数的渐近有效选择AI 解读

Let $\{x_t\}$ be a linear stationary process of the form $x_t + \Sigma_{1\leqslant i<\infty}a_ix_{t-i} = e_t$, where $\{e_t\}$ is a sequence of i.i.d. normal random variables with mean 0 and variance $\sigma^2$. Given observations $x_1, \cdots, x_n$, least squares estimates $\hat{a}(k)$ of $a' = (a_1, a_2, \cdots)$, and $\hat{\sigma}^2_k$ of $\sigma^2$ are obtained if the $k$th order autoregressive model is assumed. By using $\hat{a}(k)$, we can also estimate coefficients of…