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在回归中将时间作为解释变量的陷阱AI 解读

Regression of a trendless random walk on time produces R-squared values around .44 regardless of sample length. The residuals from the regression exhibit only about 14% as much variation as the original series even though the underlying process has no functional dependence on time. The autocorrelation structure of these “detrended” random walks is pseudo-cyclical and purely artifactual. Conventional tests for trend are strongly biased toward finding a trend when none is…

《若干常用时间序列估计量的偏差》更正AI 解读

In formula (415) the term 2 −a, +3a2 should be replaced with 2 + 5a2 with a corresponding adjustment in the last component of (4-20) which therefore should read This adjustment leads to an improved fit between simulated and theoretical results for least squares estimates. Our results have subsequently been substantiated and extended by A. M. Walker in an as yet unpublished conference paper and by Paulsen & Tjostheim (1984).

季节移动平均模型的卡尔曼滤波札记AI 解读

We show that if we apply the Kalman filter to a pure seasonal moving average model with no missing observations, then, by using a result of Ansley (1979), we can obtain significant computational savings.

未知阶数 ARMA 模型的单位根检验AI 解读

Recently, methods for detecting unit roots in autoregressive and autoregressive-moving average time series have been proposed. The presence of a unit root indicates that the time series is not stationary but that differencing will reduce it to stationarity. The tests proposed to date require specification of the number of autoregressive and moving average coefficients in the model. In this paper we develop a test for unit roots which is based on an approximation of an…

近非平稳一阶自回归模型的参数推断AI 解读

The finite sample behaviour of the score function in a first-order autoregression is investigated. An object is to interpret the transition of the distribution of the score when the model approaches a nonstationary situation with a unit root. A framework is presented wherein the nonnormality of the score is clearly seen. Also, a simple interpretation for the behaviour of the distribution in terms of two chi-squared variables is given. Approximate finite sample distributions…

关于在自回归滑动平均模型中施加平稳性的札记AI 解读

A simple reparameterization is given that can implicitly restrict the autoregressive moving average parameters to the stationary and invertible region.

高斯自回归移动平均模型大样本极大似然估计量的直接表示AI 解读

SUMMARY A simple procedure is described for obtaining the estimator of the parameters of an autoregressive-moving average process. The estimator is derived from the maximum likelihood procedure assuming Gaussian residuals by making two simplifying assumptions which are negligible in large samples. Components of the estimator are expressed as linear combinations of a suitable set of sample serial correlations or as a rational function of such linear combinations.

一种自回归移动平均模型估计方法AI 解读

The problem considered is that of estimating an autoregressive-moving average system, including estimating the degrees of the autoregressive and moving average lag operators. The basic method is that introduced by Hannan & Rissanen (1982). However, that method may sometimes overestimate the degrees and modifications are here introduced to correct this. The problem is itself due to the use of a long autoregression, of order clogT when T is large, in the first stage of the…

Durbin–Watson统计量零假设分布与功效的近似AI 解读

It is computationally complex to obtain the exact distribution of the Durbin—Watson statistic for detecting autocorrelation in regression residuals. Moreover, the distribution cannot be tabulated once and for all because of its dependence on the regressors. It is found that the distribution can be well approximated by an appropriate. Pearson distribution which is computationally simple, easily programmed and seems to be valid when the regressors are commonly observed…

乘法季节 ARMA 模型的对偶性及其他性质AI 解读

Model duality is defined between four models referred to as the primal, the dual, the autoregressive adjoint and the moving average adjoint. A duality theorem which generalizes the results of Box & Pierce (1970) and Pierce (1970) is presented. Applications of this duality theorem to autoregressive-moving average models and multiplicative seasonal autoregressive-moving average models are discussed. These applications include: (i) a convenient method for calculating the…

时间序列模型同质性的大样本检验AI 解读

Limit distributions both under the null and a sequence of alternative hypotheses are derived for the likelihood ratio and related statistics for testing the homogeneity of several autoregressive processes. These results are extended to mixed autoregressive and moving average processes.

自回归谱的同时置信带AI 解读

A shortcoming in the use of autoregressive spectral estimation has been the lack of methods for placing confidence intervals or bands on the estimated spectral density. We propose and illustrate a method for determining asymptotic simultaneous confidence bands using Scheffé projections.

时间序列模型频域估计中的偏差校正AI 解读

Exact expressions for the expectations and covariances of frequency domain estimators for integrals of the spectrum of a stationary time series are derived. It is demonstrated that the obvious correction for bias improves the estimator even when observations are missing. The techniques are applied to frequency domain estimation of model parameters, and this is illustrated by an application on a medical time series with missing observations.

多组自回归时间序列的估计与假设检验AI 解读

The analysis of a number of independent first-order autoregressive time series is considered in a normal theory context. A model is studied which allows for nonstation-ary and nonidentical distribution of the series caused by both fixed effect and random effect components.

样本谱分布泛函的极限行为AI 解读

The parameters of a stationary process can be viewed as functions of the spectral distribution function. This work concerns (estimators) parameters defined as integrals of $m (\geq 1)$-dimensional kernel functions with respect to the (sample) spectral distribution function. Conditions for asymptotic normality, almost sure convergence, and probability one bounds are derived for such estimators. The approach taken is based upon the reduction of an $m$-dimensional problem to…

依赖性对卡方与经验分布拟合检验的影响AI 解读

Suppose that a test of fit to a parametric family of distributions is employed, with critical points determined from the limiting null distribution of the test statistic for IID observations. It is shown that if the observations are in fact a stationary process satisfying a positive dependence condition, the test will reject a true null hypothesis too often. This result is established for a broad class of chi squared and empiric df tests, including the Pearson,…

简单线性模型中随机游走系数检验的比较AI 解读

The locally most powerful test is derived for the hypothesis that the regression coefficients are constant over time against the alternative that they vary according to the random walk process. When the regression equation contains the constant term only, comparisons are made with the tests suggested by LaMotte and McWhorter (1978). These are based on exact powers and on three different types of asymptotic efficiencies including the classical Pitman and Bahadur approaches…

含外生变量的向量自回归移动平均模型的快速估计方法AI 解读

A very fast and simple algorithm for estimation of the parameters of large multivariate time series and distributed lag models is presented. An analysis of the distribution of the estimates shows that they are asymptotically normal and unbiased, and that they have a variance that decreases like 1/n, n being the sample size. The algorithm is especially applicable for estimation of large multivariate models where it is generally many times faster than maximalization algorithms.

部分数据缺失或聚合时状态空间模型的固定区间估计AI 解读

Ansley & Kohn's (1982) geomertical derivation of the Kalman filter fixed-interval smoothing algorthm is extended to the case where some of the observations are missing or aggregated and the state covariance matrix may be singular. Estimates of missing observations are also obtained. The theory is then applied to the interpolation of missing data in mulativariate autoregressive-moving average modles.

时间序列模型中确定性趋势与季节成分的检验AI 解读

A univariate time series model can be set up as the sum of trend, seasonal and irregular components. The trend and seasonal components will normally be stochastic, but deterministic components arise as a special case. This paper develops a test that the trend and seasonal components are deterministic using the approach of Lehmann. The procedure is then extended to test for deterministic components in a model formulated in first differences. Both tests are exact and critical…

摘要暂缺

学习曲线的估计与检验AI 解读

This article describes a new approach to learning curve estimation. Our approach is to formulate statistical procedures that conform to alternative learning curve theories. This leads to the development of nonlinear statistical models of the learning curves. For the three data sets analyzed, autocorrelation seems to be an important problem. Parameter estimates were derived using the maximum likelihood principle in the presence of first-order autocorrelation. Nonnested tests…

用结构模型与 Box–Jenkins 模型预测经济时间序列：案例研究AI 解读

The basic structural model is a univariate time series model consisting of a slowly changing trend component, a slowly changing seasonal component, and a random irregular component. It is part of a class of models that have a number of advantages over the seasonal ARIMA models adopted by Box and Jenkins (1976). This article reports the results of an exercise in which the basic structural model was estimated for six U.K. macroeconomic time series and the forecasting…

《用结构模型与 Box–Jenkins 模型预测经济时间序列：案例研究》答复AI 解读

A. C. Harvey, P. H. J. Todd, [Forecasting Economic Time Series with Structural and Box-Jenkins Models: A Case Study]: Response, Journal of Business & Economic Statistics, Vol. 1, No. 4 (Oct., 1983), pp. 313-315