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一致的自回归谱估计AI 解读

We consider an autoregressive linear process $\{x_t\}$, a one-sided moving average, with summable coefficients, of independent identically distributed variables $\{e_t\}$ with zero mean and fourth moment, such that $\{e_t\}$ is expressible in terms of past values of $\{x_t\}$. The spectral density of $\{x_t\}$ is assumed bounded and bounded away from zero. Using data $x_1,\cdots, x_n$ from the process, we fit an autoregression of order $k$, where $k^3/n \rightarrow 0$ as $n \rightarrow \infty$…

异方差下 Chow 检验的使用AI 解读

the assumption of equality of variances of error terms between two separate sample regimes. It is shown that the test is well behaved when there are variations of variances if at least one of two sample sizes is very large. However, if two samples are of small size, even moderate heteroscedasticity has considerable effect on the level of significance of the test. In what follows, it is assumed that T1 samples belong to the first regime and T2 samples to the second regime;…

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相关观测下的指数回归AI 解读

The exponential regression model is considered in which the observations arise from a continuous autoregressive process such that the error increment has a normal distribution with zero mean and variance that decreases in proportion to the amount by which the expected value of the observation differs from its asymptote. Various methods of estimating the parameters are considered.

多元时间序列周期成分的检验AI 解读

The problem of testing for periodicities in multiple time series is considered. The test statistic proposed is based on the Euclidean norm of the matrix of periodograms. We first obtain the exact distribution of our test statistic under the hypothesis that observations are taken from an n-vector time series consisting of independent series of independent normal variables. We extend the theory to normal linear series with a specified spectral density matrix and then show that…

非线性正交多项式泛函的核估计AI 解读

Let $(X(t), Y(t))$ be a complex vector process stationary of order $k$ for any $k, k = 1,2,\cdots$, such that $Y(t)$ is expressed as a polynomial functional of degree 2 operating on $X(t)$. Then $Y(t)$ can be rewritten as a sum of orthogonal projections $G_j(K_j, Y(t)), j = 0, 1, 2$. It is shown that there is a set of functionals which approximate in mean square the projection $G_2(K_2, Y(t))$. Moreover, it is possible to determine the kernels associated with these…

不同谱的两个高斯过程之间的大样本判别AI 解读

We study the probability of error asymptotically for testing one Gaussian stochastic process against another when the mean vectors are zero and we have the choice between two given covariance matrices. It is shown that under certain conditions the probabilities of error form asymptotically a geometric progression with a ratio that is derived. The approach employs Laplace's method of approximating integrals and does not appeal to Fourier analysis; in this sense it can be said…

季节调整与变量之间的关系AI 解读

This article studies the effect of official seasonal adjustment procedures on the relations between variables. By considering time-invariant linear filters, and in particular a linear approximation to the Census Method II adjustment program, the effect of adjusting one or both of the variables in a distributed lag relation is examined, and the distortions which can arise are described. Applying the actual (nonlinear) adjustment procedure to artificial data indicates that at…

变量含测量误差的回归模型中斜率的一致估计AI 解读

Consistent estimators for the slope coefficient in a regression model, where both variables are subject to errors, do not exist without some restrictions on the model. When the serial correlation of (lag 1) of the regression is known to be nonzero, one can obtain extra information from the first differences and get a consistent estimator for the slope. It turns out that this estimator is (asymptotically) equivalent to an estimator which uses as instrumental variable the…

变量含测量误差回归模型中斜率的一致估计AI 解读

Consistent estimators for the slope coefficient in a regression model, where both variables are subject to errors, do not exist without some restrictions on the model. When the serial correlation of (lag 1) of the regression is known to be nonzero, one can obtain extra information from the first differences and get a consistent estimator for the slope. It turns out that this estimator is (asymptotically) equivalent to an estimator which uses as instrumental variable the…

合并估计的设定错误问题：一则札记AI 解读

THE PRACTICE of pooling cross section data with time series has been found to be very useful in applied econometric work. Frequently, investigators have estimated some parameters from a single cross section sample and have used these estimates as prior restrictions in the time series equation. Tobin's study of demand for food [2] is a classic example of this. Tobin estimated the income elasticity of demand for food from family budget data for 1941 and used this as prior…

自相关误差动态联立方程模型中若干有限信息估计量的比较AI 解读

Phoebus J. Dhrymes, R. Berner, D. Cummins, A Comparison of Some Limited Information Estimators for Dynamic Simultaneous Equations Models with Autocorrelated Errors, Econometrica, Vol. 42, No. 2 (Mar., 1974), pp. 311-332

计量经济模型动态模拟中预测的渐近分布AI 解读

This paper considers the asymptotic distribution of forecasts made several time periods in the future. Such forecasts typically arise in the dynamic simulation of an econometric model.

自回归信号加白噪声模型的估计AI 解读

If $x(\bullet)$ is a time series which may be written as $x(t) = s(t) + n(t)$ where $t$ is an integer, $s(\bullet)$ an autoregressive signal of order $q$ and $n(\bullet)$ white noise, then the model has $q + 2$ parameters. These are (i) the $q$ autoregressive parameters (ii) the residual variance of the autoregressive scheme and (iii) the variance of the white noise. A method is proposed to estimate the $q + 2$ parameters. This method is based on analogies with regression…

THE CLASSIC PAPER by Grunfeld and Griliches [3] contains many instructive insights into question of circumstances under which an aggregate dependent variable may be forecasted more precisely with a model based on aggregate variables as opposed to an aggregate of forecasts from individual equations. The statistical model they employ is standard regression framework, a single at macro level and a set of seemingly unrelated regressions (to use Zellner's term) at level. Under…

混合自回归滑动平均过程的精确似然函数AI 解读

Box & Jenkins (1970) develop a strategy for the analysis and forecasting of time series, based on the construction, after suitable differencing, of autoregressive-moving average models. They present a model building procedure which works very well for most general purposes, and in addition derive the exact likelihood function for both pure autoregressive and pure moving average processes, in the latter case this being a new result. In this note it is shown that a similar…

平稳过程下Whittaker周期图及相关卡方统计量的渐近分布AI 解读

We find the asymptotic distribution of two statistics that have been employed in the search for periodicities. Both statistics are based on Buys-Ballot tables. The first, the Whittaker periodogram, is computed for ordinary time series. The second, a X2 statistic, is computed for point processes. These statistics have been viewed as competitors of power spectrum estimates. We find that when autocorrelation is present in the process involved, the large-sample distributions of…

一阶自回归过程的参数估计AI 解读

Numerical comparisons are made of the distribution of the estimator of the parameter in a first-order autoregressive process. Results of Reeves (1972) are compared with those of Arató & Benczúr (1970, 1972) which use a model in continuous time.

利用水平穿越估计谱矩AI 解读

Three types of estimator of the second spectral moment of a stationary Gaussian process are considered. The integral estimator is based on the integral of the squared derivative of the process, while crossing estimators make use of the number of upcrossings of zero or nonzero levels. It is shown that the zero-crossing estimator can often compete with the integral estimator in efficiency and that it can be considerably improved by the additional use of nonzero levels.

推断与排队问题中的一个 Wiener–Hopf 积分方程AI 解读

The solution is presented to an integral equation of Wiener-Hopf type which has been recently treated numerically by Hinkley in connexion with the problem of inference about the change-point in a sequence of random variables. The closed form solution given here enables results to be obtained easily in situations where the numerical method fails. A similar integral equation arises in a queueing problem where the difference between inter-arrival and service time of a customer…

多元时间序列周期成分的检验AI 解读

The problem of testing for periodicities in multiple time series is considered. The test statistic proposed is based on the Euclidean norm of the matrix of periodograms. We first obtain the exact distribution of our test statistic under the hypothesis that observations are taken from an n-vector time series consisting of independent series of independent normal variables. We extend the theory to normal linear series with a specified spectral density matrix and then show that…

联邦储备委员会敏感价格指数预测能力的评价AI 解读

This article reviews the historical performance of the Federal Reserve Board Sensitive Price Index (SPI) in accord with the standards established for such an index by the Price Statistics Review Committee. Several empirical tests are outlined which can be used to assess the predictive performance of any leading indicator. These tests indicate that the SPI performs well as an indicator for business conditions but has little to offer for the problem of predicting price level…

美联储敏感价格指数预测能力的评价AI 解读

This article reviews the historical performance of the Federal Reserve Board Sensitive Price Index (SPI) in accord with the standards established for such an index by the Price Statistics Review Committee. Several empirical tests are outlined which can be used to assess the predictive performance of any leading indicator. These tests indicate that the SPI performs well as an indicator for business conditions but has little to offer for the problem of predicting price level…

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