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多元移动平均过程自协方差的有效估计AI 解读

This paper proposes a method for estimating the autocovariances of a d -dimensional moving average process of order q . The estimators have the same asymptotic covariance matrix as those obtained by maximizing a Gaussian likelihood, and are obtained by performing a generalized least squares regression of the periodogram on the autocovariances, thus extending Parzen's (1971) estimators for d = 1. An application to least squares prediction is described and the results of a…

ARMA 过程样本逆自相关的渐近分布AI 解读

The inverse autocorrelations of a time series are useful at the identification stage of model building. In practice these quantities must be estimated from the data and so the distributional properties of the estimators are of great importance. In this paper the asymptotic distribution of the sample inverse autocorrelations is derived, making use of the duality between the autocorrelations and inverse autocorrelations of two autoregressive-moving average processes.

利用未知水平的上穿次数估计频率AI 解读

By counting the number of upcrossings of the mean level by a stationary Gaussian process one can estimate the mean frequency of the process. Here we present a frequency estimator based on the number of upcrossings of one unknown level hoped to be near the mean, and the percentage of the total observation time spent above the level. This is equivalent to observing upcrossings of a known level in a process with unknown mean and variance. Formulae are given for the bias and…

符号秩次序统计量的几乎处处线性定理AI 解读

Almost sure asymptotic linearity of signed rank order statistic in shift parameter is studied under suitable regularity conditions and the results are extended to stationary $\phi$-mixing processes as well.

硬限幅后平稳自回归过程的参数估计AI 解读

Estimates of the parameters in normal autoregressive (AR(p)) processes may be obtained as functions of certain runs and subsequences in the associated clipped 0 − 1 processes. For example, the parameter in AR (1) is a function of the number of 1 runs only. Equivalently, this parameter can be estimated by counting only the number of axis crossings by the process. The estimates are obtained by a modification of the likelihood function of the clipped data. The loss of…

两种序列相关检验的稳健性性质AI 解读

We compare Geary's test based on the number of sign changes in residuals with the Durbin-Watson (DW) test for serial correlation. We derive the asymptotic distribution of Geary's statistic for the special case of identically distributed random variables and show that it is asymptotically distribution free for symmetric errors. Monte Carlo simulations show that the DW procedure is generally more powerful and robust than Geary's test.

对数周期图的自动平滑AI 解读

We develop an objective optimum smoothing procedure for an estimate of the log spectral density, based on smoothing the log periodogram with a smoothing spline. We call the result the optimally smoothed spline (OSS) estimate. We show that an unbiased estimate [Rcirc](λ) of the expected integrated mean square error can be obtained as a function of the smoothing, or “bandwidth” parameter λ. The smoothing parameter then is chosen as that λ that minimizes [Rcirc](λ). The degree…

出生人数时间序列模型及其结构解释AI 解读

Saboia (1977) has developed a theory relating a particular type of births autoregressive moving average (ARMA) model to the classical deterministic cohort model of population growth. Reexamination of the data used by Saboia indicates that his estimated births models contain common factors and insignificant coefficients and cannot be regarded as evidence in favor of his argument. It is shown, however, that well-known theory on the relationship between deterministic and…

对数周期图的自动平滑AI 解读

We develop an objective optimum smoothing procedure for an estimate of the log spectral density, based on smoothing the log periodogram with a smoothing spline. We call the result the optimally smoothed spline (OSS) estimate. We show that an unbiased estimate [Rcirc](λ) of the expected integrated mean square error can be obtained as a function of the smoothing, or “bandwidth” parameter λ. The smoothing parameter then is chosen as that λ that minimizes [Rcirc](λ). The degree…

重复调查中的最佳线性无偏估计量AI 解读

Summary Recent work on the problem of obtaining best linear unbiased estimators from a sample survey which is repeated on several occasions has centred on the effects of extending the model assumptions to allow for stochastic variation in the parameters being estimated. In this paper a unified approach to the problem is given using least squares theory. The results of Blight and Scott (1973) are extended, and the relationships between their results, those of Scott and Smith…

时间序列模型的可逆性与广义可逆性AI 解读

Summary A new invertibility concept was recently introduced by Granger and Andersen (1978), generalizing the classical one for time-independent models; we show that, in the case of time-dependent models, it cannot be considered any more as a generalization. We also give a modified definition, which provides a strict generalization and still preserves Granger and Andersen's results.

多元自回归模型的阶数确定AI 解读

Summary The procedure proposed by Hannan and Quinn (1979) for determining the order of univariate autoregressions is extended to multivariate autoregressions. The procedure is shown to be strongly consistent, while other similar procedures may be shown to be strongly consistent by comparison.

时间序列模型的拉格朗日乘子检验AI 解读

Summary The Lagrange-multiplier test procedure is applied to hypotheses concerning autoregressive moving-average time-series models. The portmanteau and Quenouille goodness-of fit tests are derived in this manner against specific alternative hypotheses and two other tests are obtained which have the nature of pure significance tests.

指数边际分布的自回归移动平均 EARMA(p,q) 过程AI 解读

Summary A new model for pth-order autoregressive processes with exponential marginal distributions, ear(p), is developed and an earlier model for first-order moving average exponential processes is extended to qth-order, giving an ema(q) process. The correlation structures of both processes are obtained separately. A mixed process, earma(p,q), incorporating aspects of both ear(p) and ema(q) correlation structures is then developed. The earma(p, q) process is an analog of the…

自回归模型中最小二乘估计量的渐近性质AI 解读

Consistency and asymptotic normality of least-squares estimators are discussed for the linear autoregressive model with explanatory variables. Few assumptions are made about the error sequence. The case of stochastic explanatory variables is also considered.

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…

理性预期假说的计量经济学含义AI 解读

The implications for applied econometrics of the assumption that unobservable expectations formed rationally in Muth's sense examined. The statistical properties of the resulting models and their distributed lag and time series representations described. Purely extrapolative forecasts of endogenous variables can be constructed, as alternatives to rational expectations, but less efficient. Identification and estimation considered: an order condition is that no more…

宏观经济学与现实AI 解读

Existing strategies for econometric analysis related to macroeconomics are subject to a number of serious objections, some recently formulated, some old. These objections are summarized in this paper, and it is argued that taken together they make it unlikely that macroeconomic models are in fact over identified, as the existing statistical theory usually assumes. The implications of this conclusion are explored, and an example of econometric work in a non-standard style,…

自回归移动平均过程阶数的检验方法AI 解读

SUMMARY A procedure is suggested for testing the order of an autoregressive-moving average process which is based on the same set of residual serial correlations as the Box-Pierce test. However, the present method has advantages in terms of its sensitivity to discriminating between alternative models.

逆相关函数的自回归与窗估计AI 解读

The concept of the inverse correlation function of a stationary process xt was first introduced by Cleveland (1972), who also introduced the autoregressive and the window methods for estimating this function. The asymptotic distribution of the estimates provided by these two methods is derived and their asymptotic covariance structure is shown to be in accordance with a remark of Parzen (1974). The results are extended to show that the two procedures suggested by Durbin…

多元序列相关的似然检验AI 解读

A procedure is proposed for testing the hypothesis that a sequence of vector-valued random variables is mutually independent. The test is based on the likelihood criterion for first-order autocorrelation assuming a multivariate normal distribution, is simple computationally, and provides a multivariate generalization of the serial correlation coefficient. The distribution of the test statistic is found to be closely approximated by an F distribution, even in samples of size…

随机缺失观测下的时间序列自相关估计AI 解读

Estimation of the autocorrelations of a time series is considered when some observations are missing. Missing observations are assumed to occur at random. Estimators are proposed and approximate formulae are derived for their covariance and bias. Some particular cases are discussed.

针对自相关正态备择的随机性非参数检验AI 解读

Locally most powerful rank tests of randomness against autocorrelated normal alternatives are derived. In particular, autoregressive and moving average alternatives are considered. The distribution of the statistic under the hypothesis of randomness is shown to be asymptotically normal. The small sample power of the test procedure is compared with that of two other procedures by the Monte Carlo Method.

已拟合自回归移动平均模型的设定检验AI 解读

This paper provides an extension of the application of score, or Lagrangian multiplier, tests to diagnostic checking of ARMA, autoregressive-moving average, models. The score test procedure for testing the null hypothesis of an ARMA( p,q ) process against certain ARMA ( p⊞r, q⊞s ) alternatives is considered and shown to be of the form of a pure significance test.