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参数化年龄别生育率的多元时间序列预测AI 解读

Projection of individual age-specific fertility rates is a forecasting problem of high dimension. We solve this dimensionality problem by using parametric curves to approximate the annual age-specific rates and a multivariate time series model to forecast the curve parameters. These yield forecasts of future fertility curves, which are then used to compute age-specific fertility rate forecasts. This reduces the dimensionality of the forecasting problem and also guarantees…

白噪声的自适应检验AI 解读

Since conventional tests for white noise are completely insensitive to certain alternatives, it is difficult in a particular application to decide which test to use if one has no a priori information about the kind of departure from whiteness. Therefore, an alternative test is proposed which may be applied in case of arbitrary stationary alternatives. This test procedure is adaptive in that first the real part of the finite Fourier transform of the data is used to choose…

自回归频率估计AI 解读

Presume that an autoregressive model of given order is fitted to data obtained from a realization of a sinusoidal signal embedded in white noise. This paper investigates the statistical properties of the estimate of the frequency of the signal obtained by minimizing the transfer function of the autoregression. Strong consistency and convergence in distribution of the estimate are established when the order of the autoregression is allowed to increase with sample size at an…

时间序列数据中的单位根检验AI 解读

Let Y t satisfy the stochastic difference equation for t = 1,2,…, where e t are independent and identically distributed random variables with mean zero and variance σ 2 and the initial conditions ( Y −p+1 ,…, Y 0 ) are fixed constants. It is assumed that the process is invertible and that the true, but unknown, roots m 1 , m 2 ,…, m p of satisfy the hypothesis H d : m 1 = … = m d = 1 and | m j | < 1 for j = d + 1,…, p . We present a reparameterization of the model for Y t…

近单位根模型中最小二乘估计量极限分布的计算AI 解读

We tabulate the limiting cumulative distribution and probability density functions of the least-squares estimator in a first-order autoregressive regression when the true model is near-integrated in the sense of Phillips. The results are obtained using an exact numerical method which integrates the appropriate limiting moment generating function. The adequacy of the approximation is examined for various first-order autoregressive processes with a root close to unity.

部分识别的计量经济模型AI 解读

This paper studies a class of models where full identification is not necessarily assumed. We term such models partially identified. It is argued that partially identified systems are of practical importance since empirical investigators frequently proceed under conditions that are best described as apparent identification. One objective of the paper is to explore the properties of conventional statistical procedures in the context of identification failure. Our analysis…

时间序列的留 K 法诊断AI 解读

SUMMARY We propose diagnostics for autoregressive integrated moving average (ARIMA) model fitting for time series formed by deleting observations from the data and measuring the change in the estimates of the parameters. The use of leave-one-out diagnostics is a well-established tool in regression analysis. We demonstrate the efficacy of observation-deletion-based diagnostics for ARIMA models, addressing issues special to the time series setting. It is shown that the…

线性预测模型中聚合问题的计量分析AI 解读

This paper deals with the problem of aggregation where the focus of the analysis is whether to predict aggregate variables using macro or micro equations. The GrunfeldGriliches prediction criterion for choosing between aggregate and disaggregate equations is generalized to allow for contemporaneous covariances between the disturbances of micro equations and the possibility of different parametric restrictions on the equations of the disaggregate model. A new test is proposed…

每日汇率中的信息：一个条件方差的解释AI 解读

Formal testing procedures confirm the presence of a unit root in the autoregressive polynomial of the univariate time series representation of daily exchange-rate data. The first differences of the logarithms of daily spot rates are approximately uncorrelated through time, and a generalized autoregressive conditional heteroscedasticity model with daily dummy variables and conditionally t-distributed errors is found to provide a good representation to the leptokurtosis and…

市场非均衡模型中的序列相关检验与其他设定分析AI 解读

The assumption of serial independence of disturbances is the starting point of most of the work done on analyzing market disequilibrium models. We derive tests for serial dependence given normality and homoscedasticity using the Lagrange multiplier (LM) test principle. Although the likelihood function under serial dependence is very complicated and involves multiple integrals of dimensions equal to the sample size, the test statistic we obtain through the LM principle is…

预测组合的基准化方法AI 解读

This article is concerned with the development of a statistical model-based approach to optimally combine forecasts derived from an extrapolative model, such as an autoregressive integrated moving average (ARIMA) time series model, with forecasts of a particular characteristic of the same series obtained from independent sources. The methods derived combine the strengths of all forecasting approaches considered in the combinational scheme. The implications of the general…

向量自回归移动平均模型的简约参数化AI 解读

It is not uncommon to hear the complaint that there are many difficulties in building vector autoregressive moving average (ARMA) models, such as too many parameters in a model. In this article, I show that the complaint can be avoided if a proper method is used at the model-specification stage to obtain the detailed structure of the vector process under study. Two such methods, one from the engineering literature and the other from the statistical literature, are discussed.…

漫步吉布森悖论：随机游走视角AI 解读

Abstract Evidence to support the Gibson paradox is often given in the form of a simple correlation between the nominal interest rate and the log of price level, or in the form of a simple linear regression between these two variables. Authors then show, using standard procedures of statistical inference, that the price level possesses a significant coefficient. We argue that this class of evidence is spurious since the nominal interest rate and the price level (both…

因变量在部分样本期外生时的一致估计AI 解读

Abstract This paper proposes a consistent estimation method for regression equations with a left‐hand variable that is endogenous for some observations, and exogenous for others. This method is applied to the estimation of a demand‐for‐money function for Switzerland over a time interval which includes periods of monetary control; that is periods when the quantity of money can best be viewed as exogenous.

自回归阶数选择中预测最小二乘准则的强一致性AI 解读

This note concerns the problem of order determination for autoregressive models. Rissanen's "Predictive least squares principle" prescribes that one should choose as order estimate $\hat{k}(n)$ at time $n$ the order of the model which has given the least mean square prediction error up to that time. We show that this procedure is strongly consistent, that is, that $\hat{k}(n) \rightarrow p$ a.s. as $n \rightarrow \infty$ when the data are generated by an AR process of order $p$…

无限方差自回归过程下赤池信息准则的一致性AI 解读

Suppose $\{X_n\}$ is a $p$th order autoregressive process with innovations in the domain of attraction of a stable law and the true order $p$ unknown. The estimate $\hat{p}$ of $p$ is chosen to minimize Akaike's information criterion over the integers $0, 1, \cdots, K$. It is shown that $\hat{p}$ is weakly consistent and the consistency is retained if $K \rightarrow \infty$ as $N \rightarrow \infty$ at a certain rate depending on the index of the stable law.

两个点过程之间依赖关系的估计AI 解读

To assess the dependence structure in a stationary bivariate point process the second-order distribution can be very useful. We prove that the natural estimates of this distribution, based on a realization $A_1 < A_2 < \cdots < A_{n_A}, B_1 < B_2 < \cdots < B_{n_B}$ are asymptotically normal and we present a method for constructing approximate confidence intervals for this distribution.

带脉冲时间序列的非高斯模型AI 解读

A non-Gaussian autoregressive-like model is presented for time series that exhibit occasional large increases in value, termed pulses, and exponential decay between pulses. The model differs from a first-order autoregressive process in its incorporation of feedback between the distribution of the current innovation and the history of the process. Likelihood-based methods of inference for the model are developed, and an application to endocrinological data is given.

多元时间序列的自相关与随机性检验AI 解读

There exist several tests for autocorrelation and randomness in multiple time series. Unfortunately, the exact distributions of these statistics are unknown and the asymptotic distributions that are known do not provide adequate approximation to the exact ones in small samples. In this article, the test statistics are modified. Asymptotically, these modified statistics are equivalent to their original counterparts; however, it is found that the asymptotic distributions of…

卡尔曼滤波模型的稳健化AI 解读

Kalman filter models based on the assumption of multivariate Gaussian distributions are known to be nonrobust. This means that when a large discrepancy arises between the prior distribution and the observed data, the posterior distribution becomes an unrealistic compromise between the two. In this article we discuss a rationale for how to robustify the Kalman filter. Specifically, we develop a model wherein the posterior distribution will revert to the prior when extreme…

含随机效应与 AR(1) 误差的纵向数据模型AI 解读

For longitudinal data on several individuals, linear models that contain both random effects across individuals and autocorrelation in the within-individual errors are studied. A score test for autocorrelation in the within-individual errors for the “conditional independence” random effects model is first developed. An explicit maximum likelihood estimation procedure using the scoring method for the model with random effects and (autoregressive) AR(1) errors is then derived.…

多元二元时间序列的一类 logistic 回归模型AI 解读

A logistic model for multivariate binary time series is proposed. First, we establish the equivalence between a log-linear model for the marginal distribution of a multivariate binary random vector and logistic models for the conditional distributions of each component given the others. The logistic formulation is used to describe a Markov chain for each series, which implies a Markov model for the vector of time series. A pseudolikelihood estimation procedure is presented.…

多元时间序列的自相关与随机性检验AI 解读

There exist several tests for autocorrelation and randomness in multiple time series. Unfortunately, the exact distributions of these statistics are unknown and the asymptotic distributions that are known do not provide adequate approximation to the exact ones in small samples. In this article, the test statistics are modified. Asymptotically, these modified statistics are equivalent to their original counterparts; however, it is found that the asymptotic distributions of…

含脉冲时间序列的非高斯模型AI 解读

A non-Gaussian autoregressive-like model is presented for time series that exhibit occasional large increases in value, termed pulses, and exponential decay between pulses. The model differs from a first-order autoregressive process in its incorporation of feedback between the distribution of the current innovation and the history of the process. Likelihood-based methods of inference for the model are developed, and an application to endocrinological data is given.