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机器生成 AR(1) 模型的统计推断AI 解读

Summary We have obtained the asymptotic bias and the limiting distribution for the Yule–Walker estimator of the autoregressive parameter under a considerably weaker assumption than that of independence in the noise sequence. Among other things, these suggest robustness of the classical results and throw some light on the use of simulations based on pseudorandom numbers in verifying these results.

论有效的点预测系统AI 解读

Summary Assume that a forecaster observes a sequence of random variables and issues predictions according to a point prediction systems, i.e. a rule which, at every time t, issues a point prediction for the next observation at time t+1. We introduce the concept of efficiency of a point prediction system, for the case that the joint distribution of the sequence of observations is known to belong to a parametric family, and performance is assessed by the long run sum of…

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协整系统检验的尺寸与功效AI 解读

System tests for cointegration proposed by Stock and Watson (1988), Johansen (1988), and Bewley and Yang (1995) are compared using Monte Carlo experiments that include overspecification of the lag length and data-generating processes with moving average disturbances. Both AIC and SIC are used to select the lag length of the approximating vector autoregressions. The three tests considered are found to have very different characteristics, and each dominates in some portion of…

Many panel data sets encountered in macroeconomics, international economics, regional science, and finance are characterized by cross-sectional or "spatial" dependence. Standard techniques that fail to account for this dependence will result in inconsistently estimated standard errors. In this paper we present conditions under which a simple extension of common nonparametric covariance matrix estimation techniques yields standard error estimates that are robust to very…

理解伪回归的新工具AI 解读

Some new tools for analyzing spurious regressions are presented. The theory utilizes the general representation of a stochastic process in terms of an orthonormal system and provides an extension of the Weierstrass theorem to include the approximation of continuous functions and stochastic processes by Wiener processes. The theory is applied to two classic examples of spurious regressions: regressions of stochastic trends on time polynomials and regressions among independent…

具有对称稳定冲击的最优单变量通胀预测AI 解读

Monthly inflation in the United States indicates non-normality in the form of either occasional big shocks or marked changes in the level of the series. We develop a univariate state space model with symmetric stable shocks for this series. The non-Gaussian model is estimated by the Sorenson-Alspach filtering algorithm. Even after removing conditional heteroscedasticity, normality is rejected in favour of a stable distribution with exponent 1�83. Our model can be used for…

进口需求中的跨期替代与习惯形成AI 解读

To study non-durable import demand, we extend previous work done by Clarida (1994) and Ceglowski (1991) by considering a two-good version of the lifecycle model in which we introduce time-non-separability in the households' preferences. The model is estimated using quarterly data for the USA and France. Using the information contained in the observed stochastic and deterministic trends, we derive a cointegration restriction used to estimate curvature parameters of the…

一种一般依赖检验及其应用AI 解读

We describe a test, based on the correlation integral, for the independence of a variable and a vector that can be used with serially dependent data. Monte Carlo simulations suggest that the test has good power to detect dependence in several models, performing nearly as well or better than the BDS test in univariate time series and complementing the BDS test in distributed lag models. Finally, we apply our test in conjunction with the BDS test to examine models of US…

重尾过程的样本自相关及其在 ARCH 模型中的应用AI 解读

We study the sample ACVF and ACF of a general stationary sequence under a weak mixing condition and in the case that the marginal distributions are regularly varying. This includes linear and bilinear processes with regularly varying noise and ARCH processes, their squares and absolute values. We show that the distributional limits of the sample ACF can be random, provided that the variance of the marginal distribution is infinite and the process is nonlinear. This is in…

用独立观测密度估计量强逼近弱依赖观测密度估计量AI 解读

We derive an approximation of a density estimator based on weakly dependent random vectors by a density estimator built from independent random vectors. We construct, on a sufficiently rich probability space, such a pairing of the random variables of both experiments that the set of observations $X_1,\ldots,X_n}$ from the time series model is nearly the same as the set of observations $Y_1,\ldots,Y_n}$ from the i.i.d. model. With a high probability, all sets of the form $({X_1,\ldots,X_n}\\Delta{Y_1,\ldots,Y_n})\bigcap([a_1,b_1]\times\ldots\times[a_d,b_d])$…

频域时间序列回归的高阶近似AI 解读

Second-order expansions and mean squared error approximations are given for efficient frequency domain regression estimators. While bandwidth choices do not figure in first order asymptotics for these estimators, they do influence second-order terms and it is shown how suitable choices will enhance second-order efficiency. Data-based bandwidth selection rules are given for practical implementation of these procedures. Two commonly used and asymptotically equivalent spectral…

协整与长期预测AI 解读

The authors consider the forecasting of cointegrated variables and they show that, at long horizons, nothing is lost by ignoring cointegration when forecasts are evaluated using standard multivariate forecast accuracy measures. In fact, simple univariate Box-Jenkins forecasts are just as accurate. The authors' results highlight a potentially important deficiency of standard forecast accuracy measures--they fail to value the maintenance of cointegrating relationships among…

澳大利亚通胀建模AI 解读

This article develops an empirically constant, data-coherent, error-correction model for inflation in Australia. The level of consumer prices is a markup over domestic and import costs, with adjustments for dynamics and relative aggregate demand. The authors address issues of cointegration, general to specific modeling, dynamic specification, model evaluation and testing, parameter constancy, forecasting, and exogeneity. They also test this model against existing models of…

外生性、协整与经济政策分析AI 解读

This overview examines conditions for reliable economic policy analysis based on econometric models, focusing on the econometric concepts of exogeneity, cointegration, causality, and invariance. Weak, strong, and super exogeneity are discussed in general and these concepts are then applied to the use of econometric models in policy analysis when the variables are cointegrated. Implications follow for model constancy, the Lucas critique, equation inversion, and impulse…

线性约束下多元时间序列干预效应的测量：银行业实例AI 解读

The authors consider the problem of estimating the effects of an intervention on a time-series vector subjected to a linear constraint. Minimum variance linear and unbiased estimators are provided for two different formulations of the problem--(1) when a multivariate intervention analysis is carried out and an adjustment is needed to fulfill the restriction and (2) when a univariate intervention analysis was performed on the aggregate series obtained from the linear…

协整分析中的异常值检测AI 解读

Standard unit-root and cointegration tests are sensitive to atypical events such as outliers and structural breaks. In this article, the authors use outlier-robust estimation techniques to examine the impact of these events on cointegration analysis. Their outlier-robust cointegration test provides a new diagnostic tool for signaling when standard cointegration results might be driven by a few aberrant observations. A main feature of the authors' approach is that the…

部分系统中协整秩的渐近推断AI 解读

The likelihood ratio test for cointegrating rank is analyzed for partial (or conditional) systems in the vector autoregressive error-correction model. Under the assumption of weak exogeneity for the cointegrating parameters, the asymptotic distributions are given and tables of critical values are provided. A discussion is given of some of the assumptions of the model, why they are needed, and how they are tested.

澳大利亚通胀建模AI 解读

This article develops an empirically constant, data-coherent, error-correction model for inflation in Australia. The level of consumer prices is a markup over domestic and import costs, with adjustments for dynamics and relative aggregate demand. The authors address issues of cointegration, general to specific modeling, dynamic specification, model evaluation and testing, parameter constancy, forecasting, and exogeneity. They also test this model against existing models of…

非平稳分数单整序列的渐近理论AI 解读

In this paper, we study the asymptotics of nonstationary fractional integrated time series, the long memory time series with d ≥ ½, with special attention focused on the cases when d = (2 p + 1)/2 for integer n no less than 0. There is considerable empirical evidence showing long memory of this magnitude in many economic time series including the inflation rate and the stock market volatility. A study of the large-sample property is therefore both needed and useful. Also, we…

伪结构断点现象札记AI 解读

When the disturbances of a regression model follow an I (1) process there is a tendency to estimate a break point in the middle of the sample, even though a break point does not actually exist. In this note, we provide a mathematical proof for this phenomenon.

计算 ARMA 模型自协方差的新方法：精确形式解AI 解读

In this article we present a new method for computing the theoretical autocovariance function of an autoregressive moving average model. The importance of our theorem is that it yields two interesting results: First, a closed-form solution is derived in terms of the roots of the autoregressive polynomial and the parameters of the moving average part. Second, a sufficient condition for the lack of model redundancy is obtained.

用于非平稳性检验的零频自回归谱密度估计量AI 解读

Many unit root and cointegration tests require an estimate of the spectral density function at frequency zero of some process. Commonly used are kernel estimators based on weighted sums of autocovariances constructed using estimated residuals from an AR(1) regression. However, it is known that with substantially correlated errors, the OLS estimate of the AR(1) parameter is severely biased. In this paper, we first show that this least-squares bias induces a significant…

针对季节性与非季节性序列相关备择的白噪声检验AI 解读

This paper considers tests for seasonal and nonseasonal serial correlation in time series and in the errors of regression models. The problem of testing for white noise against multiplicative seasonal ARMA(1, 1) × (1, 1), alternatives is investigated. This testing problem is nonstandard because of nuisance parameters that appear under the alternative but not under the null hypothesis. The likelihood ratio, sup Lagrange multiplier, and average exponential Lagrange multiplier…