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Fractional Time Series Modelling

分数差分时间序列建模

Aspects of model building using fractionally differenced autoregressive-moving average processes are discussed. An algorithm for approximate maximum likelihood estimation is outlined and the large-sample distribution of the maximum likelihood estimates is derived. The large-sample distribution of the residual autocorrelations is also derived and a modified portmanteau test statistic is obtained for checking model adequacy.

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Recursive Estimation of Linear Systems

线性系统的递归估计

The estimation of parameters for a scalar linear system with rational transfer function is considered, the estimates being updated each time a new data point comes to hand. Two well-known algorithms are compared by simulation with a method related to the three-stage algorithm of Hannan & Rissanen (1982); a computation scheme using Givens transformations is proposed which makes the three-stage recursive algorithm economical. A central limit theorem is proved for the…

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Generalized autoregressive conditional heteroskedasticity

广义自回归条件异方差

A natural generalization of the ARCH (Autoregressive Conditional Heteroskedastic) process introduced in Engle (1982) to allow for past conditional variances in the current conditional variance equation is proposed. Stationarity conditions and autocorrelation structure for this new class of parametric models are derived. Maximum likelihood estimation and testing are also considered. Finally an empirical example relating to the uncertainty of the inflation rate is presented.

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Estimation of Unobserved Expected Monthly Inflation Using Kalman Filtering

利用 Kalman 滤波估计不可观测的月度预期通胀

Hamilton developed a technique for estimating financial market expectations of inflation based on the observed time-series properties of interest rates and inflation. The technique is based on a state-space representation derived from an underlying vector autoregressive process of the expected real interest rate and the expected inflation rate on lagged expectations and lagged values of the observed Treasury bill rate and the actual inflation rate. This article extends this…

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Robust Estimation of Regression Models with Dependent Regressors: The Functional Least Squares Approach

相依回归量下的稳健回归估计:函数型最小二乘方法

In the case of regression models, one robust estimation procedure which has recently emerged is that of functional least squares. The procedure is based on the use of characteristic functions for which the tail behavior is relected by the behavior of these functions at the origin. Its attraction is that it is applicable to situations where the distribution of the disturbances may be long-tailed and/or asymmetric. This paper extends this theory to include a large class of…

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Asymptotic Theory for ARCH Models: Estimation and Testing

ARCH 模型的渐近理论:估计与检验

In the context of a linear dynamic model with moving average errors, we consider a heteroscedastic model which represents an extension of the ARCH model introduced by Engle [4]. We discuss the properties of maximum likelihood and least squares estimates of the parameters of both the regression and ARCH equations, and also the properties of various tests of the model that are available. We do not assume that the errors are normally distributed.

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Aproximate Distributions of the Periodogram and Related Statistics under Normality

正态性下周期图及相关统计量的近似分布

Under normality, we obtain higher-order approximations to the distributions of the periodogram and related statistics. Our approach is based on the theorem which decomposes the periodogram into the sum of two independent random variables. It is seen that this decomposition enables us to study fairly closely the higher-order properties of not only the periodogram, but also periodogram-based statistics such as the estimators of the spectrum and prediction error variance. Some…

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Forecasting with an econometric model: Some recent results using the national institute model

使用计量模型预测:National Institute 模型的若干结果

Abstract It is widely believed that the large econometric models cannot be used for forecasting without considerable intervention on the part of the forecaster. In this paper we challenge this view by reproducing a number of recent forecasts published by the National Institute but without the ad hoc interventions used at the time. We show that in no case would the forecast, produced by the model used mechanically, have been radically different from that actually published.…

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An empirical investigation into the causes of failure of the monetary model of the exchange rate

汇率货币模型失效原因的实证考察

Abstract The purpose of this paper is to attempt to provide measures of the relative importance of the principal causes of the failure of the monetary model of the exchange rate. Secondly, the random walk hypothesis for the exchange rate is tested. The methodology employed is new and has wide application elsewhere. It involves explicitly modelling the misspecification by time series techniques. The results confirm the importance of the breakdown of the PPP assumption but…

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Asymptotically Efficient Selection of the Order by the Criterion Autoregressive Transfer Function

自回归传递函数准则选阶的渐近效率

The autoregressive orders selected by the criterion autoregressive transfer function (CAT) of Parzen (1974), a new version, CAT$^\ast$, of CAT introduced by Parzen (1977), and the CAT$_2$ criterion of Bhansali (1985) are shown to be asymptotically efficient in the sense defined by Shibata (1980, 1981). A generalization of the penalty function considered by Shibata (1980) is introduced. The order selected by the CAT$_\alpha$ criterion of Bhansali (1985), with any fixed $\alpha > 1$…

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Theory of Partial Likelihood

部分似然理论

A general asymptotic theory is developed for the maximum likelihood estimator based on a partial likelihood. Conditions are given for consistency and asymptotic normality, and a method is provided for the calculation of the asymptotic efficiency of the estimator. The implications of the general theory are examined in special cases such as inference in stochastic processes, Cox regression models, and AR processes with missing segments.

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Likelihood Ratio Tests for a Change in the Multivariate Normal Mean

多元正态均值变化的似然比检验

A sequence of independent multivariate normal vectors with equal but possibly unknown variance matrices are hypothesized to have equal mean vectors, and we wish to test that the mean vectors have changed after an unknown point in the sequence. The likelihood ratio test is based on the maximum Hotelling T 2 for the sequences before and after the change point. The main result is a conservative approximation for its null distribution based on an improved Bonferroni inequality.…

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Robust Estimates for ARMA Models

ARMA 模型的稳健估计

Two new classes of robust estimates for ARMA models are introduced: estimates based on residual autocovariances (RA estimates), and estimates based on truncated residual autocovariances (TRA estimates). A heuristic derivation of the asymptotic normal distribution is given. We also perform a Monte Carlo study to compare the robustness properties of these estimates with the least squares, M, and GM estimates. In this study we consider observations that correspond to a Gaussian…

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Least Squares Regression When the Independent Variable Follows an ARIMA Process

自变量服从 ARIMA 过程时的最小二乘回归

In the regression model yt = α + βxt + ut where the disturbances ut may be autocorrelated and xt follows an ARIMA(p, 1, q) process, it is shown that the asymptotic distributions of the ordinary and generalized least squares estimates of β are identical.

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Time Series Model Specification in the Presence of Outliers

存在异常值时的时间序列模型设定

Outliers are commonplace in data analysis. Time series analysis is no exception. Noting that the effect of outliers on model identification statistics could be serious, this article is concerned with the problem of time series model specification in the presence of outliers. An iterative procedure is proposed to identify the outliers, to remove their effects, and to specify a tentative model for the underlying process. The procedure is essentially based on the iterative…

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Tests of Noncausality under Markov Assumptions for Qualitative Panel Data

马尔可夫假设下类别型面板数据的非因果性检验

For many years, social scientists have been interested in obtaining testable definitions of causality (Granger 1969, Sims 1972). Recent works include those of Chamberlain (1982) and Florens and Mouchart (1982). The present paper first clarifies the results of these latter papers by considering a unifying definition of noncausality. Then, log-likelihood ratio (LR) tests for noncausality are derived for qualitative panel data under the minimal assumption that one series is…

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Maximum Likelihood Estimation for the Near (2) Model

NEAR(2) 模型的最大似然估计

SUMMARY The NEAR(2) model is a model for nonlinear time series with exponential marginals. It formed the subject of a recent discussion paper by Lawrance and Lewis. We explore the possibility of maximum likelihood estimation with particular reference to the difficulties created by discontinuities in the likelihood function. Two exploratory techniques are proposed for resolving those difficulties. This note is an expanded version of a contribution presented orrally at the…

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Instrumental Variables Estimation of Dynamic Simultaneous Systems with ARMA Errors

具有ARMA误差的动态联立系统的工具变量估计

This paper develops the instrumental variables estimator for a possibly incomplete, dynamic economic system with vector autoregressive moving average disturbances. Its asymptotic distribution is derived and, under fairly weak conditions, it is shown that lagged endogenous variables may be validly included in the set of instruments. Statistics are proposed for testing the order of the error process and the validity of the instruments.

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Two Results Useful for Implementing Litterman's Procedure for Interpolating a Time Series

有助于实施 Litterman 时间序列插值程序的两项结果

Litterman (1983) recently suggested a modification to the rameter to be accurate. Litterman's notation is followed Chow and Lin (1971) and Fernandez (1981) procedures for throughout. interpolating monthly data from an observed quarterly time series. ~riefl~ stated, the Litterman proceduri involves obtaining generalized least squares (GLS) forecasts of the monthly 2. THE LITTERMAN PROCEDURE IN BRIEF values of interest-the GLS estimates determined from quar- Letting Y* denote…

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ARCH and Bilinear Time Series Models: Comparison and Combination

ARCH 与双线性时间序列模型:比较与结合

Two extensions to the ARMA model, bilinearity and ARCH errors are compared, and their combination is considered. Starting with the ARMA model, tests for each extension are discussed, along with various least squares and maximum likelihood estimates of the parameters and tests of the estimated models based on these. The effects each may have on the identification, estimation, and testing of the other are given, and it is seen that to distinguish between the two properly, it…

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The Construction and Use of Approximations for Missing Quarterly Observations: A Model-Based Approach

缺失季度观测的近似构造与使用:基于模型的方法

We use a model-based approach to derive quarterly figures on several variables for the aggregate labor market in the Netherlands that are only observed annually. These approximations are conditional expectations derived from univariate and bivariate quarterly time series models for the series under consideration. They are subsequently used as proxies to estimate and analyze the structural labor market equations. Attention is given to the properties of estimation procedures…

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Forecasting With Bayesian Vector Autoregressions—Five Years of Experience

使用贝叶斯向量自回归进行预测:五年经验

The results obtained in five years of forecasting with Bayesian vector autoregressions (BVAR's) demonstrate that this inexpensive, reproducible statistical technique is as accurate, on average, as those used by the best known commercial forecasting services. This article considers the problem of economic forecasting, the justification for the Bayesian approach, its implementation, and the performance of one small BVAR model over the past five years.

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