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Basic Issues on the Seasonal Adjustment of the Canadian Consumer Price Index

加拿大消费者价格指数季节调整的基本问题

This study is mainly concerned with basic issues that arise in connection with the seasonal: adjustment of the Canadian Consumer Price Index when used as a current indicator of inflation. It analyzes the seasonal characteristics of the series and evaluates whether a direct or an indirect adjustment is preferred from the viewpoint of the degree of smoothness of the monthly rate of change. The use of ARIMA extrapolations versus no ARIMA extrapolations and the application of…

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Concurrent Seasonal Adjustment With Census X-11

使用 Census X-11 进行同期季节调整

Much investigative effort is being expended worldwide toward improving seasonally adjusted estimates from the Census X-11 program. Several recent investigations have resulted in a recommendation to obtain the most recent month's adjustment by applying X-11 to data through that month (concurrent adjustment), rather than relying on projected factors obtained from an earlier run. Although there are theoretical arguments supporting the applicaton of X-11 concurrently, a…

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Forecasting Contemporaneously Aggregated Vector ARMA Processes

同期加总的向量 ARMA 过程预测

Given a multiple time series that is generated by a multivariate ARMA process and assuming the objective is to forecast a weighted sum of the individual variables, then under a mean squared error measure of forecasting precision, it is preferable to forecast the disaggregated multiple time series and aggregate the forecasts, rather than forecast the aggregated series directly, if the involved processes are known. This result fails to hold if the processes used for…

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Signal Extraction for Nonstationary Time Series

非平稳时间序列的信号提取

The nonstationary signal extraction problem is to estimate $s_t$ given observations on $z_t = s_t + n_t$ (signal plus noise) when either $s_t$ or $n_t$ or both is nonstationary. Homogeneous or explosive nonstationary time series described by models of the form $\delta(B)z_t = w_t$ where $\delta(B)$ has zeroes on or inside the unit circle and $w_t$ is stationary are considered. For certain cases, approximate solutions to the nonstationary signal extraction problem have been…

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A Smoothness Priors–State Space Modeling of Time Series with Trend and Seasonality

含趋势与季节性的时间序列平滑先验状态空间建模

A smoothness priors modeling of time series with trends and seasonalities is shown. An observed time series is decomposed into local polynomial trend, seasonal, globally stationary autoregressive and observation error components. Each component is characterized by an unknown variance–white noise perturbed difference equation constraint. The constraints or Bayesian smoothness priors are expressed in state space model form. Trading day factors are also incorporated in the…

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On the Use of the General Partial Autocorrelation Function for Order Determination in ARMA( p, q ) Processes

广义偏自相关函数用于ARMA过程定阶的局限

We show that the General Partial Autocorrelation Function (GPAC), which has recently been suggested to be used as one of a set of convenient tools for order identification in ARMA models, has unstable behavior when applied to time series of moderate length. Its use in detecting the order of MA components in real series is very limited and can only be recommended as a means to confirm a pure AR fit to the data.

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A Method for Estimating Distributed Lags When Observations are Randomly Missing

观测随机缺失时分布滞后系数的估计方法

Abstract : This paper presents a frequency-domain technique for estimating distributed lag coefficients (the impulse-response function) when observations are randomly missed. The technique treats stationary processes with randomly missed observations as amplitude-modulated processes and estimates the transfer function accordingly. Estimates of the lag coefficients are obtained by taking the inverse transform of the estimated transfer function. Results with artificially…

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Testing for Unit Roots in Seasonal Time Series

季节性时间序列的单位根检验

Regression estimators of coefficients in seasonal autoregressive models are described. The percentiles of the distributions for time series that have unit roots at the seasonal lag are computed by Monte Carlo integration for finite samples and by analytic techniques and Monte Carlo integration for the limit case. The tabled distributions may be used to test the hypothesis that a time series has a seasonal unit root.

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Random Coefficient Autoregressive Models: An Introduction.

随机系数自回归模型导论

1 Introduction.- 1.1 Introduction.- Appendix 1.1.- Appendix 1.2.- 2 Stationarity and Stability.- 2.1 Introduction.- 2.2 Singly-Infinite Stationarity.- 2.3 Doubly-Infinite Stationarity.- 2.4 The Case of a Unit Eigenvalue.- 2.5 Stability of RCA Models.- 2.6 Strict Stationarity 37 Appendix 2.1.- 3 Least Squares Estimation of Scalar Models.- 3.1 Introduction.- 3.2 The Estimation Procedure.- 3.3 Strong Consistency and the Central Limit Theorem.- 3.4 The Consistent Estimation of…

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A Method for Estimating Distributed Lags when Observations are Randomly Missing

随机缺失观测下的分布滞后估计方法

This paper presents a frequency-domain technique for estimating distributed lag coefficients (the impulse-response function) when observations are randomly missed. The technique treats stationary processes with randomly missed observations as amplitude-modulated processes and estimates the transfer function accordingly. Estimates of the lag coefficients are obtained by taking the inverse transform of the estimated transfer function. Results with artificially created data…

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Large-Sample Tests of Homogeneity for Time Series Models

时间序列模型同质性的大样本检验

Limit distributions both under the null and a sequence of alternative hypotheses are derived for the likelihood ratio and related statistics for testing the homogeneity of several autoregressive processes. These results are extended to mixed autoregressive and moving average processes.

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Simultaneous Confidence Bands for Autoregressive Spectra

自回归谱的同时置信带

A shortcoming in the use of autoregressive spectral estimation has been the lack of methods for placing confidence intervals or bands on the estimated spectral density. We propose and illustrate a method for determining asymptotic simultaneous confidence bands using Scheffé projections.

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Estimation and Hypothesis Testing for Collections of Autoregressive Time Series

多条自回归时间序列的估计与假设检验

The analysis of a number of independent first-order autoregressive time series is considered in a normal theory context. A model is studied which allows for nonstation-ary and nonidentical distribution of the series caused by both fixed effect and random effect components.

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Spectral Factorization of Nonstationary Moving Average Processes

非平稳移动平均过程的谱分解

We solve here the general nonstationary multivariate MA spectral factorization problem, i.e. the problem of obtaining all the possible MA models (with time-dependent coefficients) corresponding to a given (time-dependent) autocovariance function. Our result (Theorem 8) relies on a symbolic generalization (Theorem 1) of the classical factorization property of the characteristic polynomial associated with stationary autocovariance functions, and is obtained by means of a…

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Asymptotic Conditional Inference for Regular Nonergodic Models with an Application to Autoregressive Processes

正则非遍历模型的渐近条件推断及其自回归应用

A conditional limit theorem is derived for a certain class of stochastic processes whose distributions constitute a nonergodic family. The limit theorem allows us to study the asymptotic behaviour under the conditional model of some standard statistical procedures by making use of results for ergodic families. Explosive Gaussian autoregressive processes are studied in some detail. Here the conditional process is shown to be a nonexplosive Gaussian autoregression bearing a…

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Regression Models with Time Series Errors

具有时间序列误差的回归模型

The time series regression models in which the errors of regression equations follow stationary or nonstationary autoregressive moving average models are considered. Convergence properties of the sample autocorrelation function of observed series and the least squares estimates of the linear regression parameters are shown. Based upon these results, a procedure for specifying the tentative order of the mixed ARMA errors is proposed. Two examples are given.

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Consistent Estimates of Autoregressive Parameters and Extended Sample Autocorrelation Function for Stationary and Nonstationary ARMA Models

平稳与非平稳 ARMA 模型的自回归参数一致估计与扩展样本自相关函数

A unified approach for the tentative specification of the order of mixed stationary and nonstationary ARMA models is proposed. For the ARMA models, an iterative regression procedure is given to produce consistent estimates of the autoregressive parameters. An extended sample autocorrelation function based on these consistent estimates is then defined and used for order determination. One of the advantages of this new approach is that it eliminates the need to determine,…

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Dynamic Representation of Multivariate Time Series Data

多元时间序列数据的动态表示

In this article we describe a procedure for representing multivariate time series data by means of interactive, computer-generated dynamic imagery with computer-music accompaniment. This innovation conveys the novel insights that dynamic imagery can provide; yet, the imagery is developed from principles that make the representation useful when examined either statically or dynamically. This is because the development of the dynamic representation is guided by the same…

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Estimating Missing Observations in Economic Time Series

经济时间序列中缺失观测的估计

Two related problems are considered. The first concerns the maximum likelihood estimation of the parameters in an ARIMA model when some of the observations are missing or subject to temporal aggregation. The second concerns the estimation of the missing observations. Both problems can be solved by setting up the model in state space form and applying the Kalman filter.

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Efficiency of a Kernel Density Estimator under an Autoregressive Dependence Model

自回归依赖模型下核密度估计量的效率

The problem of estimating the probability density function of a strictly stationary process is considered. To study the effect of a dependence structure on the efficiency of a kernel density estimator, the mean integrated squared error (MISE) of the Fourier integral estimator (FIE) is derived on the assumption that the observed data are generated by a first-order autoregressive process. Numerical results for the normal and Cauchy densities show that even moderate departures…

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Residual-Based Procedures for Prediction and Estimation in a Nonlinear Simultaneous System

非线性联立系统中基于残差的预测与估计程序

This paper proposes the residual-based stochastic predictor as an alternative procedure for obtaining forecasts with a static nonlinear econometric model. This procedure modifies the usual Monte Carlo approach to stochastic simulations of the model in that calculated residuals over the sample period are used as proxies for disturbances instead of random draws from some assumed parametric distribution. In compar-ison with the Monte Carlo predictor, the residual-based should…

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Testing Misspecification in Vector Time Series Models with Exogenous Variables

含外生变量的向量时间序列模型误设检验

SUMMARY In this paper we consider the application of hypothesis testing procedures to ARMAX systems. The score, or Lagrangian multiplier, principle is used to obtain mis-specification tests appropriate to these models. The structure of the information or sensitivity matrix is investigated in order to discuss the identifiability of alternative models and is used to show the existence of a set of admissible alternatives that are locally equivalent to one another. This notion…

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Nonlinear Regression with Dependent Observations

相依观测下的非线性回归

This paper provides general conditions which ensure consistency and asymptotic normality for the nonlinear least squares estimator. These conditions apply to time-series, cross-section, panel, or experimental data for single equations as well as systems of equations. The regression errors may be serially correlated and/or heteroscedastic. For an important special case, we propose a new covariance matrix estimator which is consistent regardless of the presence of…

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