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无限阶协整向量自回归过程AI 解读

Estimation of cointegrated systems via autoregressive approximation is considered in the framework developed by Saikkonen (1992, Econometric Theory 8, 1-27). The asymptotic properties of the estimated coefficients of the autoregressive error correction model (ECM) and the pure vector autoregressive (VAR) representations are derived under the assumption that the autoregressive order goes to infinity with the sample size. These coefficients are often used for analyzing the…

利用无限阶向量自回归过程检验因果关系AI 解读

Tests for Granger-causality have been performed in numerous empirical studies. These tests are usually based on finite order vector autoregressive (VAR) processes, and the assumption is made that the model fitted to the available data corresponds to the true data generating mechanism. In the present study, the more general assumption is made that a finite order VAR model is fitted to a potentially infinite order process. The order is assumed to increase with the sample size.…

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阶梯形 VARMA 模型的设定AI 解读

The echelon form of a vector autoregressive moving average (VARMA) model is considered. Its advantages over other identified VARMA representations are discussed. Furthermore, a general strategy for specifying echelon form VARMA models from data is presented. Specifically, procedures for choosing the Kronecker indices that characterize an echelon form are reviewed. The feasibility of the method is demonstrated by analyzing a well-known set of flour price time series and the…

通过向量自回归模型估计正交化脉冲响应AI 解读

Impulse response functions from time series models are standard tools for analyzing the relationship between economic variables. The asymptotic distribution of orthogonalized impulse responses is derived under the assumption that finite order vector autoregressive (VAR) models are fitted to time series generated by possibly infinite order processes. The resulting asymptotic distributions of forecast error variance decompositions are also given.

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多元时间序列结构稳定性的预测检验AI 解读

Comparing forecasts with actually observed values is one possible way to check the structural stability of time series. In this study, prediction tests based on this principle are investigated in the context of multiple time series analysis. It is found that the power of tests based on univariate series may exceed that of tests based on multivariate series and vice versa. Therefore, it is proposed to use both kinds of tests in practice. The tests are used to investigate the…

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估计向量自回归过程的移动平均系数的渐近分布AI 解读

The coefficients of the moving average (MA) representation of a vector autoregressive (VAR) process are the dynamic multipliers of the system. These quantities are often used to analyze the relationships between the variables involved. Assuming that the actual data generation process is stationary and has a VAR representation of unknown and possibly infinite order, the asymptotic distribution of the MA coefficients is derived. A computationally simple formula for the…

系统性缺失观测下向量 ARMA 过程的预测AI 解读

The following two predictors are compared for time series with systematically missing observations: (a) A time series model is fitted to the full series Xt , and forecasts are based on this model, (b) A time series model is fitted to the series with systematically missing observations Y τ, and forecasts are based on the resulting model. If the data generation processes are known vector autoregressive moving average (ARMA) processes, the first predictor is at least as…

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同期加总的向量 ARMA 过程预测AI 解读

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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用于多元时间序列建模的折扣多项式AI 解读

It is proposed to adopt Schmidt's (1974) modified polynomial lag models for multiple time series analysis. The resulting method can be regarded as a compromise between modelling pure autoregressive and autoregressive-moving average processes. While being as easy to specify and estimate as the former, the resulting class of models avoids some disadvantages that result from fitting pure autoregressive structures. As an example, data of Quenouille (1957) are analysed.

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