MAXIMUM-LIKELIHOOD-ESTIMATION AND INFERENCE ON COINTEGRATION - WITH APPLICATIONS TO THE DEMAND FOR MONEY
MAXIMUM-LIKELIHOOD-ESTIMATION AND INFERENCE ON COINTEGRATION - WITH APPLICATIONS TO THE DEMAND FOR MONEY
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DOI：
10.1111/j.1468-0084.1990.mp52002003.x
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发表时间：
1990-05-01
影响因子：
2.5
通讯作者：
JUSELIUS, K
中科院分区：
文献类型：
--
作者：
JOHANSEN, S;JUSELIUS, K
在过去的几年里，许多论文都致力于协整标题下的长期关系的estitnation和测试。格兰杰（1981），格兰杰和韦斯（1983），Engle和格兰杰（1987），Stock（1987），菲利普斯和Oullaris（1986），（1987），Johansen（1988 b），（1989），Johansenand Juselius（1988），典型分析。Box and Tiao（1981），Velu，Wichem and Reinsel（1987），佩纳and Box（1987）.降秩回归，Velu，Reinsel和Wichem（1986），Ahn和Reinsel（1987），共同趋势。Stock和沃森（1987），带积分回归的回归，菲利普斯（1987），菲利普斯和Park（1986 a），（1988 b），（1989），以及单位根检验标题下的结果，例如参见西姆斯，Stock和沃森（1986）。《经济动态与控制杂志》（Journal of Economic Dynamics and Cotitrol）（1988）也有一期专刊讨论了同样的问题。(1.1)下文），并将协整假设公式化为长期影响矩阵II= afi“的降秩假设。本文的主要目的是结合两个例子来说明极大似然法。结果涉及协整模型中的最大似然估计和似然比检验的计算在线性约束下的协整向量0和权重。这些结果是对Johansen（1988 b）中的方法的修改，并应用了偏典型相关的多变量技术，见安德森（1984）或左宗棠（1981）。为了证明这一点，我们将Johamen（1989）的结果应用于似UuKxl比检验的渐近分布。这些分布是根据一个多偶布朗运动过程给出的，并在附录中列出。利用通常的x分布作为似然比检验分布的近似，可以推导出在线性约束下的似然比分布的推论。我们还应用极限分布的taximum liketifood估计的Wald测试的假设约a和0。
Many papers have over the last few years been devoted to the estitnation and testing of long-run relations under the heading of cointegration. Granger (1981), Granger and Weiss (1983), Engle and Granger (1987), Stock (1987), Phillips and Oullaris (1986),(1987), Johansen (1988b),(1989), Johansenand Juselius (1988), canonical analysis. Box and Tiao (1981), Velu, Wichem and Reinsel (1987), Pena and Box (1987). reduced rank regression, Velu, Reinsel and Wichem (1986), and Ahn and Reinsel (1987), common trends. Stock and Watson (1987), regression with integrated regressors, Phillips (1987), Phillips and Park (1986a),(1988b),(1989), as weU as under the heading testing for unit roots, see for instance Sims, Stock, and Watson (1986). There is a special issue of this BULLETIN (1986) dealing mainly with cointegration and a special issue of the Journal of Economic Dynamics and Cotitrol (1988) deeding with the same problems.We start with a vector autoregressive model (cf.(1.1) below) and formulate the hypothesis of cointegration as the hypothesis of reduced rank of the longrun impact matrix II= afi'. The main purpose of this paper is to demonstrate the method of maximum likelihood in connection with two examples. The results concern the calculation of the maximum likelihood estimators and likelihood ratio tests in the model for cointegration under linear restrictions on the cointegration vectors 0 and weights a. These results are modifications of die procedure^ ven in Johansen (1988b) and apply the multivariate technique of partial canonical correlations, see Anderson (1984) or Tso (1981). For ii^ erence we apply the results of Johamen (1989) on the asymptotic distribution of thelikelUuKxl ratio test. These disttibutiom are givai in terms of a multivmate Brownian motion process and are tabidated in the Appendix. Inferences on a aiyd fiimder linear restrictions can be amducted using the usual x^ distribution as an approximation to the distribution of likelihood ratio test. We also apply the limiting distribution of the tnaximum liketifaood estimator to a Wald test for hypotheses about a and 0.