Kristensen, Dennis; Rahbek, Anders Testing and inference in nonlinear cointegrating vector error correction models. (English) Zbl 1290.62080 Econom. Theory 29, No. 6, 1238-1288 (2013). Summary: We analyze estimators and tests for a general class of vector error correction models that allows for asymmetric and nonlinear error correction. For a given number of cointegration relationships, general hypothesis testing is considered, where testing for linearity is of particular interest. Under the null of linearity, parameters of nonlinear components vanish, leading to a nonstandard testing problem. We apply so-called sup-tests to resolve this issue, which requires development of new (uniform) functional central limit theory and results for convergence of stochastic integrals. We provide a full asymptotic theory for estimators and test statistics. The derived asymptotic results prove to be nonstandard compared to results found elsewhere in the literature due to the impact of the estimated cointegration relations. This complicates implementation of tests motivating the introduction of bootstrap versions that are simple to compute. A simulation study shows that the finite-sample properties of the bootstrapped tests are satisfactory with good size and power properties for reasonable sample sizes. Cited in 11 Documents MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62M07 Non-Markovian processes: hypothesis testing 60F17 Functional limit theorems; invariance principles PDFBibTeX XMLCite \textit{D. Kristensen} and \textit{A. Rahbek}, Econom. Theory 29, No. 6, 1238--1288 (2013; Zbl 1290.62080) Full Text: DOI References: [1] Matrix Differential Calculus with Applications in Statistics and Econometrics (1988) · Zbl 0651.15001 [2] DOI: 10.1017/S0266466611000041 · Zbl 1228.62112 [3] Journal of Business & Economic Statistics 17 pp 195– (1996) [4] DOI: 10.1017/S0266466609990776 · Zbl 1294.62192 [5] DOI: 10.1016/j.jeconom.2010.03.003 · Zbl 1431.62358 [6] DOI: 10.1016/j.jeconom.2006.11.002 · Zbl 1418.62355 [7] DOI: 10.1111/1468-0262.00257 · Zbl 1018.62064 [8] DOI: 10.1214/aop/1176990334 · Zbl 0742.60053 [9] DOI: 10.1214/aoms/1177693494 · Zbl 0218.60048 [10] DOI: 10.1016/j.jeconom.2010.03.010 · Zbl 1431.62393 [11] DOI: 10.1111/j.1368-423X.2004.00147.x · Zbl 1114.91338 [12] Journal of Time Series Econometrics (2009) [13] Studies in Nonlinear Dynamics & Econometrics 9 (2005) [14] Econometric Theory 21 pp 946– (2005) [15] Econometrica 68 pp 23– (2001) [16] DOI: 10.1111/j.1467-9892.2011.00722.x · Zbl 1273.62212 [17] Handbook of Econometrics IV pp 2247– (1994) [18] DOI: 10.1214/009053606000001181 · Zbl 1114.62089 [19] Econometric Theory 22 pp 279– (2006) [20] DOI: 10.1016/j.jeconom.2010.01.007 · Zbl 1431.62633 [21] DOI: 10.1017/S0266466609990430 · Zbl 1294.62200 [22] DOI: 10.1016/S0304-4076(98)00044-X · Zbl 1041.62522 [23] DOI: 10.1017/S1365100504030019 [24] Convergence of Stochastic Processes (1984) [25] Statistica Sinica 17 pp 115– (2007) [26] DOI: 10.3982/ECTA6979 · Zbl 1152.91737 [27] DOI: 10.1016/S0304-4076(02)00093-3 · Zbl 1038.62084 [28] DOI: 10.1111/1468-0262.00180 · Zbl 0999.62050 [29] DOI: 10.1016/S0304-4076(00)00075-0 · Zbl 0967.62063 [30] DOI: 10.1016/j.spl.2005.04.057 · Zbl 1076.62020 [31] Biometrika 74 pp 33– (1987) [32] Handbook of Econometrics 4 pp 2111– (1994) · Zbl 0982.62503 [33] DOI: 10.1111/j.1368-423X.2004.00134.x · Zbl 1064.62096 [34] Markov Chains and Stochastic Stability (1993) · Zbl 0925.60001 [35] DOI: 10.1016/j.jeconom.2004.03.001 · Zbl 1335.62145 [36] Likelihood-Based Inference in Cointegrated Vector Autoregressive Models (1996) [37] Econometrica 59 pp 1551– (1992) [38] Econometric Theory 23 pp 761– (2007) [39] DOI: 10.1016/S0304-4076(02)00097-0 · Zbl 1044.62092 [40] Weak Convergence and Empirical Processes (1996) [41] DOI: 10.1017/S0266466600006629 · Zbl 04532465 [42] DOI: 10.1017/S0266466611000648 · Zbl 1239.62110 [43] DOI: 10.2307/2171789 · Zbl 0862.62090 [44] DOI: 10.1017/S026646661000023X · Zbl 1210.62124 [45] DOI: 10.1017/S0266466600013189 · Zbl 04510758 [46] DOI: 10.1017/S0266466608080663 · Zbl 1231.62163 [47] DOI: 10.1016/j.jeconom.2005.06.018 · Zbl 1418.62354 [48] Martingale Limit Theory and Its Applications (1980) [49] Palgrave Handbook of Econometrics: Econometric Theory 1 pp 578– (2006) [50] Econometric Theory 24 pp 294– (2008) [51] DOI: 10.3982/ECTA9099 · Zbl 1274.62223 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.