Kim, Jaehee; Lee, Geung-Hee Local Fourier tests for structural change based on residuals. (English) Zbl 1360.62130 Commun. Stat., Theory Methods 46, No. 1, 133-147 (2017). Summary: We propose a structural change test based on the recursive residuals with the local Fourier series estimators. The statistical properties of the proposed test are derived and the empirical properties are shown via simulation. We also consider other structural change tests based on CUSUM, MOSUM, moving estimates (ME), and empirical distribution functions with the recursive residuals and the ordinary residuals. Empirical powers are calculated in various structural change models for the comparison of those tests. These structural change tests are applied to South Korea’s gross domestic product (GDP), South Korean Won to US Dollar currency exchange rates, and South Korea’s Okun’s law. MSC: 62G05 Nonparametric estimation 62G20 Asymptotic properties of nonparametric inference 62E17 Approximations to statistical distributions (nonasymptotic) 62P05 Applications of statistics to actuarial sciences and financial mathematics 62P20 Applications of statistics to economics 91B72 Spatial models in economics 91G70 Statistical methods; risk measures Keywords:Brownian bridge process; change-point model; CUSUM; local Fourier estimator; MOSUM; moving estimate; sample Fourier coefficients; stochastic process PDFBibTeX XMLCite \textit{J. Kim} and \textit{G.-H. Lee}, Commun. Stat., Theory Methods 46, No. 1, 133--147 (2017; Zbl 1360.62130) Full Text: DOI References: [1] DOI: 10.1111/j.1368-423X.2006.00190.x · Zbl 1106.62067 · doi:10.1111/j.1368-423X.2006.00190.x [2] DOI: 10.2307/2171863 · Zbl 0844.62032 · doi:10.2307/2171863 [3] DOI: 10.2307/2998540 · Zbl 1056.62523 · doi:10.2307/2998540 [4] DOI: 10.1111/1368-423X.00102 · Zbl 1032.62064 · doi:10.1111/1368-423X.00102 [5] DOI: 10.2307/1267643 · Zbl 0436.62090 · doi:10.2307/1267643 [6] Brown L.R., J. R. Stat. Soc. B 37 pp 149– (1975) [7] DOI: 10.1214/aos/1176350699 · Zbl 0637.62041 · doi:10.1214/aos/1176350699 [8] DOI: 10.1093/biomet/82.3.603 · Zbl 0830.62079 · doi:10.1093/biomet/82.3.603 [9] DOI: 10.1017/S0266466600009695 · Zbl 04527979 · doi:10.1017/S0266466600009695 [10] Csörgö M., Limit Theorems in Change-Point Analysis (1997) · Zbl 0884.62023 [11] DOI: 10.1214/aos/1176348257 · Zbl 0776.62032 · doi:10.1214/aos/1176348257 [12] DOI: 10.1016/j.jspi.2003.07.014 · Zbl 1075.62054 · doi:10.1016/j.jspi.2003.07.014 [13] DOI: 10.1111/1467-9892.00100 · Zbl 0908.62055 · doi:10.1111/1467-9892.00100 [14] DOI: 10.1080/10485251003721232 · Zbl 1359.62106 · doi:10.1080/10485251003721232 [15] Krämer, W., Ploberger, W., Alt, R., Testing for structural change in dynamic models. Econometrica 56 pp 1355–1369– (1988) · Zbl 0655.62107 [16] DOI: 10.1080/07474939508800311 · Zbl 0832.62085 · doi:10.1080/07474939508800311 [17] DOI: 10.1214/aos/1176344954 · Zbl 0451.62040 · doi:10.1214/aos/1176344954 [18] DOI: 10.1017/S0266466600005302 · doi:10.1017/S0266466600005302 [19] DOI: 10.2307/2951597 · Zbl 0744.62155 · doi:10.2307/2951597 [20] DOI: 10.1214/aos/1176346788 · Zbl 0554.62035 · doi:10.1214/aos/1176346788 [21] DOI: 10.1214/aos/1176345714 · Zbl 0484.62098 · doi:10.1214/aos/1176345714 [22] DOI: 10.1016/j.strueco.2008.02.001 · doi:10.1016/j.strueco.2008.02.001 [23] DOI: 10.1080/07474930500406053 · Zbl 1080.62012 · doi:10.1080/07474930500406053 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.