Hallin, Marc; Jurečková, Jana Optimal tests for autoregressive models based on autoregression rank scores. (English) Zbl 0962.62084 Ann. Stat. 27, No. 4, 1385-1414 (1999). Summary: Locally asymptotically optimal tests based on autoregression rank scores are constructed for testing linear constraints on the structural parameters of AR processes. Such tests are asymptotically distribution free and do not require the estimation of nuisance parameters. They constitute robust, flexible and quite powerful alternatives to existing methods such as the classical correlogram-based parametric tests, the Gaussian Lagrange multiplier tests the optimal non-Gaussian and ranked residual tests described by J.-P. Kreiss [ibid. 18, No. 3, 1470-1482 (1990; Zbl 0706.62077)] as well as to the aligned rank tests of M. Hallin and M.L. Puri [J. Multivariate Anal. 50, No. 2, 175-237 (1994; Zbl 0805.62050)].Optimality requires a nontrivial extension of existing asymptotic representation results to the case of unbounded score functions (such as the Gaussian quantile function). The problem of testing AR\((p-1)\) against AR\((p)\) dependence is considered as an illustration. Asymptotic local powers and asymptotic relative efficiencies are explicitly computed. In the special case of van der Waerden scores, the asymptotic relative efficiency with respect to optimal correlogram-based procedures is uniformly larger than one. Cited in 12 Documents MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62F05 Asymptotic properties of parametric tests 62F35 Robustness and adaptive procedures (parametric inference) 62G10 Nonparametric hypothesis testing Keywords:time series; autoregressive models; asymptotic tests; autoregression rank scores Citations:Zbl 0706.62077; Zbl 0805.62050 Software:AS 229 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] BAHADUR, R. R. 1966. A note on quantiles in large samples. Ann. Math. Statist. 37 557 580. Z. · Zbl 0147.18805 · doi:10.1214/aoms/1177699450 [2] BROCKWELL, P. J. and DAVIS, R. A. 1991. Time Series: Theory and Methods, 2nd ed. Springer, New York. Z. · Zbl 0709.62080 [3] CHANDA, K. C., PURI, M. L. and RUYMGAART, F. 1990. Asymptotic normality of L-statistics based Z. on m n -decomposable time series. J. Multivariate Anal. 35 260 275. · Zbl 0778.62080 · doi:10.1016/0047-259X(90)90028-G [4] CHERNOFF, H. and SAVAGE, I. R. 1958. 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