Semiparametric estimation from time series with long-range dependence. (English) Zbl 0808.62081
Summary: This paper studies the behaviour, in the presence of long-memory time- series dependence, of semiparametric averaged derivative statistics, which are useful in statistical inference on index models. They were shown to be asymptotically normal under weak dependence conditions by the second author [Rev. Econ. Stud. 56, No. 4, 511-534 (1989; Zbl 0681.62101)] and under serial independence by J. L. Powell et al. [Econometrica 57, No. 6, 1403-1430 (1989; Zbl 0683.62070)]. We find that an element of long-range dependence can lead either to a nonnormal limiting distribution, or else to a normal one with a limiting variance which differs from that which obtains in case of weak dependence, implying that inferences incorrectly based on weak-dependence assumptions will be invalid.
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62G07 | Density estimation |
| 62P20 | Applications of statistics to economics |
Keywords:
long-memory time-series dependence; semiparametric averaged derivative statistics; index models; long-range dependence; nonnormal limiting distributionReferences:
| [1] | Adenstedt, R.: On large-sample estimation for the mean of a stationary random sequence. Annals of statistics 2, 1095-1107 (1974) · Zbl 0296.62081 |
| [2] | Amemiya, T.: Regression analysis when the dependent variable is truncated normal. Econometrica 41, 997-1016 (1973) · Zbl 0282.62061 |
| [3] | Cheng, B.; Robinson, P. M.: Density estimation in strongly dependent nonlinear time series. Statistica sinica 1, 335-359 (1991) · Zbl 0823.62031 |
| [4] | Dagenias, M. G.: The tobit model with serial correlation. Economics letters 10, 263-267 (1982) |
| [5] | Dehling, H.; Taqqu, M. S.: The empirical process of some long-range dependent sequences with an application to U-statistics. Annals of statistics 17, 1767-1783 (1989) · Zbl 0696.60032 |
| [6] | Denker, M.; Keller, G.: On U-statistics and v. Mises statistics for weakly dependent processes. Zeitschrift für wahrscheinlichkeitstheorie und verwandte gebiete 64, 505-522 (1983) · Zbl 0519.60028 |
| [7] | Dobrushin, R. C.; Major, P.: Non-central limit theorems for non-linear functionals of Gaussian fields. Zeitschrift für wahrscheinlichkeitstheorie und verwandte gebiete 50, 27-52 (1979) · Zbl 0397.60034 |
| [8] | Grether, D. M.; Maddala, G. S.: A time series model with qualitative variables. Games, economic decisions, time series analysis, 291-305 (1982) · Zbl 0484.62119 |
| [9] | Hall, P.; Heyde, C. C.: Martingale limit theory and its applications. (1980) · Zbl 0462.60045 |
| [10] | Ibragimov, I. A.; Linnik, Y. V.: Independent and statistical sequences of random variables. (1971) · Zbl 0219.60027 |
| [11] | Ibragimov, I. A.; Rozanov, Y. A.: Gaussian random processes. (1978) · Zbl 0392.60037 |
| [12] | Philip, W.: The central limit problem for mixing sequences of random variables. Zeitschrift für wahrscheinlichkeitstheorie und verwandte gebiete 12, 155-171 (1969) · Zbl 0174.49904 |
| [13] | Poirier, D. J.; Ruud, P. A.: Probit with dependent observations. Review of economic studies 55, 593-614 (1988) · Zbl 0652.62026 |
| [14] | Powell, J.; Stock, J.; Stoker, T.: Semiparametric estimation of index coefficients. Econometrica 57, 1403-1430 (1989) · Zbl 0683.62070 |
| [15] | Quandt, R. E.: Autocorrelated errors in simple disequilibrium models. Economics letters 7, 55-62 (1981) |
| [16] | Robinson, P. M.: On the asymptotic properties of estimators of models containing limited dependent variables. Econometrica 50, 27-41 (1982) · Zbl 0524.62117 |
| [17] | Robinson, P. M.: Estimation of disequilibrium and limited dependent variable models with serially dependent residuals. Economics letters 23, 53-57 (1987) · Zbl 1328.62636 |
| [18] | Robinson, P. M.: Root-N-consistent semiparametric regression. Econometrica 56, 931-954 (1988) · Zbl 0647.62100 |
| [19] | Robinson, P. M.: Hypothesis testing in semiparametric and nonparametric models for econometric time series. Review of economic studies 56, 511-534 (1989) · Zbl 0681.62101 |
| [20] | Robinson, P. M.: Time series with strong dependence. Advances in econometrics: the sixth world congress 1 (1990) |
| [21] | Robinson, P. M.: Nonparametric function estimation for long-memory time series. Semiparametric and nonparametric methods in statistics and econometrics, 437-457 (1991) · Zbl 0850.62349 |
| [22] | Sapra, S. K.: A conditional least squares estimation procedure for a disequilibrium market model with autocorrelated errors. Economics letters 20, 251-254 (1986) · Zbl 1328.62637 |
| [23] | Stoker, T. M.: Tests of additive derivative constraints. Review of economic studies 56, 538-552 (1989) · Zbl 0679.62099 |
| [24] | Taqqu, M. S.: Weak convergence to fractional Brownian motion and to the rosenblatt process. Zeitschrift für wahrscheinlichkeitstheorie und verwandte gebiete 31, 287-302 (1975) · Zbl 0303.60033 |
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.
