Abstract
This paper gives the asymptotic theory of a class of rankorder statistics {TN} for two-sample problem pertaining to empirical processes based on the squared residuals from two classes of ARCH models. An important aspect is that, unlike the residuals of ARMA models, the asymptotics of {TN} depend on those of ARCH volatility estimators. Such asymptotics provide a useful guide to the reliability of confidence intervals, asymptotic relative efficiency and ARCH affection. We consider these aspects of {TN} for some ARCH residual distributions via numerical illustrations. Moreover, a measure of robustness for {TN} is introduced. These studies help to highlight some important features of ARCH residuals in comparison with the i.i.d. or ARMA settings.
| Original language | English |
|---|---|
| Pages (from-to) | 301-324 |
| Number of pages | 24 |
| Journal | Stochastic Processes and their Applications |
| Volume | 104 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2003 Apr 1 |
| Externally published | Yes |
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Keywords
- ARCH model
- Asymptotic relative efficiency
- Confidence intervals
- Empirical processes
- Robustness
- Squared residuals
- Two-sample rank order statistics
ASJC Scopus subject areas
- Statistics, Probability and Uncertainty
- Mathematics(all)
- Statistics and Probability
Cite this
Asymptotics of rank order statistics for ARCH residual empirical processes. / Chandra, S. Ajay; Taniguchi, Masanobu.
In: Stochastic Processes and their Applications, Vol. 104, No. 2, 01.04.2003, p. 301-324.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Asymptotics of rank order statistics for ARCH residual empirical processes
AU - Chandra, S. Ajay
AU - Taniguchi, Masanobu
PY - 2003/4/1
Y1 - 2003/4/1
N2 - This paper gives the asymptotic theory of a class of rankorder statistics {TN} for two-sample problem pertaining to empirical processes based on the squared residuals from two classes of ARCH models. An important aspect is that, unlike the residuals of ARMA models, the asymptotics of {TN} depend on those of ARCH volatility estimators. Such asymptotics provide a useful guide to the reliability of confidence intervals, asymptotic relative efficiency and ARCH affection. We consider these aspects of {TN} for some ARCH residual distributions via numerical illustrations. Moreover, a measure of robustness for {TN} is introduced. These studies help to highlight some important features of ARCH residuals in comparison with the i.i.d. or ARMA settings.
AB - This paper gives the asymptotic theory of a class of rankorder statistics {TN} for two-sample problem pertaining to empirical processes based on the squared residuals from two classes of ARCH models. An important aspect is that, unlike the residuals of ARMA models, the asymptotics of {TN} depend on those of ARCH volatility estimators. Such asymptotics provide a useful guide to the reliability of confidence intervals, asymptotic relative efficiency and ARCH affection. We consider these aspects of {TN} for some ARCH residual distributions via numerical illustrations. Moreover, a measure of robustness for {TN} is introduced. These studies help to highlight some important features of ARCH residuals in comparison with the i.i.d. or ARMA settings.
KW - ARCH model
KW - Asymptotic relative efficiency
KW - Confidence intervals
KW - Empirical processes
KW - Robustness
KW - Squared residuals
KW - Two-sample rank order statistics
UR - http://www.scopus.com/inward/record.url?scp=0037396671&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0037396671&partnerID=8YFLogxK
U2 - 10.1016/S0304-4149(02)00239-9
DO - 10.1016/S0304-4149(02)00239-9
M3 - Article
VL - 104
SP - 301
EP - 324
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
SN - 0304-4149
IS - 2
ER -