No CrossRef data available.
Article contents
LOCAL INSTRUMENTAL VARIABLE METHOD FOR THE GENERALIZED ADDITIVE-INTERACTIVE NONLINEAR VOLATILITY MODEL ESTIMATION
Published online by Cambridge University Press: 20 January 2012
Abstract
In this article we consider a new separable nonparametric volatility model that includes second-order interaction terms in both mean and conditional variance functions. This is a very flexible nonparametric ARCH model that can potentially explain the behavior of the wide variety of financial assets. The model is estimated using the generalized version of the local instrumental variable estimation method first introduced in Kim and Linton (2004, Econometric Theory 20, 1094–1139). This method is computationally more effective than most other nonparametric estimation methods that can potentially be used to estimate components of such a model. Asymptotic behavior of the resulting estimators is investigated and their asymptotic normality is established. Explicit expressions for asymptotic means and variances of these estimators are also obtained.
- Type
- Research Article
- Information
- Copyright
- Copyright © Cambridge University Press 2011
References
REFERENCES
Ango
Nze, P.
(1992) Criteres
d’ergodicite de quelques modeles a representation
markovenne. Les Comptes
Rendus de l’Académie des Sciences Paris
315(1),
1301–1304.Google Scholar
Auestad, B.
& Tjostheim, D.
(1990) Identification
of nonlinear time series: First order
characterization and order
estimation.
Biometrika
77,
669–687.Google Scholar
Bera, A.K.
& Lee, S.
(1990) On the
Formulation of a General Structure for Conditional
Heteroskedasticity.
Mimeo,
University of
Illinois.Google Scholar
Black, F.
(1976) Studies in
stock price volatility changes.
Proceedings of the 1976 Meeting of the
Business and Economic Statistics Section,
pp. 177–181.
American Statistical
Association.Google Scholar
Bollerslev, T.
(1986) Generalized
autoregressive conditional
heteroskedasticity.
Journal of Econometrics
31,
307–327.Google Scholar
Breiman, L.
& Friedman, J.H.
(1985) Estimating
optimal transformations for multiple regression
and correlation (with discussion).
Journal of the American Statistical
Association
80,
580–619.CrossRefGoogle Scholar
Buja, A.,
Hastie, T.,
& Tibshirani, R.
(1989) Linear
smoothers and additive models (with
discussion). Annals of
Statistics
17,
453–555.Google Scholar
Engle, R.F.
(1982) Autoregressive
conditional heteroscedasticity with estimates of
the variance of United Kingdom
inflation.
Econometrica
50(4),
987–1007.Google Scholar
Engle, R.F.
& Ng, V.K.,
(1993) Measuring and
testing the impact of news on
volatility. The Journal of
Finance
48(5),
1749–1778.CrossRefGoogle Scholar
Fan, J.
& Yao, Q.
(2003) Nonlinear Time Series:
Nonparametric and Parametric Methods.
Springer.Google Scholar
Hastie, T.
& Tibshirani, R.
(1987) Generalized
additive models: Some
applications. Journal of the
American Statistical Association
82,
371–386.Google Scholar
Kim, W.
& Linton, O.B.
(2004) The LIVE method
for generalized additive volatility
models. Econometric
Theory
20(6),
1094–1139.Google Scholar
Li, Q.,
Hsiao, C.,
& Zinn, J.
(2003) Consistent
specification test for
semiparametric/nonparametric models based on
series estimation methods.
Journal of Econometrics
112,
295–325.Google Scholar
Linton, O.B.
& Nielsen, J.
(1995) A kernel method
of estimating structured nonparametric regression
based on marginal integration.
Biometrika
82,
93–100.Google Scholar
Lu, Z.
& Jiang, Z.
(2001) L1 geometric
ergodicity of a multivariate nonlinear AR model
with an ARCH term.
Statistics & Probability
Letters
51,
121–130.CrossRefGoogle Scholar
Masry, E.
(1996a) Multivariate
local polynomial regression for time series:
Uniform strong consistency and
rates. Journal of Time
Series Analysis
17,
571–599.Google Scholar
Masry, E.
(1996b) Multivariate
regression estimation: Local polynomial fitting
for time series.
Stochastic Processes and Their
Applications
65,
81–101.Google Scholar
Newey, W.K.
(1994) Kernel
estimation of partial means.
Econometric Theory
10,
233–253.CrossRefGoogle Scholar
Pagan, A.R.
& Hong, Y.S.
(1991) Nonparametric estimation and
the risk premium. In Barnett, W.,
Powell, J.,
& Tauchen, G.E.
(eds.), Nonparametric and Semiparametric
Methods in Econometrics and Statistics.
Cambridge University
Press.Google Scholar
Pagan, A.R.
& Schwert, G.W.
(1990) Alternative
models for conditional stock
volatility. Journal of
Econometrics
45,
267–290.CrossRefGoogle Scholar
Rio, E.
(1993) Covariance
inequalities for strongly mixing
processes. Annales de
l’institut Henri Poincaré (B) Probabilités et
Statistiques
29(4),
587–597.Google Scholar
Sentana, E.
(1995) Quadratic ARCH
models. Review of Economic
Studies
62,
639–661.CrossRefGoogle Scholar
Sperlich, S.,
Tjostheim, D.,
& Yang, L.
(2002) Nonparametric
estimation and testing of interaction in additive
models. Econometric
Theory
18,
197–251.Google Scholar
Stone, C.J.
(1994) The use of
polynomial splines and their tensor products in
multivariate function estimation (with
discussion). Annals of
Statistics
22,
118–184.Google Scholar
Tjostheim, D.
& Auestad, B.
(1994) Nonparametric
identification of nonlinear time series:
Projections. Journal of
the American Statistical Association
89,
1398–1409.Google Scholar
Yang, L.,
Härdle, W.,
& Nielsen, J.P.
(1999) Nonparametric
autoregression with multiplicative volatility and
additive mean. Journal of
Time Series Analysis
20,
579–604.Google Scholar