, LARCH ? Lip 4 (?) as well as Assumption Co(? LARCH , ?) when condition (41) holds. We assumed that ? ? ? ? a i (?) are C 2 (?) functions for any i ? N. Thus in order to check the conditions of Theorem 3.2, we first have to prove that ? ? ? LARCH ? Lip 4 (?)
Asymptotic properties of quasi-maximum likelihood estimators for ARMA models with time-dependent coefficients, Statistical Inference for Stochastic Processes, vol.9, pp.279-330, 2006. ,
Asymptotic behavior of the Laplacian quasi-maximum likelihood estimator of affine causal processes, Electronic Journal of Statistics, vol.11, pp.452-479, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01249503
Non-parametric estimation of time varying AR(1)-processes with local stationarity and periodicity, Electronic Journal of Statistics, vol.12, pp.2323-2354, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01527749
Multiple breaks detection in general causal time series using penalized quasi-likelihood, Elec. Journal Statist, pp.435-477, 2012. ,
Asymptotic normality of the quasi-maximum likelihood estimator for multidimensional causal processes, Ann. Statist, vol.37, pp.2730-2759, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00193955
Convergence of probability measures, 1999. ,
On the Kullback-Leibler information divergence of locally stationary processes, Stochastic Processes and Applications, vol.62, pp.139-168, 1996. ,
Fitting time series models to nonstationary processes, Annals of Statistics, vol.25, pp.1-37, 1997. ,
A Likelihood Approximation for Locally Stationnary Processes, Annals of Statistics, vol.28, pp.1762-1794, 2000. ,
Empirical spectral processes for locally stationary time series, Bernoulli, vol.15, pp.1-39, 2009. ,
Locally Stationary Processes, Time Series Analysis: Methods and Applications, vol.30, 2012. ,
Nonparametric quasi-maximum likelihood estimation for Gaussian locally stationary processes, The Annals of Statistics, vol.34, pp.2790-2824, 2006. ,
Towards a general theory for nonlinear locally stationary processes, Bernoulli, vol.25, pp.1013-1044, 2019. ,
Statistical Inference for Time Varying ARCH processes, The Annals of Statistics, vol.34, pp.1075-1114, 2006. ,
Weak dependence: With Examples and Applications, Lecture Notes in Statistics, vol.190, 2007. ,
URL : https://hal.archives-ouvertes.fr/hal-00686031
Coupling for ? ?Dependent Sequences and Applications, Journal of Theoretical Probability, vol.17, pp.861-885, 2004. ,
A long memory property of stock market returns and a new model, J. Empirical Finance, vol.1, pp.83-106, 1993. ,
On weak dependence conditions for Poisson autoregressions, Statistics and Probability Letters, vol.82, pp.942-948, 2012. ,
Inference and testing for structural change in general Poisson autoregressive models, Electronic Journal of Statistics, vol.9, pp.1267-1314, 2015. ,
A fixed point approach to model random fields, ALEA Lat. Am. J. Probab. Math. Stat, vol.3, pp.111-132, 2007. ,
URL : https://hal.archives-ouvertes.fr/hal-00141713
Weakly dependent chains with infinite memory, Stochastic Processes and Applications, vol.118, pp.1997-2013, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00199890
, GARCH Models: Structure, Statistical Inference and Financial Applications, 2010.
Inconsistency of the MLE and inference based on weighted LS for LARCH models, Journal of Econometrics, vol.159, pp.151-165, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00732536
Stationary ARCH models: dependence structure and Central Limit Theorem, Econometric Theory, vol.1, pp.3-22, 2000. ,
LARCH, leverage and long memory, Journal of Financial Econometrics, vol.2, pp.177-210, 2003. ,
Asymptotic theory for a vector ARMA-GARCH model, Econometric Theory, vol.19, pp.280-310, 2003. ,
Frequency and phase estimation in time series with quasi periodic components, Journal of Time Series Analysis, vol.33, pp.13-31, 2012. ,
On the mesurability and consistency of minimum contrast estimates, Metrika, vol.14, pp.249-334, 1969. ,
Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression, Journal of Econometrics, vol.47, pp.67-84, 1991. ,
A time varying GARCH() model and related statistical inference, Statistics & Probability Letters, vol.83, pp.1983-1990, 2013. ,
Stochastic curve estimation 3. NSF-CBMS Regional Conference Series in Probability and Statistics, 1991. ,
Estimation in conditionally heteroscedastic time series models, Lecture Notes in Statistics, vol.181, 2005. ,
Parameter stability and semiparametric inference in timevarying ARCH models, Journal of Royal Statistical Society Series B, vol.79, pp.1391-1414, 2017. ,