Nonlinear Time Series Models

Assume that for \(t \in \mathbb{Z}\), (Z t ) and \((Z_{t}^{{\ast}})\) are respectively uncorrelated and independent sequences of r.v’s having identical marginal distribution F(⋅ ), with zero mean and variance \(\sigma _{Z}^{2} <\infty\).

[1]  György Terdik.  Bilinear stochastic models and related problems of nonlinear time series analysis : a frequency domain approach , 1999 .

[2]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[3]  J. Zakoian,et al.  Threshold Arch Models and Asymmetries in Volatility , 1993 .

[4]  Stationarity of a Family of GARCH Processes , 2009 .

[5]  W. Härdle,et al.  A Review of Nonparametric Time Series Analysis , 1997 .

[6]  Jiahui Wang,et al.  Modeling Financial Time Series with S-PLUS® , 2003 .

[7]  G. Schwert.  Why Does Stock Market Volatility Change Over Time? , 1988 .

[8]  J. Zakoian.  Threshold heteroskedastic models , 1994 .

[9]  P. Robinson,et al.  Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression , 1991 .

[10]  Robert F. Engle,et al.  Risk and Volatility: Econometric Models and Financial Practice , 2004 .

[11]  Adrian Pagan,et al.  The econometrics of financial markets , 1996 .

[12]  Timo Teräsvirta,et al.  Properties of Moments of a Family of GARCH Processes , 1999 .

[13]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

[14]  A. Doucet,et al.  Particle Markov chain Monte Carlo methods , 2010 .

[15]  Richard A. Davis,et al.  Handbook of Financial Time Series , 2009 .

[16]  Jan Korbel,et al.  Modeling Financial Time Series , 2013 .

[17]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .

[18]  M. Friedman.  Nobel Lecture: Inflation and Unemployment , 1977, Journal of Political Economy.

[19]  L. Glosten,et al.  On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks , 1993 .

[20]  C. Granger,et al.  On the invertibility of time series models , 1978 .

[21]  Richard A. Davis,et al.  Break Detection for a Class of Nonlinear Time Series Models , 2008 .

[22]  Sidney Resnick,et al.  Sample correlation behavior for the heavy tailed general bilinear process , 2000 .

[23]  Richard T. Baillie,et al.  Modeling Long Memory and Structural Breaks in Conditional Variances: an Adaptive FIGARCH Approach , 2009, ICER 2007.

[24]  A. Brandt.  The stochastic equation Yn+1=AnYn+Bn with stationary coefficients , 1986 .

[25]  James Davidson,et al.  Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model , 2004 .

[26]  Christian Conrad,et al.  Fractionally Integrated APARCH Modeling of Stock Market Volatility: A multi-country study , 2008 .

[27]  Piotr Kokoszka,et al.  GARCH processes: structure and estimation , 2003 .

[28]  H. Iemoto.  Modelling the persistence of conditional variances , 1986 .

[29]  V. J. Mathews,et al.  Polynomial Signal Processing , 2000 .

[30]  Jiti Gao,et al.  Nonlinear Time Series: Semiparametric and Nonparametric Methods , 2019 .

[31]  D. B. Preston.  Spectral Analysis and Time Series , 1983 .

[32]  Roger W. Brockett.  Volterra series and geometric control theory , 1976, Autom..

[33]  Dag Tjøstheim,et al.  Some recent theory for autoregressive count time series , 2012 .

[34]  D. Tjøstheim.  Non-linear Time Series: A Selective Review* , 1994 .

[35]  M. West,et al.  Bayesian forecasting and dynamic models , 1989 .

[36]  Mi-Ja Woo,et al.  Threshold ARCH(1) processes: asymptotic inference , 2001 .

[37]  Philip Hans Franses,et al.  Non-Linear Time Series Models in Empirical Finance , 2000 .

[38]  C. Granger,et al.  Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns , 2004 .

[39]  Timo Teräsvirta,et al.  Multivariate GARCH models To appear in T. G. Andersen, R. A. Davis, J.-P. Kreiss and T. Mikosch, eds. Handbook of Financial Time Series. New York: Springer. , 2008 .

[40]  Richard A. Davis,et al.  Introduction to time series and forecasting , 1998 .

[41]  Yiu Kuen Tse,et al.  The conditional heteroscedasticity of the yen-dollar exchange rate , 1998 .

[42]  Fabio Fornari,et al.  SIGN- AND VOLATILITY-SWITCHING ARCH MODELS: THEORY AND APPLICATIONS TO INTERNATIONAL STOCK MARKETS , 1997 .

[43]  Christian Conrad,et al.  Inequality Constraints in the Fractionally Integrated GARCH Model , 2006 .

[44]  Francis X. Dieobold.  Modeling The persistence Of Conditional Variances: A Comment , 1986 .

[45]  G. Schwert,et al.  Heteroskedasticity in Stock Returns , 1989 .

[46]  James D. Hamilton.  A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle , 1989 .

[47]  Lanh Tat Tran,et al.  On the first-order bilinear time series model , 1981, Journal of Applied Probability.

[48]  R. Baillie,et al.  Fractionally integrated generalized autoregressive conditional heteroskedasticity , 1996 .

[49]  Enrique Sentana.  Quadratic Arch Models , 1995 .

[50]  Richard A. Davis,et al.  Maximum likelihood estimation for all-pass time series models , 2006 .

[51]  Sidney I. Resnick,et al.  Prediction of Stationary Max-Stable Processes , 1993 .

[52]  Moving average conditional heteroskedastic processes , 1995 .

[53]  Robert F. Engle,et al.  Stock Volatility and the Crash of '87: Discussion , 1990 .

[54]  W. Dunsmuir,et al.  Observation-driven models for Poisson counts , 2003 .

[55]  H. Tong,et al.  ON ESTIMATING THRESHOLDS IN AUTOREGRESSIVE MODELS , 1986 .

[56]  Jianqing Fan.  Nonlinear Time Series , 2003 .

[57]  M. McAleer,et al.  Stationarity and the existence of moments of a family of GARCH processes , 2002 .

[58]  L. Bauwens,et al.  Multivariate GARCH Models: A Survey , 2003 .

[59]  Howell Tong,et al.  Non-Linear Time Series , 1990 .

[60]  D. Guégan,et al.  The Stationary Seasonal Hyperbolic Asymmetric Power ARCH model , 2007 .

[61]  Alain Latour,et al.  Integer‐Valued GARCH Process , 2006 .

[62]  R. Chou,et al.  ARCH modeling in finance: A review of the theory and empirical evidence , 1992 .

[63]  Thomas Mikosch,et al.  Changes of structure in financial time series and the GARCH model , 2004 .

[64]  Anil K. Bera,et al.  A Class of Nonlinear ARCH Models , 1992 .

[65]  I. Basawa,et al.  Stationarity and moment structure for Box-Cox transformed threshold GARCH(1,1) processes , 2004 .

[66]  C. Granger,et al.  A long memory property of stock market returns and a new model , 1993 .

[67]  C. Granger,et al.  Modelling Nonlinear Economic Relationships , 1995 .

[68]  Richard A. Davis,et al.  Time Series: Theory and Methods , 2013 .

[69]  Daniel B. Nelson.  CONDITIONAL HETEROSKEDASTICITY IN ASSET RETURNS: A NEW APPROACH , 1991 .

[70]  R. Cont.  Empirical properties of asset returns: stylized facts and statistical issues , 2001 .

[71]  M. Nisio,et al.  On polynomial approximation for strictly stationary processes , 1960 .

[72]  Richard A. Davis,et al.  Maximum Likelihood Estimation for an Observation Driven Model for Poisson Counts , 2005 .

[73]  Christian H. Weiß,et al.  Modelling time series of counts with overdispersion , 2009, Stat. Methods Appl..

[74]  Richard E. Quandt,et al.  The Estimation of Structural Shifts by Switching Regressions , 1973 .

[75]  Konstantinos Fokianos,et al.  Some recent progress in count time series , 2011 .

[76]  T. V. Ramanathan,et al.  Integer autoregressive models with structural breaks , 2013 .

[77]  Timo Teräsvirta,et al.  An Introduction to Univariate GARCH Models , 2006 .