Summary
The dependence structure of a family of self exciting threshold autoregressive moving average (SETARMA) models, is investigated. An alternative representation for this class of models is proposed and the exact autocorrelation function is derived in the case of two regimes. Some practical implications of the theoretical results are analysed and discussed via several examples of SETARMA structures of fixed orders
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References
Amendola A., Niglio M., Vitale C., (2006), The moments of SETARMA models, Statistics & Probability Letters, 76, 625–633.
Brännäs K., De Gooijer J.G., (2004), Asymmetries in conditional mean and variance: Modelling stock returns by asMA-asQGARCH, Journal of Forecasting, 23, 155–171.
Box G.E.P., Jenkins G.M., (1976), Time series analysis, forecasting and control, Holden-Day, San Francisco.
Brock W.A., De Lima P.J.F., (1996), Nonlinear time series complexity theory and finance, in Handbook of Statistics, 14, Elsevier.
Brockwell P.J., Liu J., Tweedie R., (1992), On the extence of stationary threshold autoregressive moving-average processes, Journal of Time Series Analysis, 13, 95–107.
Cont R., (2001), Empirical properties of asset returns: stylized facts and statistical issue, Quantitative Finance, 1, 223–236.
De Gooijer J., (1998), On threshold moving-average models, Journal of Time Series Analysis, 19, 1–18.
Engle R.F., (1982) Autoregrassive conditional heteroskedasticity with estimates of the variance for U.K. inflation, Econometrica, 50, 987–1008.
Fan J, Yao Q., (2003), Nonlinear time series: parametric and nonparametric methods, Springer, New York.
Franses P.H., Van Dijk D., (2000), Non-linear time series models in empirical finance, Cambridge University Press, Cambridge.
Granger C.W.J., Teräsvirta T., (1993), Modelling nonlinear relationships, Oxford University Press, Oxford.
Ling S., Tong H., (2005), Testing for a linear MA model against threshold MA models, The Annals of Statistics, 33, 2529–2552.
Liu J., Li W.K., Li C.W., (1997), On a threshold autoregression with conditional heteroskedasticity, Journal of Statistical Planning & Inference, 62, 279–300.
Liu J., Susko E., (1992), On strict stationary and ergodicity of a nonlinear ARMA model, Journal of Applied Probabilyty, 29, 363–373.
Nielsen H.A., Madsen H., (2001), A generalization of some classical time series tools, Computational Statistics & Data Analysis, 37, 13–31.
Pagan A., (1996), The econometrics of financial market, Journal of Empirical Finance, 3, 15–102.
Priestley M. B., (1988), Non-Linear and Non-Stationary Time Series Analysis, Academic Press, San Diego.
Tjøstheim D., (1994), Non-linear time series: a selective review, Scandinavian Journal of Statistics, 21, 97–130.
Tong H., (1983), Threshold models in nonlinear time series analysis, Springer-Verlag, New York.
Tong H., (1990), Non-linear time series: A dynamical system approach, Clarendon Press, Oxford.
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Amendola, A., Niglio, M., Vitale, C. (2007). The Autocorrelation Functions in SETARMA Models. In: Kontoghiorghes, E.J., Gatu, C. (eds) Optimisation, Econometric and Financial Analysis. Advances in Computational Management Science, vol 9. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36626-1_7
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DOI: https://doi.org/10.1007/3-540-36626-1_7
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