Year 2011,
Volume: 3 Issue: 1, 251 - 261, 01.06.2011
Abstract
This study aims to construct continuous-time autoregressive (CAR) model and continuous-time GARCH (COGARCH) model from discrete time data of foreign exchange rate of United States Dollar (USD) versus Turkish Lira (TRY). These processes are solutions to stochastic differential equation Lévy-driven processes. We have shown that CAR(1) and COGARCH(1,1) processes are proper models to represent foreign exchange rate of USD and TRY for different periods of time February 2002- June 2010
Keywords
References
- O. A. Dickey, and W. A. Fuller, “Distribution for the estimates for auto- regressive time series with a unit root”, J. Amer. Statist. Assoc., 74:427--431, 1979
- Brockwell P.J., Continuous-Time ARMA Processes, [in] Rao C.R. and
- Shanbhag D.N. (editors), Stochastic Processes: Theory and Methods,“Handbook of Statistics” 2000, 19, p.249-276.
- R. F. Engle, “Autoregressive conditional heteroscedasticity with estimates of the variance of united kingdom inflation”, Econometrica, 50:987--1007, 1982
- C. Klüppelberg, A. Lindner, and R. Maller, “A continuous time GARCH
- process driven by a Levy process: stationarity and second order behavior”, J. Appl. Prob.,41(3):601--622, 2004
- E.P.G Box, M.G Jenkins., C.G Reinsel. Time Series Analysis- Forecasting and Control, Prentice-Hall,1994
- P.J. Brockwell and R.A. Davis. Itroduction to Time Series and Forecasting, Springer,2001, p.p. 22-60
- S. J. Taylor, “Financial returns modeled by the product of two stochastic processes: a study of daily sugar prices 1961-79”. In O. D. Anderson, editor, Time Series Analysis:Theory and Practice, volume 1, pages 203--226. North- Holland, Amsterdam, 1982
- D. B. Nelson, “ARCH models as diffusion approximations”, J. Econometrics, 45:7-38,1990
- J. C. Duan, , “Augmented GARCH(p; q) process and its diffusion limit”, J. Econometrics,79-97, 1997
- Benth E.B., Benth J.B., Koekebakker S., Stochastic Modelling of Electricity and Related Markets. World Scientific, Singapore 2008
- Brockwell P.J., Lévy-Driven CARMA Processes, “Annals of the Institute of 1, 53 Statistical Mathematics” 200, p. 113-124
Year 2011,
Volume: 3 Issue: 1, 251 - 261, 01.06.2011
Abstract
References
- O. A. Dickey, and W. A. Fuller, “Distribution for the estimates for auto- regressive time series with a unit root”, J. Amer. Statist. Assoc., 74:427--431, 1979
- Brockwell P.J., Continuous-Time ARMA Processes, [in] Rao C.R. and
- Shanbhag D.N. (editors), Stochastic Processes: Theory and Methods,“Handbook of Statistics” 2000, 19, p.249-276.
- R. F. Engle, “Autoregressive conditional heteroscedasticity with estimates of the variance of united kingdom inflation”, Econometrica, 50:987--1007, 1982
- C. Klüppelberg, A. Lindner, and R. Maller, “A continuous time GARCH
- process driven by a Levy process: stationarity and second order behavior”, J. Appl. Prob.,41(3):601--622, 2004
- E.P.G Box, M.G Jenkins., C.G Reinsel. Time Series Analysis- Forecasting and Control, Prentice-Hall,1994
- P.J. Brockwell and R.A. Davis. Itroduction to Time Series and Forecasting, Springer,2001, p.p. 22-60
- S. J. Taylor, “Financial returns modeled by the product of two stochastic processes: a study of daily sugar prices 1961-79”. In O. D. Anderson, editor, Time Series Analysis:Theory and Practice, volume 1, pages 203--226. North- Holland, Amsterdam, 1982
- D. B. Nelson, “ARCH models as diffusion approximations”, J. Econometrics, 45:7-38,1990
- J. C. Duan, , “Augmented GARCH(p; q) process and its diffusion limit”, J. Econometrics,79-97, 1997
- Benth E.B., Benth J.B., Koekebakker S., Stochastic Modelling of Electricity and Related Markets. World Scientific, Singapore 2008
- Brockwell P.J., Lévy-Driven CARMA Processes, “Annals of the Institute of 1, 53 Statistical Mathematics” 200, p. 113-124
There are 13 citations in total.
Details
| Other ID | JA65NY99UG |
|---|---|
| Authors | |
| Publication Date | June 1, 2011 |
| IZ | https://izlik.org/JA86LM52JH |
| Published in Issue | Year 2011 Volume: 3 Issue: 1 |