A note on the non-negativity of continuous-time ARMA and GARCH processes
نویسندگان
چکیده
A general approach for modeling the volatility process in continuous-time is based on the convolution of a kernel with a non-decreasing Lévy process, which is non-negative if the kernel is non-negative. Within the framework of Continuous-time Auto-Regressive Moving-Average (CARMA) processes, we derive a necessary condition for the kernel to be non-negative, and propose a numerical method for checking the non-negativity of a kernel function. These results can be lifted to solving a similar problem with another approach to modeling volatility via the COntinuous-time Generalized AutoRegressive Conditional Heteroscedastic (COGARCH) processes.
منابع مشابه
Monitoring Financial Processes with ARMA-GARCH Model Based on Shewhart Control Chart (Case Study: Tehran Stock Exchange)
Financial surveillance is an interesting area after financial crisis in recent years. In this subject, important financial indices are monitored using control charts. Control chart is a powerful instrument for detecting assignable causes which is considerably developed in industrial and service environments. In this paper, a monitoring procedure based on Shewhart control chart is proposed to mo...
متن کاملL Evy-driven Continuous-time Arma Processes
Gaussian ARMA processes with continuous time parameter, otherwise known as stationary continuous-time Gaussian processes with rational spectral density , have been of interest for many years. In the last twenty years there has been a resurgence of interest in continuous-time processes, partly as a result of the very successful application of stochastic diierential equation models to problems in...
متن کاملConditional distributions of Mandelbrot-Van Ness fractional Lévy processes and continuous-time ARMA-GARCH-type models with long memory
Long memory effects can be found in different kind of data from finance to hydrology. Therefore, models which can reflect these properties have become more popular in recent years especially in the fields of time series analysis, econometrics and financial mathematics. Mandelbrot-Van Ness fractional Lévy processes allow for such stationary long memory effects in their increments and have been u...
متن کاملA Note on the Covariance Structure of a Continuous-time Arma Process
We have derived some matrix equations for speedy computation of the conditional covariance kernel of a discrete-time process obtained from irregularly sampling an underlying continuous-time ARMA process. These results are applicable to both stationary and non-stationary ARMA processes. We have also demonstrated that these matrix results can be useful in shedding new insights on the covariance s...
متن کاملWind speed forecasting based on autoregressive moving average- exponential generalized autoregressive conditional heteroscedasticity-generalized error distribution (ARMA-EGARCH-GED) model
With the increase of wind power as a renewable energy source in many countries, wind speed forecasting has become more and more important to the planning of wind speed plants, the scheduling of dispatchable generation and tariffs in the day-ahead electricity market, and the operation of power systems. However, the uncertainty of wind speed makes troubles in them. For this reason, a wind speed f...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Statistics and Computing
دوره 19 شماره
صفحات -
تاریخ انتشار 2009