4. Course Outline: (i) Review of Linear ARMA/ARIMA Time Series Models and their Properties. (ii) An Introduction to Spectral Analysis of Time Series. (iii) Fractional Differencing and Long Memory Time Series Modelling. (iv) Generalized Fractional Processes. Gegenbaur Processes. (v) Topics from Financial Time Series/Econometrics: ARCH and GARCH Models. (vi ) Time Series Modelling of Durations: A...

This paper selects the daily return data of CSI 300 index from January 2, 2014 to September 30, 2020 study characteristics volatility. An ARMA(3,3) model was fitted log returns using R software, and ARCH effect found exist. The were then with an ARMA(3,3)-GARCH(1,1) model, fitting tested, finally short-term predicted. results empirical analysis show that series has such as non-normal distributi...

In this paper, the S&P 500 stock index is studied for its time varying volatility and stylized facts. The ARMA mean equation with asymmetric power ARCH errors is used to model the series correlations and the conditional heteroscadesticity in the asset returns. The conditional distributions of the standardized residuals are assumed to be the normal distribution, the t distribution or the skew-t ...

In the context of carbon neutrality and air pollution prevention, it is great research significance to achieve high-accuracy prediction quality index. this paper, Beijing used as study area; data from January 2014 December 2019 are training set, 2020 2021 test set. The CEEMDAN-ARMA-LSTM model constructed in paper for analysis. CEEMDAN decompose improve information utilization. smooth non-white ...

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...

In recent years, fractionally-differenced processes have received a great deal of attention due to their flexibility in financial applications with long-memory. This paper revisits the class of generalized fractionally-differenced processes generated by Gegenbauer polynomials and the ARMA structure (GARMA) with both the long-memory and time-dependent innovation variance. We establish the existe...