Parameter Estimation For ARTFIMA Time Series

Long memory is a typical feature of many financial time series.The ARFIMA model proposed by Granger(1980)and Hosking(1981)is an important tool for the analysis of long memory time series.However,studies have shown that the ARFIMA model is no longer effective in the case of weak long-term correlation of sequences.Therefore,Meerschaert et al.(2014)proposed the ARTFIMA model.It is noted that ARTFIMA time series exhibit semi-long range dependence.Their covariance function resembles long range dependence for short-term lags,but eventually decays exponentially fast.This model can fit the time series with both short-term memory and long-term memory.This thesis conducts a further study on the ARTFIMA model based on the research of Sabzikar et al.(2019).We use the maximum likelihood method to estimate the parameters of the ARTFIMA model and consider the convergence and asymptotic normality of the estimators.In addition,we propose a new parameter estimation method by combining semiparameter method and maximum likelihood method.Then we compare the two methods by numerical simulations.The results show that when the model has significant long-term memory,the two-step method is more accurate,while the maximum likelihood method performs better in other cases.We further consider the ARTFIMA model with exogenous regressors.We estimate the parameters of this new model by the maximum likelihood method and prove the convergence of the estimator.Finally,we conduct empirical analysis on the retail price index data.The results show that ARTFIMA model performs better than ARFIMA model.