University of Isfahan Mathematics and Society 2345-6493 2 4 2018 02 20 An estimation of minimum second powers in Arch model parameters in the presence of missing data An estimation of minimum second powers in Arch model parameters in the presence of missing data 1 10 21618 10.22108/msci.2018.21618 FA Mohammadreza Salehirad Allameh Tabataba'i University Reza Habibi Journal Article 2014 10 01 Many financial and economic time series exhibit high volatility in certain periods and have relatively less clustered volatility in others, indicating cluster-wise volatility. Assuming constant variance in such cases is not reasonable. One of the modeling tools for these variations is the use of Autoregressive Conditional Heteroscedastic (ARCH) and Generalized Autoregressive Conditional Heteroscedastic (GARCH) models. The ARCH model has various applications in econometrics and finance, including the study of volatility changes related to stock indices, gold prices, and exchange rates. One of the common methods for estimating ARCH model parameters is the Quasi-Maximum Likelihood Estimator (QMLE) method. As this estimator does not have a closed form, the estimator of the Minimum Second Powers is used for estimating ARCH model parameters, which is more efficient compared to other estimators. Missing data in time series are common, and therefore, we obtain the two-stage Minimum Second Powers estimator in the presence of missing data. This estimator has the same asymptotic efficiency as the Quasi-Maximum Likelihood Estimator. We prove its strong consistency and asymptotic normality and confirm these results through simulations. The results are applied to the data of the Tehran Stock Exchange overall index. Many financial and economic time series exhibit high volatility in certain periods and have relatively less clustered volatility in others, indicating cluster-wise volatility. Assuming constant variance in such cases is not reasonable. One of the modeling tools for these variations is the use of Autoregressive Conditional Heteroscedastic (ARCH) and Generalized Autoregressive Conditional Heteroscedastic (GARCH) models. The ARCH model has various applications in econometrics and finance, including the study of volatility changes related to stock indices, gold prices, and exchange rates. One of the common methods for estimating ARCH model parameters is the Quasi-Maximum Likelihood Estimator (QMLE) method. As this estimator does not have a closed form, the estimator of the Minimum Second Powers is used for estimating ARCH model parameters, which is more efficient compared to other estimators. Missing data in time series are common, and therefore, we obtain the two-stage Minimum Second Powers estimator in the presence of missing data. This estimator has the same asymptotic efficiency as the Quasi-Maximum Likelihood Estimator. We prove its strong consistency and asymptotic normality and confirm these results through simulations. The results are applied to the data of the Tehran Stock Exchange overall index. https://math-sci.ui.ac.ir/article_21618_7af2c931142898b7056e1dda5b33cf8e.pdf