Research On Long Memory In Time Series And Empirical Study

Since Hurst exponent was proposed in 1950s,the long memory time series has caused extensive attention and has been widely applied in hydrology,climatology and especially in finance.After Granger and other researchers gave the definition of long memory in terms of modem econometrics in 80s last century,the long memory theory experienced rapid development.However,there are still problems unsolved both in theory and in practice.The aim of this article is threefold.One in theory is to study the capacity of the A-PARCH model in capturing the long memory in time series,and one is to make the comparison among various existing hypothesis tests against spurious long memory series,according to the size and power of the tests.The last is to investigate the stock market efficiency through evaluating the long memory in volatility of stock market indices.Since structure breaks might cause the positive bias in estimation and the FIGARCH or HYGARCH model fail to explain this problem,we propose the structure-changing long memory model to fit the high frequency volatility.The main contents and conclusions of this paper are given as follows:First of all,we derive the theoretical autocorrelation function(ACF)of the A-PARCH model with high order(p?2),and study its statistical properties.And with the help of theoretical autocorrelogram,the capacity of the A-PARCH model in capturing long memory in time series is studied.Then,we analyze the impact of asymmetric parameter ? on theoretical ACF.Furtherly,under the assumption of the persistence fixed,we investigate the impact of the power parameter S on theoretical ACF and its role in capturing long memory in the A-PARCH processes.From numerical illustrations,we find that the A-PARCH models with nonzero asymmetric parameter ?have more capacity in capturing the long memory than those with zero value.Furthermore,the long memory in A-PARCH processes with the same persistence also could be differentFurthermore,we summarize and analyze the available documents focused on hypothesis tests against spurious long memory series both in time domain and in spectral domain.Based on the modified Local Whittle estimator given by Hou and Perron(2014),we propose the modified Kuswanto test and the modified Shao test.And we undertake extensive Monte Carlo simulations to compare their performance with other hypothesis tests,constructed under the null of true long memory versus the alternative of spurious long memory due to level shifts or breaks.Overall,the power of modified Kuswanto test outperforms Kuswanto test proposed by Kuswanto(2011),while the improvement in the power of modified Shao test is not obvious.For the alternatives that series subject to only one stochastic break,the best performances are given by modified Shao test,with Shao test as second best.For the situation where time series are composed of a fractionally integrated component with long memory parameter and some contamination in the form of level shifts,the performance of modified LW test proposed by Kruse(2015)is the best among others.Last but not least,under the existence of structure breaks,we propose the structure-changing FIGARCH and HYGARCH models,that are RS-FIGARCH and RS-HYGARCH,in order to estimate the long memory in volatility of stock market indices.In addition,we apply the GPH estimator,Local Whittle estimator and LWLFC estimator to estimate the long memory in squared returns of the stock indices.With this knowledge,the stock market efficiency is examined,and some insightful results are found that both Shanghai and Shenzhen stock market data refuse the hypothesis of weak-form efficient market.