Long-Memory and Spurious Breaks in Ecological Experiments

The impact of long-memory on the Before-After-Control-Impact (BACI) design and a commonly used nonparametric alternative, Randomized Intervention Analysis (RIA), is examined. It is shown the corrections used based on short-memory processes are not adequate. Long-memory series are also known to exhibit spurious structural breaks that can be mistakenly attributed to an intervention. Two examples from the literature are used as illustrations.

Exploring Long-Memory Process in the Prediction of Interval-Valued Financial Time Series and Its Application

Long-memory process has been widely studied in classical financial time series analysis,which has merely been reported in the field of interval-valued financial time series.The aim of this paper is to explore long-memory process in the prediction of interval-valued time series(IvTS).To model the long-memory process,two novel interval-valued time series prediction models named as interval-valued vector autoregressive fractionally integrated moving average(IV-VARFIMA)and ARFIMAX-FIGARCH were established.In the developed long-memory pattern,both of the short term and long-term influences contained in IvTS can be included.As an application of the proposed models,interval-valued form of WTI crude oil futures price series is predicted.Compared to current IvTS prediction models,IV-VARFIMA and ARFIMAX-FIGARCH can provide better in-sample and out-of-sample forecasts.

Monitoring Mean and Variance Change-Points in Long-Memory Time Series

This paper proposes two ratio-type statistics to sequentially detect mean and variance change-points in the long-memory time series.The limiting distributions of monitoring statistics under the no change-point null hypothesis,alternative hypothesis as well as change-point misspecified hypothesis are proved.In particular,a sieve bootstrap approximation method is proposed to determine the critical values.Simulations indicate that the new monitoring procedures have better finite sample performance than the available off-line tests when the change-point nears to the beginning time of monitoring,and can discriminate between mean and variance change-point.Finally,the authors illustrate their procedures via two real data sets:A set of annual volume of discharge data of the Nile river,and a set of monthly temperature data of northern hemisphere.The authors find a new variance change-point in the latter data.

Chaos game representation(CGR)-walk model for DNA sequences

Chaos game representation （CGR） is an iterative mapping technique that processes sequences of units, such as nucleotides in a DNA sequence or amino acids in a protein, in order to determine the coordinates of their positions in a continuous space. This distribution of positions has two features： one is unique, and the other is source sequence that can be recovered from the coordinates so that the distance between positions may serve as a measure of similarity between the corresponding sequences. A CGR-walk model is proposed based on CGR coordinates for the DNA sequences. The CGR coordinates are converted into a time series, and a long-memory ARFIMA （p, d, q） model, where ARFIMA stands for autoregressive fractionally integrated moving average, is introduced into the DNA sequence analysis. This model is applied to simulating real CGR-walk sequence data of ten genomic sequences. Remarkably long-range correlations are uncovered in the data, and the results from these models are reasonably fitted with those from the ARFIMA （p, d, q） model.

Chaos game representation walk model for the protein sequences

A new chaos game representation of protein sequences based on the detailed hydrophobic-hydrophilic （HP） model has been proposed by Yu et al （Physica A 337（2004） 171）. A CGR-walk model is proposed based on the new CGR coordinates for the protein sequences from complete genomes in the present paper. The new CCR coordinates based on the detailed HP model are converted into a time series, and a long-memory ARFIMA（p, d, q） model is introduced into the protein sequence analysis. This model is applied to simulating real CCR-walk sequence data of twelve protein sequences. Remarkably long-range correlations are uncovered in the data and the results obtained from these models are reasonably consistent with those available from the ARFIMA（p, d, q） model.

Autoregressive Fractionally Integrated Moving Average-Generalized Autoregressive Conditional Heteroskedasticity Model with Level Shift Intervention

In this paper, we introduce the class of autoregressive fractionally integrated moving average-generalized autoregressive conditional heteroskedasticity?(ARFIMA-GARCH) models with level shift type intervention that are capable of capturing three key features of time series: long range dependence, volatility?and level shift. The main concern is on detection of mean and volatility level shift in a fractionally integrated time series with volatility. We will denote such a time series as level shift autoregressive fractionally integrated moving average (LS-ARFIMA) and level shift generalized autoregressive conditional heteroskedasticity (LS-GARCH). Test statistics that are useful to examine if mean and volatility level shifts are present in an autoregressive fractionally integrated moving average-generalized autoregressive conditional heteroskedasticity (ARFIMA-GARCH) model are derived. Quasi maximum likelihood estimation of the model is also considered.

Modelling the dynamics of stock market in the gulf cooperation council countries:evidence on persistence to shocks

This study examines the statistical properties required to model the dynamics of both the returns and volatility series of the daily stock market returns in six Gulf Cooperation Council countries,namely Bahrain,Oman,Kuwait,Qatar,Saudi Arabia,and the United Arab Emirates,under different financial and economic circumstances.The empiri-cal investigation is conducted using daily data from June 1,2005 to July 1,2019.The analysis is conducted using a set of double long-memory specifications with some significant features such as long-range dependencies,asymmetries in conditional variances,non-linearity,and multiple seasonality or time-varying correlations.Our study indicates that the joint dual long-memory process can adequately estimate long-memory dynamics in returns and volatility.The in-sample diagnostic tests as well as out-of-sample forecasting results demonstrate the prevalence of the Autoregressive Fractionally Integrated Moving Average and Hyperbolic Asymmetric Power Autoregressive Conditional Heteroskedasticity modeling process over other competing models in fitting the first and the second conditional moments of the market returns.Moreover,the empirical results show that the proposed model offers an interesting framework to describe the long-range dependence in returns and seasonal persistence to shocks in conditional volatility and strongly support the estimation of dynamic returns that allow for time-varying correlations.A noteworthy finding is that the long-memory dependencies in the conditional variance processes of stock market returns appear important,asymmetric,and differ in their volatility responses to unexpected shocks.Our evidence suggests that these markets are not completely efficient in processing regional news,thus providing a sound alternative for regional portfolio diversification.

Modeling Seasonal Fractionally Integrated Autoregressive Moving Average-Generalized Autoregressive Conditional Heteroscedasticity Model with Seasonal Level Shift Intervention

This paper introduces the class of seasonal fractionally integrated autoregressive moving average-generalized conditional heteroskedastisticty (SARFIMA- GARCH) models, with level shift type intervention that are capable of capturing simultaneously four key features of time series: seasonality, long range dependence, volatility and level shift. The main focus is on modeling seasonal level shift (SLS) in fractionally integrated and volatile processes. A natural extension of the seasonal level shift detection test of the mean for a realization of time series satisfying SLS-SARFIMA and SLS-GARCH models was derived. Test statistics that are useful to examine if seasonal level shift in an SARFIMA-GARCH model is statistically plausible were established. Estimation of SLS-SARFIMA and SLS-GARCH parameters was also considered.