Memory Time Series Research Articles

EXACT LOCAL WHITTLE ESTIMATION IN LONG MEMORY TIME SERIES WITH MULTIPLE POLES

A generalization of the Exact Local Whittle estimator in Shimotsu and Phillips (2005,Annals of Statistics33, 1890–1933) is proposed for jointly estimating all the memory parameters in general long memory time series that possibly display standard, seasonal, and/or other cyclical strong persistence. Consistency and asymptotic normality are proven for stationary, nonstationary, and noninvertible series, permitting straightforward standard inference of interesting hypotheses such as the existence of unit roots and equality of memory parameters at some or all seasonal frequencies, which can be used as a prior test for the application of seasonal differencing filters. The effects of unknown deterministic terms are also discussed. Finally, the finite sample performance is analyzed in an extensive Monte Carlo exercise and an application to an U.S. Industrial Production index.

Traffic flow combination forecasting method based on improved LSTM and ARIMA

Traffic flow forecasting is hot spot research of intelligent traffic system construction. The existing traffic flow prediction methods have problems such as poor stability, high data requirements, or poor adaptability. In this paper, we define the traffic data time singularity ratio in the dropout module and propose a combination prediction method based on the improved long short-term memory neural network and time series autoregressive integrated moving average model (SDLSTM-ARIMA), which is derived from the Recurrent Neural Networks (RNN) model. It compares the traffic data time singularity with the probability value in the dropout module and combines them at unequal time intervals to achieve an accurate prediction of traffic flow data. Then, we design an adaptive traffic flow embedded system that can adapt to Java, Python and other languages and other interfaces. The experimental results demonstrate that the method based on the SDLSTM - ARIMA model has higher accuracy than the similar method using only autoregressive integrated moving average or autoregressive. Our embedded traffic prediction system integrating computer vision, machine learning and cloud has the advantages such as high accuracy, high reliability and low cost. Therefore, it has a wide application prospect.

Intelligent Hybrid Model to Enhance Time Series Models for Predicting Network Traffic

Network traffic analysis and predictions have become vital for monitoring networks. Network prediction is the process of capturing network traffic and examining it deeply to decide what is the occurrence in the network. The accuracy of analysis and estimation of network traffic are increasingly becoming significant in achieving guaranteed Quality of Service (QoS) in the network. The main aim of the presented research is to propose a new methodology to improve network traffic prediction by using sequence mining. The significance of this important topic lies in the urge to contribute to solving the research problem in network traffic prediction intelligently. We propose an integrated model that combines clustering with existing series models to enhance prediction the network traffic. Clustering granules are obtained using fuzzy c-means to analyze the network data for improving the existing time series. The novelty of the proposed research has used the clustering approach to handle the ambiguity from the entire network data for enhancing the existing time series models. Furthermore, we have suggested using the weighted exponential smoothing model as preprocessing stages for increasing the reliability of the proposed model. In this research paper, machine intelligence proposed to predict network traffic. The machine intelligence is working as pre-processing for enhancing the existing time series models. The machine intelligence combines non-crisp Fuzzy-C-Means (FCM) clustering and the weight exponential method for improving deep learning Long Short-Time Memory(LSTM)and Adaptive Neuro-Fuzzy Inference System (ANFIS)time series models. The ANFIS and LSMT time series models are applied to predict network traffic. Two real network traffic traces were conducted to test the proposed time series models. The empirical results of proposed to enhanced LSTM 97.95% and enhanced ANFIS model is R = 96.78% for cellular traffic data, with respect to the correlation indicator. It is observed that the proposed model outperforms alternative time series models. A comparative prediction results between the proposed model and existing time series models are presented. The comparisons indicate that the presented model outperforms the opponent models; the proposed method optimises the deep learning LSTM and ANFIS time series models. The proposed methodology offers more effective approach to the prediction of network traffic.

Traffic flow combination forecasting method based on improved LSTM and ARIMA

Traffic flow forecasting is hot spot research of intelligent traffic system construction. The existing traffic flow prediction methods have problems such as poor stability, high data requirements, or poor adaptability. In this paper, we define the traffic data time singularity ratio in the dropout module and propose a combination prediction method based on the improved long short-term memory neural network and time series autoregressive integrated moving average model (SDLSTM-ARIMA), which is derived from the recurrent neural networks (RNN) model. It compares the traffic data time singularity with the probability value in the dropout module and combines them at unequal time intervals to achieve an accurate prediction of traffic flow data. Then, we design an adaptive traffic flow embedded system that can adapt to Java, Python and other languages and other interfaces. The experimental results demonstrate that the method based on the SDLSTM-ARIMA model has higher accuracy than similar methods using only autoregressive integrated moving average. Our embedded traffic prediction system integrating computer vision, machine learning and cloud has the advantages such as high accuracy, high reliability and low cost. Therefore, it has a wide application prospects.

Spatial long memory

We discuss developments and future prospects for statistical modeling and inference for spatial data that have long memory. While a number of contributons have been made, the literature is relatively small and scattered, compared to the literatures on long memory time series on the one hand, and spatial data with short memory on the other. Thus, over several topics, our discussions frequently begin by surveying relevant work in these areas that might be extended in a long memory spatial setting.

Saddlepoint approximations for short and long memory time series: A frequency domain approach

Saddlepoint techniques provide numerically accurate, small sample approximations to the distribution of estimators and test statistics. Except for a few simple models, these approximations are not available in the framework of stationary time series. We contribute to fill this gap. Under short or long range serial dependence, for Gaussian and non Gaussian processes, we show how to derive and implement saddlepoint approximations for two relevant classes of frequency domain statistics: ratio statistics and Whittle’s estimator. We compare our new approximations to the ones obtained by the standard asymptotic theory and by two widely-applied bootstrap methods. The numerical exercises for Whittle’s estimator show that our approximations yield accuracy’s improvements, while preserving analytical tractability. A real data example concludes the paper.

A New Ratio Statistic to Test Mean Change Point in Long Memory Time Series

In this paper, we propose a new ratio statistic to test mean change point in long memory time series. We derive the test statistic converges to a non-degenerate distribution under the null hypothesis and that it diverges to infinity under the alternative of a change-point with constant height. Furthermore, we estimate the long memory parameters and approximate the critical values of the statistic by the Sieve Bootstrap method. We show the size and power properties of our test through numerical simulations and the performance is inspiring. Finally, we illustrate the effectiveness of this method through a set of actual data.

Empirical Likelihood for a Long Range Dependent Process Subordinated to a Gaussian Process

This article develops empirical likelihood methodology for a class of long range dependent processes driven by a stationary Gaussian process. We consider population parameters that are defined by estimating equations in the time domain. It is shown that the standard block empirical likelihood (BEL) method, with a suitable scaling, has a non‐standard limit distribution based on a multiple Wiener–Itô integral. Unlike the short memory time series case, the scaling constant involves unknown population quantities that may be difficult to estimate. Alternative versions of the empirical likelihood method, involving the expansive BEL (EBEL) methods are considered. It is shown that the EBEL renditions do not require an explicit scaling and, therefore, remove this undesirable feature of the standard BEL. However, the limit law involves the long memory parameter, which may be estimated from the data. Results from a moderately large simulation study on finite sample properties of tests and confidence intervals based on different empirical likelihood methods are also reported.

A simulation smoother for long memory time series with correlated and heteroskedastic additive noise

The purpose of this paper is to extend the work of So (1999) by accommodating heteroskedasticity in long memory processes and correlation in disturbances. We propose an alternative representation of long memory processes from which we develop filtering equations, prediction densities and a simulation smoother for latent state variables as in the classical Kalman filter. We illustrate the simulation smoother introduced in this paper by estimating a class of long memory models with heteroskedastic correlated additive noises.

Modelling and forecasting long memory time series with exponential and switching GARCH models

Modelling and forecasting long memory time series with exponential and switching GARCH models

Modelling and forecasting long memory time series with Exponential and Switching GARCH models

There is some evidence that structural change or stochastic regime switching and long memory are intimately related concepts. However, long memory and regime switching in a stochastic process are properties that could be easily confused in a financial study. Using a modelling approach, the aim is to distinguish regime switching behaviour from long memory for the financial time series. In an empirical study the forecasting performance of symmetric, asymmetric, long memory and Markov switching GARCH model are compared using Tehran stock market daily returns. The results indicate that in out of sample performance, long memory exponential GARCH (FIEGARCH) model outperforms the competing models. To ensure the validity of the results, the value at risk (VaR) forecasts are obtained for each model and a loss function is calculated. A simple rule for distinguishing between long memory and structural break in financial and economic time series is suggested.

似然比扫描法在长记忆时间序列均值多变点中的应用

似然比扫描法在长记忆时间序列均值多变点中的应用

Editorial, September 2018

On behalf of both the editorial board and the readership of the Journal of Time Series Analysis, I would like to take this opportunity to thank Professor Andrew Harvey for his many years of dedicated service to our journal. Andrew stepped down as a co-editor with effect from 31 May 2018. I am, however, delighted to announce that Andrew has agreed to remain on the editorial board as an advisory editor, as from 1 June 2018. Andrew was first appointed to the editorial board of the Journal of Time Series Analysis in 1989. I have greatly benefitted from his support, help and advice since I took over as editor of the journal. I would like to personally thank Andrew for all he has done for me and for our journal. Shiqing Ling is Professor of at the Hong Kong University of Science and Technology. His research involves change-point problems, empirical processes, financial econometrics, large sample theory, long memory time series, non-stationary time series and nonlinear time series. He is a leading expert in the field of time series analysis and has made a number of fundamental contributions to the area, including asymptotic theory of unit-root GARCH process, inference of GARCH-type models and threshold time series model, and proposed the self-weight estimation method for heavy-tailed time series models.

Testing for the mean shifts for long memory time series in presence of breaks in variance

This paper considers the detection problem of mean shifts in presence of variance changes for long memory time series. In performing the test, we employ the Ratio test introduced by Horváth L. et al. (2008). Given for the case of breaks in variance, the asymptotic properties of the tests are established. It is shown that the test statistics are not robust due to neglected of variance changes. And the numerical simulation results are consistent with our theoretical analysis.

On a class of estimation and test for long memory

This paper proposes a new analysis method of the estimation and test for long memory time series. We first introduce the definitions of the time scale series, strong variance scale exponent and weak variance scale exponent, and establish the mathematical equations for the variance scale exponents, with which the time series of the white noise, short memory and long memory can be accurately identified. Two statistics for the hypothesis tests of white noise, short memory and long memory time series are constructed, and the Monte Carlo performance for MSE of the weak variance scale exponent estimator and the empirical size and power of SLmemory statistic is subsequently demonstrated, giving practical recommendations of finite-sample. Finally, brief empirical examples are provided based on Sino–US stock index logarithmic return rate data.

长记忆时间序列均值多变点滑动比检验及应用

长记忆时间序列均值多变点滑动比检验及应用

Adjusted blockwise empirical likelihood for long memory time series models

In this paper, we introduce an adjusted blockwise empirical likelihood (ABEL) method for long memory time series models. By dividing time series into blocks and by adding an appropriate adjustment term, we construct the ABEL ratio and the confidence interval for the mean of the process. Under mild conditions, we show that Wilks’ theorem still holds for the ABEL ratio by choosing a specific block correction factor. The Monte Carlo simulation studies are reported to assess the finite sample performance of the proposed ABEL method.

LLN for Quadratic Forms of Long Memory Time Series and Its Applications in Random Matrix Theory

We show that a weak concentration property for quadratic forms of isotropic random vectors ${\bf x}$ is necessary and sufficient for the validity of the Marchenko-Pastur theorem for sample covariance matrices of random vectors having the form $C{\bf x}$, where $C$ is any rectangular matrix with orthonormal rows. We also obtain some general conditions guaranteeing the weak concentration property.

Recurrent Neural Network For Forecasting Time Series With Long Memory Pattern

Recurrent Neural Network as one of the hybrid models are often used to predict and estimate the issues related to electricity, can be used to describe the cause of the swelling of electrical load which experienced by PLN. In this research will be developed RNN forecasting procedures at the time series with long memory patterns. Considering the application is the national electrical load which of course has a different trend with the condition of the electrical load in any country. This research produces the algorithm of time series forecasting which has long memory pattern using E-RNN after this referred to the algorithm of integrated fractional recurrent neural networks (FIRNN).The prediction results of long memory time series using models Fractional Integrated Recurrent Neural Network (FIRNN) showed that the model with the selection of data difference in the range of [-1,1] and the model of Fractional Integrated Recurrent Neural Network (FIRNN) (24,6,1) provides the smallest MSE value, which is 0.00149684.

On the memory of products of long range dependent time series

This paper derives the memory of the product series xtyt, where xt and yt are stationary long memory time series of orders dx and dy, respectively. Special attention is paid to the case of squared series and products of series driven by a common stochastic factor. It is found that the memory of products of series with non-zero means is determined by the maximal memory of the factor series, whereas the memory is reduced if the series are mean zero.