Unit-roots test for time-series data with a linear time trend

1991 ◽  
Vol 47 (2-3) ◽  
pp. 285-303 ◽  
Author(s):  
Saïd E. Saïd
Keyword(s):  
Time Series ◽  
Time Trend ◽  
Time Series Data ◽  
Linear Time ◽  
Unit Roots ◽  
Series Data ◽  
Linear Time Trend

scholarly journals Time-series analysis of the risk factors for haemorrhagic fever with renal syndrome: comparison of statistical models

2006 ◽  
Vol 135 (2) ◽  
pp. 245-252 ◽  
Author(s):  
W. HU ◽  
K. MENGERSEN ◽  
P. BI ◽  
S. TONG
Keyword(s):  
Time Series ◽  
Water Level ◽  
Crop Production ◽  
Time Series Data ◽  
Linear Time ◽  
Additive Model ◽  
Series Data ◽  
Haemorrhagic Fever ◽  
Independent Variables ◽  
China Model

Three conventional regression models were compared using the time-series data of the occurrence of haemorrhagic fever with renal syndrome (HFRS) and several key climatic and occupational variables collected in low-lying land, Anhui Province, China. Model I was a linear time series with normally distributed residuals; model II was a generalized linear model with Poisson-distributed residuals and a log link; and model III was a generalized additive model with the same distributional features as model II. Model I was fitted using least squares whereas models II and III were fitted using maximum likelihood. The results show that the correlations between the HFRS incidence and the independent variables measured (i.e. difference in water level, autumn crop production and density of Apodemus agrarius) ranged from −0·40 to 0·89. The HFRS incidence was positively associated with density of A. agrarius and crop production, but was inversely associated with difference in water level. The residual analyses and the examination of the accuracy of the models indicate that model III may be the most suitable in the assessment of the relationship between the incidence of HFRS and the independent variables.

Short-Term Time Series Prediction for a Logistics Outsourcing Company

2013 ◽  
pp. 150-160
Author(s):  
Angeliki Papana
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Linear Time ◽  
Time Series Prediction ◽  
Service Level ◽  
Optimal Choice ◽  
Series Data ◽  
Short Term ◽  
Univariate Time Series ◽  
Nonlinear Components

In this chapter, tools from univariate time series analysis and forecasting are presented and applied. Time series components, such as trend and seasonality are introduced and discussed, while time series methods are analyzed based on the type of the time series components. In the literature, linear methods are the most commonly used. However, real time series data often include nonlinear components, so linear time series forecasting may not be the optimal choice. Therefore, also a basic nonlinear forecasting method is presented. The necessity of these methods to logistics service providers and 3PL companies is presented by case studies that present how the operational and management costs can be cut down in order to ensure a service level. Short term forecasts are useful in all the units of activation of 3PL companies, i.e. supplies, production, distribution, storage, transportation, and service of customers.

scholarly journals Linear time-varying models can reveal non-linear interactions of biomolecular regulatory networks using multiple time-series data

2008 ◽  
Vol 24 (10) ◽  
pp. 1286-1292 ◽  
Author(s):  
Jongrae Kim ◽  
Declan G. Bates ◽  
Ian Postlethwaite ◽  
Pat Heslop-Harrison ◽  
Kwang-Hyun Cho
Keyword(s):  
Time Series ◽  
Regulatory Networks ◽  
Time Series Data ◽  
Linear Time ◽  
Series Data ◽  
Multiple Time ◽  
Time Varying ◽  
Multiple Time Series ◽  
Linear Interactions ◽  
Time Varying Models

scholarly journals Linear Time Complexity Time Series Clustering with Symbolic Pattern Forest

2019 ◽  
Author(s):  
Xiaosheng Li ◽  
Jessica Lin ◽  
Liang Zhao
Keyword(s):  
Time Series ◽  
Data Storage ◽  
Time Complexity ◽  
Clustering Algorithm ◽  
Time Series Data ◽  
Linear Time ◽  
Series Data ◽  
Data Generation ◽  
Time Series Clustering ◽  
Group Structures

With increasing powering of data storage and advances in data generation and collection technologies, large volumes of time series data become available and the content is changing rapidly. This requires the data mining methods to have low time complexity to handle the huge and fast-changing data. This paper presents a novel time series clustering algorithm that has linear time complexity. The proposed algorithm partitions the data by checking some randomly selected symbolic patterns in the time series. Theoretical analysis is provided to show that group structures in the data can be revealed from this process. We evaluate the proposed algorithm extensively on all 85 datasets from the well-known UCR time series archive, and compare with the state-of-the-art approaches with statistical analysis. The results show that the proposed method is faster, and achieves better accuracy compared with other rival methods.

scholarly journals Let's Do the Time Warp Again: Non-linear time series matching as a tool for sequentially structured data in ecology

2021 ◽  
Author(s):  
Jens C Hegg ◽  
Brian P Kennedy
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Linear Time ◽  
Temporal Structure ◽  
Structured Data ◽  
Series Data ◽  
Small Scale ◽  
Temporal Data ◽  
Ecological Data ◽  
Aggregation Techniques

Ecological patterns are often fundamentally chronological. However, generalization of data is necessarily accompanied by a loss of detail or resolution. Temporal data in particular contains information not only in data values but in the temporal structure, which is lost when these values are aggregated to provide point estimates. Dynamic Time Warping (DTW) is a time series comparison method that is capable of efficiently comparing series despite temporal offsets that confound other methods. The DTW method is both efficient and remarkably flexible, capable of efficiently matching not only time series but any sequentially structured dataset, which has made it a popular technique in machine learning, artificial intelligence, and big data analytical tasks. DTW is rarely used in ecology despite the ubiquity of temporally structured data. As technological advances have increased the richness of small-scale ecological data, DTW may be an attractive analysis technique because it is able to utilize the additional information contained in the temporal structure of many ecological datasets. In this study we use an example dataset of high-resolution fish movement records obtained from otolith microchemistry to compare traditional analysis techniques with DTW clustering. Our results suggest that DTW is capable of detecting subtle behavioral patterns within otolith datasets which traditional data aggregation techniques cannot. These results provide evidence that the DTW method may be useful across many of the temporal data types commonly collected in ecology, as well other sequentially ordered "pseudo time series" data such as classification of species by shape.

scholarly journals Study the Trend Pattern in COVID-19 using Spline-Based Time Series Model: A Bayesian Paradigm

2020 ◽  
Author(s):  
Varun Agiwal ◽  
Jitendra Kumar ◽  
Yau Chun Yip
Keyword(s):  
Time Series ◽  
Time Trend ◽  
Spline Function ◽  
Linear Time ◽  
Linear Trend ◽  
Model Parameters ◽  
Linear Pattern ◽  
Linear Time Trend ◽  
Proposed Model ◽  
Non Linear

A vast majority of the countries is under the economic and health crises due to the current epidemic of coronavirus disease 2019 (COVID-19). The present study analyzes the COVID-19 using time series, which is an essential gizmo for knowing the enlargement of infection and its changing behavior, especially the trending model. We have considered an autoregressive model with a non-linear time trend component that approximately converted into the linear trend using the spline function. The spline function split the COVID-19 series into different piecewise segments between respective knots and fitted the linear time trend. First, we obtain the number of knots with its locations in the COVID-19 series and then the estimation of the best-fitted model parameters are determined under Bayesian setup. The results advocate that the proposed model/methodology is a useful procedure to convert the non-linear time trend into a linear pattern of newly coronavirus case for various countries in the pandemic situation of COVID-19.

Introduction to Linear Time Series Models

2019 ◽  
pp. 7-22
Author(s):  
Jeffrey S. Racine
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Linear Time ◽  
Series Data ◽  
Time Series Models ◽  
Cross Sectional ◽  
Economic Interpretation

This chapter introduces time series data and outlines how it differs from cross sectional data. It also highlights how the object of interest when modelling time series data is the forecast, which differs from the object of interest in cross-sectional modelling, which is typically some parameter of interest that has an economic interpretation.

Time Series Regression with Mixtures of Integrated Processes

1995 ◽  
Vol 11 (5) ◽  
pp. 1033-1094 ◽  
Author(s):  
Yoosoon Chang ◽  
Peter C.B. Phillips
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Time Series Data ◽  
Unit Roots ◽  
Ordinary Least Squares ◽  
Series Data ◽  
Vector Autoregressions ◽  
Time Series Regression ◽  
First Order ◽  
Unknown Mixture

The paper develops a statistical theory for regressions with integrated regressors of unknown order and unknown cointegrating dimension. In practice, we are often unsure whether unit roots or cointegration is present in time series data, and we are also uncertain about the order of integration in some cases. This paper addresses issues of estimation and inference in cases of such uncertainty. Phillips (1995, Econometrica 63, 1023–1078) developed a theory for time series regressions with an unknown mixture of 1(0) and 1(1) variables and established that the method of fully modified ordinary least squares (FM-OLS) is applicable to models (including vector autoregressions) with some unit roots and unknown cointegrating rank. This paper extends these results to models that contain some I(0), I(1), and I(2) regressors. The theory and methods here are applicable to cointegrating regressions that include unknown numbers of I(0), I(1), and I(2) variables and an unknown degree of cointegration. Such models require a somewhat different approach than that of Phillips (1995). The paper proposes a residual-based fully modified ordinary least-squares (RBFMOLS) procedure, which employs residuals from a first-order autoregression of the first differences of the entire regressor set in the construction of the FMOLS estimator. The asymptotic theory for the RBFM-OLS estimator is developed and is shown to be normal for all the stationary coefficients and mixed normal for all the nonstationary coefficients. Under Gaussian assumptions, estimation of the cointegration space by RBFM-OLS is optimal even though the dimension of the space is unknown.

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