scholarly journals Bayesian Unit Root Test for AR(1) Model with Trend Approximated

2020 ◽  
Vol 8 (2) ◽  
pp. 425-461
Author(s):  
Jitendra Kumar ◽  
Varun Varun ◽  
Dhirendra Kumar ◽  
Anoop Chaturvedi
Keyword(s):  
Unit Root ◽  
Time Trend ◽  
Spline Function ◽  
Linear Time ◽  
Linear Trend ◽  
Unit Root Test ◽  
Posterior Odds ◽  
Linear Time Trend ◽  
Proposed Model ◽  
Non Linear

The objective of present study is to develop a time series model for handling the non-linear trend process using a spline function. Spline function is a piecewise polynomial segment concerning the time component. The main advantage of spline function is the approximation, non linear time trend, but linear time trend between the consecutive join points. A unit root hypothesis is projected to test the non stationarity due to presence of unit root in the proposed model. In the autoregressive model with linear trend, the time trend vanishes under the unit root case. However, when non-linear trend is present and approximated by the linear spline function, through the trend component is absent under the unit root case, but the intercept term makes a shift with r knots. For decision making under the Bayesian perspective, the posterior odds ratio is used for hypothesis testing problems. We have derived the posterior probability for the assumed hypotheses under appropriate prior information. A simulation study and an empirical application are presented to examine the performance of theoretical outcomes.

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.

scholarly journals Subsampling Intervals in Autoregressive Models with Linear Time Trend

Econometrica ◽  
2001 ◽  
Vol 69 (5) ◽  
pp. 1283-1314 ◽  
Author(s):  
Joseph P. Romano ◽  
Michael Wolf
Keyword(s):  
Time Trend ◽  
Linear Time ◽  
Autoregressive Models ◽  
Linear Time Trend

scholarly journals Unit Roots in Time Series with Changepoints

2017 ◽  
Vol 6 (6) ◽  
pp. 127
Author(s):  
Ed Herranz ◽  
James Gentle ◽  
George Wang
Keyword(s):  
Time Series ◽  
Unit Root ◽  
Null Hypothesis ◽  
Structural Changes ◽  
Linear Trend ◽  
Unit Root Test ◽  
Unit Roots ◽  
Cointegration Analysis ◽  
Unit Root Tests ◽  
Standard Unit

Many financial time series are nonstationary and are modeled as ARIMA processes; they are integrated processes (I(n)) which can be made stationary (I(0)) via differencing n times. I(1) processes have a unit root in the autoregressive polynomial. Using OLS with unit root processes often leads to spurious results; a cointegration analysis should be used instead. Unit root tests (URT) decrease spurious cointegration. The Augmented Dickey Fuller (ADF) URT fails to reject a false null hypothesis of a unit root under the presence of structural changes in intercept and/or linear trend. The Zivot and Andrews (ZA) (1992) URT was designed for unknown breaks, but not under the null hypothesis. Lee and Strazicich (2003) argued the ZA URT was biased towards stationarity with breaks and proposed a new URT with breaks in the null. When an ARMA(p,q) process with trend and/or drift that is to be tested for unit roots and has changepoints in trend and/or intercept two approaches that can be taken: One approach is to use a unit root test that is robust to changepoints. In this paper we consider two of these URT's, the Lee-Strazicich URT and the Hybrid Bai-Perron ZA URT(Herranz, 2016.)  The other approach we consider is to remove the deterministic components with changepoints using the Bai-Perron breakpoint detection method (1998, 2003), and then use a standard unit root test such as ADF in each segment. This approach does not assume that the entire time series being tested is all I(1) or I(0), as is the case with standard unit root tests. Performances of the tests were compared under various scenarios involving changepoints via simulation studies.  Another type of model for breaks, the Self-Exciting-Threshold-Autoregressive (SETAR) model is also discussed.

ASYMPTOTIC DISTRIBUTIONS FOR UNIT ROOT TEST STATISTICS IN NEARLY INTEGRATED SEASONAL AUTOREGRESSIVE MODELS

2000 ◽  
Vol 16 (2) ◽  
pp. 200-230 ◽  
Author(s):  
Seiji Nabeya
Keyword(s):  
Least Squares ◽  
Unit Root ◽  
Linear Trend ◽  
Unit Root Test ◽  
Ordinary Least Squares ◽  
Asymptotic Distributions ◽  
Autoregressive Models ◽  
Test Statistics ◽  
Autoregressive Parameter ◽  
Ordinary Least Squares Estimator

Seasonal autoregressive models with an intercept or linear trend are discussed. The main focus of this paper is on the models in which the intercept or trend parameters do not depend on the season. One of the most important results from this study is the asymptotic distribution for the ordinary least squares estimator of the autoregressive parameter obtained under nearly integrated condition, and another is the approximation to the limiting distribution of the t-statistic under the null for testing the unit root hypothesis.

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