scholarly journals GENERALIZED LAPLACE INFERENCE IN MULTIPLE CHANGE-POINTS MODELS

2021 ◽  
pp. 1-31
Author(s):  
Alessandro Casini ◽  
Pierre Perron
Keyword(s):  
Asymptotic Distribution ◽  
Structural Changes ◽  
Linear Time ◽  
Bayesian Estimator ◽  
Change Points ◽  
Finite Sample ◽  
Time Series Regression ◽  
Long Span ◽  
Inference Methods ◽  
Theoretical Side

Under the classical long-span asymptotic framework, we develop a class of generalized laplace (GL) inference methods for the change-point dates in a linear time series regression model with multiple structural changes analyzed in, e.g., Bai and Perron (1998,Econometrica66, 47–78). The GL estimator is defined by an integration rather than optimization-based method and relies on the LS criterion function. It is interpreted as a classical (non-Bayesian) estimator, and the inference methods proposed retain a frequentist interpretation. This approach provides a better approximation about the uncertainty in the data of the change-points relative to existing methods. On the theoretical side, depending on some input (smoothing) parameter, the class of GL estimators exhibits a dual limiting distribution, namely the classical shrinkage asymptotic distribution or a Bayes-type asymptotic distribution. We propose an inference method based on highest density regions using the latter distribution. We show that it has attractive theoretical properties not shared by the other popular alternatives, i.e., it is bet-proof. Simulations confirm that these theoretical properties translate to good finite-sample performance.

scholarly journals A POWERFUL TEST OF THE AUTOREGRESSIVE UNIT ROOT HYPOTHESIS BASED ON A TUNING PARAMETER FREE STATISTIC

2009 ◽  
Vol 25 (6) ◽  
pp. 1515-1544 ◽  
Author(s):  
Morten Ørregaard Nielsen
Keyword(s):  
Asymptotic Distribution ◽  
Unit Root ◽  
Linear Time ◽  
Nonparametric Test ◽  
Tuning Parameter ◽  
Ratio Test ◽  
Local Power ◽  
Finite Sample ◽  
Power Of The Test ◽  
The Family

This paper presents a family of simple nonparametric unit root tests indexed by one parameter,d, and containing the Breitung (2002,Journal of Econometrics108, 342–363) test as the special cased= 1. It is shown that (a) each member of the family withd> 0 is consistent, (b) the asymptotic distribution depends ondand thus reflects the parameter chosen to implement the test, and (c) because the asymptotic distribution depends ondand the test remains consistent for alld> 0, it is possible to analyze the power of the test for different values ofd. The usual Phillips–Perron and Dickey–Fuller type tests are indexed by bandwidth, lag length, etc., but have none of these three properties.It is shown that members of the family withd< 1 have higher asymptotic local power than the Breitung (2002) test, and whendis small the asymptotic local power of the proposed nonparametric test is relatively close to the parametric power envelope, particularly in the case with a linear time trend. Furthermore, generalized least squares (GLS) detrending is shown to improve power whendis small, which is not the case for the Breitung (2002) test. Simulations demonstrate that when applying a sieve bootstrap procedure, the proposed variance ratio test has very good size properties, with finite-sample power that is higher than that of the Breitung (2002) test and even rivals the (nearly) optimal parametric GLS detrended augmented Dickey–Fuller test with lag length chosen by an information criterion.

scholarly journals Parsing Expression Grammars and Their Induction Algorithm

2020 ◽  
Vol 10 (23) ◽  
pp. 8747
Author(s):  
Wojciech Wieczorek ◽  
Olgierd Unold ◽  
Łukasz Strąk
Keyword(s):  
Genetic Programming ◽  
Roc Curve ◽  
Classification Performance ◽  
Grammatical Inference ◽  
Inference Algorithm ◽  
Finite Sample ◽  
Induction Method ◽  
Grammar Learning ◽  
Area Under Roc Curve ◽  
Inference Methods

Grammatical inference (GI), i.e., the task of finding a rule that lies behind given words, can be used in the analyses of amyloidogenic sequence fragments, which are essential in studies of neurodegenerative diseases. In this paper, we developed a new method that generates non-circular parsing expression grammars (PEGs) and compares it with other GI algorithms on the sequences from a real dataset. The main contribution of this paper is a genetic programming-based algorithm for the induction of parsing expression grammars from a finite sample. The induction method has been tested on a real bioinformatics dataset and its classification performance has been compared to the achievements of existing grammatical inference methods. The evaluation of the generated PEG on an amyloidogenic dataset revealed its accuracy when predicting amyloid segments. We show that the new grammatical inference algorithm achieves the best ACC (Accuracy), AUC (Area under ROC curve), and MCC (Mathew’s correlation coefficient) scores in comparison to five other automata or grammar learning methods.

scholarly journals Profile Inferences on Restricted Additive Partially Linear EV Models

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Xiuli Wang
Keyword(s):  
Least Squares ◽  
Asymptotic Distribution ◽  
The Other ◽  
Finite Sample ◽  
Test Statistic ◽  
Two Stage ◽  
Chi Square ◽  
Partially Linear ◽  
Profile Least Squares ◽  
Restricted Estimator

We consider the testing problem for the parameter and restricted estimator for the nonparametric component in the additive partially linear errors-in-variables (EV) models under additional restricted condition. We propose a profile Lagrange multiplier test statistic based on modified profile least-squares method and two-stage restricted estimator for the nonparametric component. We derive two important results. One is that, without requiring the undersmoothing of the nonparametric components, the proposed test statistic is proved asymptotically to be a standard chi-square distribution under the null hypothesis and a noncentral chi-square distribution under the alternative hypothesis. These results are the same as the results derived by Wei and Wang (2012) for their adjusted test statistic. But our method does not need an adjustment and is easier to implement especially for the unknown covariance of measurement error. The other is that asymptotic distribution of proposed two-stage restricted estimator of the nonparametric component is asymptotically normal and has an oracle property in the sense that, though the other component is unknown, the estimator performs well as if it was known. Some simulation studies are carried out to illustrate relevant performances with a finite sample. The asymptotic distribution of the restricted corrected-profile least-squares estimator, which has not been considered by Wei and Wang (2012), is also investigated.

scholarly journals Parametric Methodologies for Detecting Changes in Maximum Temperature of Tlaxco, Tlaxcala, México

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Silvia Herrera Cortés ◽  
Bulmaro Juárez Hernández ◽  
Victor Hugo Vázquez Guevara ◽  
Hugo Adán Cruz Suárez
Keyword(s):  
Linear Time ◽  
Score Test ◽  
Change Points ◽  
Quality Analysis ◽  
Maximum Temperature ◽  
Ratio Test ◽  
Comparison Results ◽  
Binary Segmentation ◽  
Temperature Records ◽  
Sarima Models

In this paper, comparison results of parametric methodologies of change points, applied to maximum temperature records from the municipality of Tlaxco, Tlaxcala, México, are presented. Methodologies considered are likelihood ratio test, score test, and binary segmentation (BS), pruned exact linear time (PELT), and segment neighborhood (SN). In order to compare such methodologies, a quality analysis of the data was performed; in addition, lost data were estimated with linear regression, and finally, SARIMA models were adjusted.

ESTIMATION OF CHANGE-POINTS IN LINEAR AND NONLINEAR TIME SERIES MODELS

2014 ◽  
Vol 32 (2) ◽  
pp. 402-430 ◽  
Author(s):  
Shiqing Ling
Keyword(s):  
Time Series ◽  
Asymptotic Theory ◽  
Nonlinear Time Series ◽  
Change Points ◽  
Time Series Models ◽  
Finite Sample ◽  
Asymptotically Normal ◽  
Estimated Parameters ◽  
Linear And Nonlinear ◽  
Economic Studies

This paper develops an asymptotic theory for estimated change-points in linear and nonlinear time series models. Based on a measurable objective function, it is shown that the estimated change-point converges weakly to the location of the maxima of a double-sided random walk and other estimated parameters are asymptotically normal. When the magnitude d of changed parameters is small, it is shown that the limiting distribution can be approximated by the known distribution as in Yao (1987, Annals of Statistics 15, 1321–1328). This provides a channel to connect our results with those in Picard (1985, Advances in Applied Probability 17, 841–867) and Bai, Lumsdaine, and Stock (1998, Review of Economic Studies 65, 395–432), where the magnitude of changed parameters depends on the sample size n and tends to zero as n → ∞. The theory is applied for the self-weighted QMLE and the local QMLE of change-points in ARMA-GARCH/IGARCH models. A simulation study is carried out to evaluate the performance of these estimators in the finite sample.

TESTING FOR A CHANGE IN CORRELATION AT AN UNKNOWN POINT IN TIME USING AN EXTENDED FUNCTIONAL DELTA METHOD

2011 ◽  
Vol 28 (3) ◽  
pp. 570-589 ◽  
Author(s):  
Dominik Wied ◽  
Walter Krämer ◽  
Herold Dehling
Keyword(s):  
Monte Carlo ◽  
Stock Returns ◽  
Structural Changes ◽  
Null Distribution ◽  
Delta Method ◽  
Local Power ◽  
Finite Sample ◽  
Empirical Correlations ◽  
Functional Delta Method ◽  
Unknown Point

We propose a new test against a change in correlation at an unknown point in time based on cumulated sums of empirical correlations. The test does not require that inputs are independent and identically distributed under the null. We derive its limiting null distribution using a new functional delta method argument, provide a formula for its local power for particular types of structural changes, give some Monte Carlo evidence on its finite-sample behavior, and apply it to recent stock returns.

scholarly journals Indirect Inference Estimation of Spatial Autoregressions

Econometrics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 34
Author(s):  
Yong Bao ◽  
Xiaotian Liu ◽  
Lihong Yang
Keyword(s):  
Monte Carlo ◽  
Least Squares ◽  
Asymptotic Distribution ◽  
Monte Carlo Study ◽  
Ordinary Least Squares ◽  
Indirect Inference ◽  
Finite Sample ◽  
Spatial Unit ◽  
Asymptotically Normal ◽  
Distribution Result

The ordinary least squares (OLS) estimator for spatial autoregressions may be consistent as pointed out by Lee (2002), provided that each spatial unit is influenced aggregately by a significant portion of the total units. This paper presents a unified asymptotic distribution result of the properly recentered OLS estimator and proposes a new estimator that is based on the indirect inference (II) procedure. The resulting estimator can always be used regardless of the degree of aggregate influence on each spatial unit from other units and is consistent and asymptotically normal. The new estimator does not rely on distributional assumptions and is robust to unknown heteroscedasticity. Its good finite-sample performance, in comparison with existing estimators that are also robust to heteroscedasticity, is demonstrated by a Monte Carlo study.

scholarly journals Quantile Regression with Clustered Data

2016 ◽  
Vol 5 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Paulo M.D.C. Parente ◽  
João M.C. Santos Silva
Keyword(s):  
Quantile Regression ◽  
Covariance Matrix ◽  
Asymptotic Distribution ◽  
Simulation Study ◽  
Consistent Estimator ◽  
Regression Estimator ◽  
Finite Sample ◽  
Specification Test ◽  
Asymptotically Normal ◽  
Cluster Correlation

AbstractWe study the properties of the quantile regression estimator when data are sampled from independent and identically distributed clusters, and show that the estimator is consistent and asymptotically normal even when there is intra-cluster correlation. A consistent estimator of the covariance matrix of the asymptotic distribution is provided, and we propose a specification test capable of detecting the presence of intra-cluster correlation. A small simulation study illustrates the finite sample performance of the test and of the covariance matrix estimator.

Sign in / Sign up

Export Citation Format

Share Document