TRUNCATED SUM OF SQUARES ESTIMATION OF FRACTIONAL TIME SERIES MODELS WITH DETERMINISTIC TRENDS

We consider truncated (or conditional) sum of squares estimation of a parametric model composed of a fractional time series and an additive generalized polynomial trend. Both the memory parameter, which characterizes the behavior of the stochastic component of the model, and the exponent parameter, which drives the shape of the deterministic component, are considered not only unknown real numbers but also lying in arbitrarily large (but finite) intervals. Thus, our model captures different forms of nonstationarity and noninvertibility. As in related settings, the proof of consistency (which is a prerequisite for proving asymptotic normality) is challenging due to nonuniform convergence of the objective function over a large admissible parameter space, but, in addition, our framework is substantially more involved due to the competition between stochastic and deterministic components. We establish consistency and asymptotic normality under quite general circumstances, finding that results differ crucially depending on the relative strength of the deterministic and stochastic components. Finite-sample properties are illustrated by means of a Monte Carlo experiment.

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SUP-TESTS FOR LINEARITY IN A GENERAL NONLINEAR AR(1) MODEL

Econometric Theory ◽

10.1017/s0266466609990430 ◽

2009 ◽

Vol 26 (4) ◽

pp. 965-993 ◽

Cited By ~ 7

Author(s):

Christian Francq ◽

Lajos Horvath ◽

Jean-Michel Zakoïan

Keyword(s):

Time Series ◽

Asymptotic Distribution ◽

Null Hypothesis ◽

Nuisance Parameter ◽

Time Series Models ◽

Ratio Test ◽

Finite Sample ◽

Chi Square ◽

Finite Sample Properties ◽

Linearity Testing

We consider linearity testing in a general class of nonlinear time series models of order one, involving a nonnegative nuisance parameter that (a) is not identified under the null hypothesis and (b) gives the linear model when equal to zero. This paper studies the asymptotic distribution of the likelihood ratio test and asymptotically equivalent supremum tests. The asymptotic distribution is described as a functional of chi-square processes and is obtained without imposing a positive lower bound for the nuisance parameter. The finite-sample properties of the sup-tests are studied by simulations.

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LIKELIHOOD-BASED INFERENCE IN TRENDING TIME SERIES WITH A ROOT NEAR UNITY

Econometric Theory ◽

10.1017/s0266466601176036 ◽

2001 ◽

Vol 17 (6) ◽

pp. 1082-1112 ◽

Cited By ~ 5

Author(s):

Zhijie Xiao

Keyword(s):

Time Series ◽

Joint Estimation ◽

Unit Root Tests ◽

Time Series Models ◽

Least Squares Regression ◽

Finite Sample ◽

Testing Procedures ◽

Monte Carlo Experiments ◽

Autoregressive Parameter ◽

Nonlinear Equation Systems

This paper studies likelihood-based estimation and tests for autoregressive time series models with deterministic trends and general disturbance distributions. In particular, a joint estimation of the trend coefficients and the autoregressive parameter is considered. Asymptotic analysis on the M-estimators is provided. It is shown that the limiting distributions of these estimators involve nonlinear equation systems of Brownian motions even for the simple case of least squares regression. Unit root tests based on M-estimation are also considered, and extensions of the Neyman–Pearson test are studied. The finite sample performance of these estimators and testing procedures is examined by Monte Carlo experiments.

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

Econometric Theory ◽

10.1017/s0266466614000863 ◽

2014 ◽

Vol 32 (2) ◽

pp. 402-430 ◽

Cited By ~ 7

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.

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Finite-sample properties of estimators for first and second order autoregressive processes

Statistical Inference for Stochastic Processes ◽

10.1007/s11203-021-09262-4 ◽

2021 ◽

Author(s):

Sigrunn H. Sørbye ◽

Pedro G. Nicolau ◽

Håvard Rue

Keyword(s):

Time Series ◽

Polynomial Regression ◽

Gaussian Copula ◽

Finite Sample ◽

Coefficient Estimates ◽

Ecological Data ◽

Data Set ◽

Finite Sample Properties ◽

The Relationship ◽

Corrected Coefficient

AbstractThe class of autoregressive (AR) processes is extensively used to model temporal dependence in observed time series. Such models are easily available and routinely fitted using freely available statistical software like . A potential problem is that commonly applied estimators for the coefficients of AR processes are severely biased when the time series are short. This paper studies the finite-sample properties of well-known estimators for the coefficients of stationary AR(1) and AR(2) processes and provides bias-corrected versions of these estimators which are quick and easy to apply. The new estimators are constructed by modeling the relationship between the true and originally estimated AR coefficients using weighted orthogonal polynomial regression, taking the sampling distribution of the original estimators into account. The finite-sample distributions of the new bias-corrected estimators are approximated using transformations of skew-normal densities, combined with a Gaussian copula approximation in the AR(2) case. The properties of the new estimators are demonstrated by simulations and in the analysis of a real ecological data set. The estimators are easily available in our accompanying -package for AR(1) and AR(2) processes of length 10–50, both giving bias-corrected coefficient estimates and corresponding confidence intervals.

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Dynamic Factor Copula Models with Estimated Cluster Assignments

Finance and Economics Discussion Series ◽

10.17016/feds.2021.029 ◽

2021 ◽

Vol 2021 (026) ◽

pp. 1-52

Author(s):

Dong Hwan Oh ◽

◽

Andrew J. Patton ◽

Keyword(s):

Time Series ◽

Clustering Algorithm ◽

Ad Hoc ◽

High Dimensional ◽

Dynamic Factor ◽

Finite Sample ◽

Copula Models ◽

Finite Sample Properties ◽

Out Of Sample ◽

Individual Variables

This paper proposes a dynamic multi-factor copula for use in high dimensional time series applications. A novel feature of our model is that the assignment of individual variables to groups is estimated from the data, rather than being pre-assigned using SIC industry codes, market capitalization ranks, or other ad hoc methods. We adapt the k-means clustering algorithm for use in our application and show that it has excellent finite-sample properties. Applying the new model to returns on 110 US equities, we find around 20 clusters to be optimal. In out-of-sample forecasts, we find that a model with as few as five estimated clusters significantly outperforms an otherwise identical model with 21 clusters formed using two-digit SIC codes.

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Confidence Regions for Parameters in Stationary Time Series Models With Gaussian Noise

Frontiers in Physics ◽

10.3389/fphy.2021.801692 ◽

2022 ◽

Vol 9 ◽

Author(s):

Xiuzhen Zhang ◽

Riquan Zhang ◽

Zhiping Lu

Keyword(s):

Time Series ◽

Empirical Likelihood ◽

Long Memory ◽

Score Function ◽

Real Data ◽

Confidence Regions ◽

Stationary Time Series ◽

Time Series Models ◽

Finite Sample ◽

Memory Time

This article develops two new empirical likelihood methods for long-memory time series models based on adjusted empirical likelihood and mean empirical likelihood. By application of Whittle likelihood, one obtains a score function that can be viewed as the estimating equation of the parameters of the long-memory time series model. An empirical likelihood ratio is obtained which is shown to be asymptotically chi-square distributed. It can be used to construct confidence regions. By adding pseudo samples, we simultaneously eliminate the non-definition of the original empirical likelihood and enhance the coverage probability. Finite sample properties of the empirical likelihood confidence regions are explored through Monte Carlo simulation, and some real data applications are carried out.

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On strong consistency and asymptotic normality of one-step Gauss-Newton estimators in ARMA time series models

Statistics ◽

10.1080/02331888.2020.1830095 ◽

2020 ◽

Vol 54 (5) ◽

pp. 1030-1057

Author(s):

Pierre Duchesne ◽

Pierre Lafaye de Micheaux ◽

Joseph François Tagne Tatsinkou

Keyword(s):

Time Series ◽

Asymptotic Normality ◽

Strong Consistency ◽

Time Series Models ◽

One Step ◽

Consistency And Asymptotic Normality

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Nonparametric Instrumental-Variable Estimation

The Stata Journal Promoting communications on statistics and Stata ◽

10.1177/1536867x1801800411 ◽

2018 ◽

Vol 18 (4) ◽

pp. 937-950 ◽

Cited By ~ 2

Author(s):

Denis Chetverikov ◽

Dongwoo Kim ◽

Daniel Wilhelm

Keyword(s):

Instrumental Variable ◽

Estimation Methods ◽

Monte Carlo Experiment ◽

Finite Sample ◽

Gasoline Demand ◽

Tuning Parameters ◽

Demand Functions ◽

Instrumental Variable Estimation ◽

Finite Sample Properties ◽

Shape Restriction

In this article, we introduce the commands npiv and npivcv, which implement nonparametric instrumental-variable (NPIV) estimation methods without and with a cross-validated choice of tuning parameters, respectively. Both commands can impose the constraint that the resulting estimated function is monotone. Using such a shape restriction may significantly improve the performance of the NPIV estimator (Chetverikov and Wilhelm, 2017, Econometrica 85: 1303–1320) because the ill-posedness of the NPIV estimation problem leads to unconstrained estimators that suffer from particularly poor statistical properties such as high variance. However, the constrained estimator that imposes the monotonicity significantly reduces variance by removing nonmonotone oscillations of the estimator. We provide a small Monte Carlo experiment to study the estimators’ finite-sample properties and an application to the estimation of gasoline demand functions.

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DETECTION OF NONCONSTANT LONG MEMORY PARAMETER

Econometric Theory ◽

10.1017/s0266466613000303 ◽

2013 ◽

Vol 29 (5) ◽

pp. 1009-1056 ◽

Cited By ~ 6

Author(s):

Frédéric Lavancier ◽

Remigijus Leipus ◽

Anne Philippe ◽

Donatas Surgailis

Keyword(s):

Time Series ◽

Long Memory ◽

General Setting ◽

Partial Sums ◽

Gradual Change ◽

Test Statistics ◽

Finite Sample ◽

Testing Procedures ◽

Finite Sample Properties ◽

Memory Parameter

This article deals with detection of a nonconstant long memory parameter in time series. The null hypothesis presumes stationary or nonstationary time series with a constant long memory parameter, typically an I (d) series with d > −.5 . The alternative corresponds to an increase in persistence and includes in particular an abrupt or gradual change from I (d1) to I (d2), −.5 < d1 < d2. We discuss several test statistics based on the ratio of forward and backward sample variances of the partial sums. The consistency of the tests is proved under a very general setting. We also study the behavior of these test statistics for some models with a changing memory parameter. A simulation study shows that our testing procedures have good finite sample properties and turn out to be more powerful than the KPSS-based tests (see Kwiatkowski, Phillips, Schmidt and Shin, 1992) considered in some previous works.

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GOODNESS-OF-FIT TESTS FOR MULTIVARIATE COPULA-BASED TIME SERIES MODELS

Econometric Theory ◽

10.1017/s0266466615000419 ◽

2016 ◽

Vol 33 (2) ◽

pp. 292-330 ◽

Cited By ~ 4

Author(s):

Betina Berghaus ◽

Axel Bücher

Keyword(s):

Time Series ◽

Goodness Of Fit ◽

Mixing Time ◽

Parametric Bootstrap ◽

Stationary Time Series ◽

Time Series Models ◽

Finite Sample ◽

Copula Functions ◽

Cross Sectional ◽

Goodness Of Fit Tests

In recent years, stationary time series models based on copula functions became increasingly popular in econometrics to model nonlinear temporal and cross-sectional dependencies. Within these models, we consider the problem of testing the goodness-of-fit of the parametric form of the underlying copula. Our approach is based on a dependent multiplier bootstrap and it can be applied to any stationary, strongly mixing time series. The method extends recent i.i.d. results by Kojadinovic et al. (2011) and shares the same computational benefits compared to methods based on a parametric bootstrap. The finite-sample performance of our approach is investigated by Monte Carlo experiments for the case of copula-based Markovian time series models.

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