scholarly journals ADAPTIVE LONG MEMORY TESTING UNDER HETEROSKEDASTICITY

2016 ◽  
Vol 33 (3) ◽  
pp. 755-778 ◽  
Author(s):  
David Harris ◽  
Hsein Kew
Keyword(s):  
Long Memory ◽  
Score Test ◽  
Monte Carlo Experiment ◽  
Finite Sample ◽  
Large Power ◽  
Finite Sample Properties ◽  
Weighted Score ◽  
Unknown Form ◽  
Arfima Model ◽  
Asymptotically Efficient

This paper considers adaptive hypothesis testing for the fractional differencing parameter in a parametric ARFIMA model with unconditional heteroskedasticity of unknown form. A weighted score test based on a nonparametric variance estimator is proposed and shown to be asymptotically equivalent, under the null and local alternatives, to the Neyman-Rao effective score test constructed under Gaussianity and known variance process. The proposed test is therefore asymptotically efficient under Gaussianity. The finite sample properties of the test are investigated in a Monte Carlo experiment and shown to provide potentially large power gains over the usual unweighted long memory test.

Short-Term Noise and the Robustness of Two Log-Periodogram Estimators in Long Memory Series

2013 ◽  
Vol 313-314 ◽  
pp. 1235-1238
Author(s):  
Lu Deng
Keyword(s):  
Long Memory ◽  
Finite Sample ◽  
Short Term ◽  
Noise Simulation ◽  
Finite Sample Properties ◽  
Positive Roots ◽  
The Mean ◽  
Mean Square Errors ◽  
Larger Sample ◽  
Memory Series

This paper focuses on the robustness of estimates and its mechanism with presence of short-term noise. Simulation results show that although AG estimator derives lower bias and better robustness than the GPH in most situations, the modification effects are evident only when the short noise has small negative roots. The problem of over-modification on larger negative roots and the under-modification on the positive roots are still lack of advanced study. The standard deviation it is not sensitive to short-term noise but the mean square errors increase sharply with short-term noise. Besides, the power and practical size of the test was affected too. Larger sample size is suggested to gain more robust finite sample properties.

scholarly journals Nonparametric Instrumental-Variable Estimation

2018 ◽  
Vol 18 (4) ◽  
pp. 937-950 ◽  
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.

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

2019 ◽  
Vol 36 (4) ◽  
pp. 751-772 ◽  
Author(s):  
Javier Hualde ◽  
Morten Ørregaard Nielsen
Keyword(s):  
Time Series ◽  
Asymptotic Normality ◽  
Relative Strength ◽  
Sum Of Squares ◽  
Monte Carlo Experiment ◽  
Time Series Models ◽  
Finite Sample ◽  
Generalized Polynomial ◽  
Finite Sample Properties ◽  
Deterministic Components

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.

ASYMPTOTICALLY EFFICIENT MEDIAN REGRESSION IN THE PRESENCE OF HETEROSKEDASTICITY OF UNKNOWN FORM

2001 ◽  
Vol 17 (4) ◽  
pp. 765-784 ◽  
Author(s):  
Quanshui Zhao
Keyword(s):  
Least Squares Method ◽  
Generalized Least Squares ◽  
Least Absolute Deviation ◽  
Finite Sample ◽  
Median Regression ◽  
Absolute Deviation ◽  
Least Absolute Deviation Regression ◽  
Unknown Form ◽  
The One ◽  
Asymptotically Efficient

We consider a linear model with heteroskedasticity of unknown form. Using Stone's (1977, Annals of Statistics 5, 595–645) k nearest neighbors (k-NN) estimation approach, the optimal weightings for efficient least absolute deviation regression are estimated consistently using residuals from preliminary estimation. The reweighted least absolute deviation or median regression estimator with the estimated weights is shown to be equivalent to the estimator using the true but unknown weights under mild conditions. Asymptotic normality of the estimators is also established. In the finite sample case, the proposed estimators are found to outperform the generalized least squares method of Robinson (1987, Econometrica 55, 875–891) and the one-step estimator of Newey and Powell (1990, Econometric Theory 6, 295–317) based on a Monte Carlo simulation experiment.

scholarly journals DETECTION OF NONCONSTANT LONG MEMORY PARAMETER

2013 ◽  
Vol 29 (5) ◽  
pp. 1009-1056 ◽  
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.

scholarly journals MODELING MULTIPLE REGIMES IN FINANCIAL VOLATILITY WITH A FLEXIBLE COEFFICIENT GARCH(1,1) MODEL

2009 ◽  
Vol 25 (1) ◽  
pp. 117-161 ◽  
Author(s):  
Marcelo C. Medeiros ◽  
Alvaro Veiga
Keyword(s):  
Asymptotic Properties ◽  
Monte Carlo Experiment ◽  
Type Model ◽  
Finite Sample ◽  
Financial Volatility ◽  
Proposed Model ◽  
Multiple Regimes ◽  
Finite Sample Properties ◽  
Quasi Maximum Likelihood ◽  
Errors Estimation

In this paper a flexible multiple regime GARCH(1,1)-type model is developed to describe the sign and size asymmetries and intermittent dynamics in financial volatility. The results of the paper are important to other nonlinear GARCH models. The proposed model nests some of the previous specifications found in the literature and has the following advantages. First, contrary to most of the previous models, more than two limiting regimes are possible, and the number of regimes is determined by a simple sequence of tests that circumvents identification problems that are usually found in nonlinear time series models. The second advantage is that the novel stationarity restriction on the parameters is relatively weak, thereby allowing for rich dynamics. It is shown that the model may have explosive regimes but can still be strictly stationary and ergodic. A simulation experiment shows that the proposed model can generate series with high kurtosis and low first-order autocorrelation of the squared observations and exhibit the so-called Taylor effect, even with Gaussian errors. Estimation of the parameters is addressed, and the asymptotic properties of the quasi-maximum likelihood estimator are derived under weak conditions. A Monte-Carlo experiment is designed to evaluate the finite-sample properties of the sequence of tests. Empirical examples are also considered.

scholarly journals FRACTIONAL COINTEGRATION IN STOCHASTIC VOLATILITY MODELS

2008 ◽  
Vol 24 (5) ◽  
pp. 1207-1253 ◽  
Author(s):  
Afonso Gonçalves da Silva ◽  
Peter M. Robinson
Keyword(s):  
Stochastic Volatility ◽  
Latent Variables ◽  
Factor Model ◽  
Strong Dependence ◽  
Common Factor ◽  
Monte Carlo Experiment ◽  
Finite Sample ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Finite Sample Properties

Asset returns are frequently assumed to be determined by one or more common factors. We consider a bivariate factor model where the unobservable common factor and idiosyncratic errors are stationary and serially uncorrelated but have strong dependence in higher moments. Stochastic volatility models for the latent variables are employed, in view of their direct application to asset pricing models. Assuming that the underlying persistence is higher in the factor than in the errors, a fractional cointegrating relationship can be recovered by suitable transformation of the data. We propose a narrow band semiparametric estimate of the factor loadings, which is shown to be consistent with a rate of convergence, and its finite-sample properties are investigated in a Monte Carlo experiment.

Adjustments of Rao’s Score Test for Distributional and Local Parametric Misspecifications

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Anil K. Bera ◽  
Yannis Bilias ◽  
Mann J. Yoon ◽  
Süleyman Taşpınar ◽  
Osman Doğan
Keyword(s):  
Test Procedure ◽  
Score Test ◽  
Score Function ◽  
Monte Carlo Study ◽  
Fundamental Principle ◽  
Finite Sample ◽  
Special Cases ◽  
Finite Sample Properties ◽  
Data Generating Process ◽  
Rao's Score Test

AbstractRao’s (1948) seminal paper introduced a fundamental principle of testing based on the score function and the score test has local optimal properties. When the assumed model is misspecified, it is well known that Rao’s score (RS) test loses its optimality. A model could be misspecified in a variety of ways. In this paper, we consider two kinds: distributional and parametric. In the former case, the assumed probability density function differs from the data generating process. Kent (1982) and White (1982) analyzed this case and suggested a modified version of the RS test that involves adjustment of the variance. In the latter case, the dimension of the parameter space of the assumed model does not match with that of the true one. Using the distribution of the RS test under this situation, Bera and Yoon (1993) developed a modified RS test that is valid under the local parametric misspecification. This involves adjusting both the mean and variance of the standard RS test. This paper considers the joint presence of the distributional and parametric misspecifications and develops a modified RS test that is valid under both types of misspecification. Earlier modified tests under either type of misspecification can be obtained as the special cases of the proposed test. We provide three examples to illustrate the usefulness of the suggested test procedure. In a Monte Carlo study, we demonstrate that the modified test statistics have good finite sample properties.

SEMIPARAMETRIC INDEPENDENCE TESTING FOR TIME SERIES OF COUNTS AND THE ROLE OF THE SUPPORT

2018 ◽  
Vol 35 (6) ◽  
pp. 1111-1145 ◽  
Author(s):  
David Harris ◽  
Brendan McCabe
Keyword(s):  
Time Series ◽  
Likelihood Ratio ◽  
Negative Binomial ◽  
Score Test ◽  
Finite Sample ◽  
Natural Numbers ◽  
Score Tests ◽  
First Order ◽  
Semiparametric Likelihood ◽  
Asymptotically Efficient

This article considers testing for independence in a time series of small counts within an Integer Autoregressive (INAR) model, taking a semiparametric approach that avoids any distributional assumption on the arrivals process of the model. The nature of the testing problem is shown to differ depending on whether or not the support of the arrivals distribution is the full set of natural numbers (as would be the case for Poisson or Negative Binomial distributions for example) or some strict subset of the natural numbers (such as for a Binomial or Uniform distribution). The theory for these two cases is studied separately.For the case where the arrivals have support on the natural numbers, a new asymptotically efficient semiparametric test, the effective score (Neyman-Rao) test, is derived. The semiparametric Likelihood-Ratio, Wald and score tests are shown to be asymptotically equivalent to the effective score test, and hence also asymptotically efficient. Asymptotic relative efficiency calculations demonstrate that the semiparametric effective score test can provide substantial power advantages over the first order autocorrelation coefficient, which is most commonly applied in practice.For the case where the arrivals have support that is a strict subset of the natural numbers, the theory is considerably altered because the support of the observations becomes different under the null and alternative hypotheses. The semiparametric Likelihood-Ratio, Wald and score tests become asymptotically degenerate in this case, while the effective score test remains valid. Remarkably, in this case the effective score test is also found to have power against local alternatives that shrink to the null at the rate T−1. In rare cases where the arrival support is partly or totally known, additional tests exploiting this information are considered.Finite sample properties of the tests in these various cases demonstrate the semiparametric effective score test can provide substantial power advantages over the first order autocorrelation test implied by a parametric Poisson specification. The simulations also reveal situations in which the first order autocorrelation is preferable in finite samples, so a hybrid of the effective score and autocorrelation tests is proposed to capture most of the benefits of each test.

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