The strengths and weaknesses of L2 approximable regressors (original) (raw)

Autoregressive Approximation in Nonstandard Situations: Empirical Evidence y

2005

This paper investigates the empirical properties of autoregressive approximations to two classes of process for which the usual regularity conditions do not apply; namely the non-invertible and fractionally integrated processes considered in Poskitt (2005). In that paper the theoretical consequences of fltting long autoregressions under regularity conditions that allow for these two situations was considered, and convergence rates for the sample autocovariances and autoregressive coe‐cients established. We now consider the flnite-sample properties of alternative estimators of the AR parameters of the approximating AR(h) process and corresponding estimates of the optimal approximating order h. The estimators considered include the Yule-Walker, Least Squares, and Burg estimators.

Asymptotic Properties of OLS Estimates in Autoregressions with Bounded or Slowly Growing Deterministic Trends

Communications in Statistics - Theory and Methods, 2006

We propose a general method of modeling deterministic trends for autoregressions. The method relies on the notion of L 2 -approximable regressors previously developed by the author. Some facts from the theory of functions play an important role in the proof. In its present form, the method encompasses slowly growing regressors, such as logarithmic trends, and leaves open the case of polynomial trends.

On the errors committed by sequences of estimator functionals

Mathematical Methods of Statistics, 2011

Chapter 1. Introduction to the Thesis 1. From the ancients to 1640 2. The first limit theorem and the variable N ε 2.1. Improvements on the Bernoulli bound 2.2. Uniformity and the Vapnik-Chervonenkis inequalities 2.3. CLT-based approximations for the tail of N ε 2.4. Full circle: Calculating the quantiles of the limiting distribution 2.5. A new type of sequential confidence bands for the Nelson-Aalen estimator 3. Gorgias' revenge: Model selection and pragmatism 3.1. Two-stage model selection procedures 3.2. The way ahead: Non-asymptotic model-selection 3.3. A connection between the AIC and N ε 4. Non-standard alternative models: Regression with jumps

A general asymptotic theory for time-series models

Statistica Neerlandica, 2010

This paper develops a general asymptotic theory for the estimation of strictly stationary and ergodic time series models. Under simple conditions that are straightforward to check, we establish the strong consistency, the rate of strong convergence and the asymptotic normality of a general class of estimators that includes LSE, MLE, and some M-type estimators. As an application, we verify the assumptions for the long-memory fractional ARIMA model. Other examples include the GARCH(1,1) model, random coefficient AR(1) model and the threshold MA(1) model.

Alternative Asymptotics and the Partially Linear Model with Many Regressors

2010

Abstract Non-standard distributional approximations have received considerable attention in recent years. They often provide more accurate approximations in small samples, and theoretical improvements in some cases. This paper shows that the seemingly unrelated ���many instruments asymptotics��� and ���small bandwidth asymptotics��� share a common structure, where the object determining the limiting distribution is a V-statistic with a remainder that is an asymptotically normal degenerate U-statistic.

Fixed-smoothing Asymptotics and Ac- Curate F Approximation Using Vector Autoregressive Covariance Ma

2014

Kiefer, N. M., Vogelsang, T. J., and Bunzel, H. (2000), “Simple Robust Testing of Regression Hypotheses,” Econometrica, 68, 695–714. [311,314] King, M. L. (1980), “Robust Tests for Spherical Symmetry and Their Application to Least Squares Regression,” The Annals of Statistics, 8, 1265–1271. [316] ——— (1987), “Towards a Theory of Point Optimal Testing,” Econometric Reviews, 6, 169–218. [315] Lehmann, E. L., and Romano, J. P. (2005), Testing Statistical Hypotheses, New York: Springer. [316] Müller, U. K. (2004), “A Theory of Robust Long-Run Variance Estimation,” Working paper, Princeton University. [311,314] ——— (2007), “A Theory of Robust Long-Run Variance Estimation,” Journal of Econometrics, 141, 1331–1352. [311,314,318,321] ——— (2011), “Efficient Tests Under a Weak Convergence Assumption,” Econometrica, 79, 395–435. [315] Müller, U. K., and Watson, M. W. (2008), “Testing Models of Low-Frequency Variability,” Econometrica, 76, 979–1016. [314] ——— (2013), “Measuring Uncertainty Abou...

OLS Asymptotics for Vector Autoregressions with Deterministic Regressors

2007

We consider a mixed vector autoregressive model with deterministic exogenous regressors and an autoregressive matrix that has characteristic roots inside the unit circle. The errors are (2+\epsilon)-integrable martingale differences with heterogeneous second-order conditional moments. The behavior of the ordinary least squares (OLS) estimator depends on the rate of growth of the exogenous regressors. For bounded or slowly growing regressors we prove asymptotic normality. In case of quickly growing regressors (e.g., polynomial trends) the result is negative: the OLS asymptotics cannot be derived using the conventional scheme and any diagonal normalizer.

Asymptotic Behaviour of Estimators of the Parameters of Nearly Unstable INAR(1) Models

Contributions to Statistics, 2003

A sequence of first-order integer-valued autoregressive ty p e (INAR(1)) pro cesses is investigated, where the autoregressive ty p e coefficients converge to 1. It is shown th a t th e lim iting d istribution of th e joint conditional least squares estim ators for this coefficient and for th e m ean of th e innovation is norm al. Consequences for sequences of G alton-W atso n branching processes w ith unob servable im m igration, where the m ean of th e offspring d istrib u tio n converges to 1 (which is th e critical value), are discussed. 1 In trod u ction In many practical situations one has to deal with non-negative integer-valued time series. Examples of such tim e series, known as counting processes, arise in several fields of medicine (see, e.g., Cardinal et.al. [5] and Franke and Seligmann [9]). To construct counting processes A l-O sh and Alzaid [1] proposed a particular class of models, the so-called IN A R (1) model. Later A l-O sh and Alzaid [2], Du and Li [8] and Latour [12] generalized this model by introducing the INAR(p) and GINAR(p) models. These processes can be considered as discrete analogues of the scalar-and vector-valued AR(p) processes, because their correlation structure is similar. The present paper deals with so-called nearly unstable IN A R (1) models. It is, in fact, a sequence of IN A R (1) models where the autoregressive type coefficient a n is close to one, more precisely, a n = 1-Yn/ n with Yn ^ 7, where 7 ^ 0. This parametrization has been suggested by Chan and Wei [6] for the usual A R (1) model. The main m otivation of our investigation comes from econometrics, where the so-called 'unit root problem' plays an important role (see, e.g., the monograph of Tanaka [15]). We considered in [10] the conditional least squares estim ate (CLSE)