A proof of a relationship between the generalized variances for associated autoregressive and moving average processes

Summary In this paper we give a simple proof of the result that, for any integer,r, given two processes of orderr, one autoregressive and the other moving average but both with the same parameters, then the generalized variance of all ordersk2r, for the autoregressive process, is exactly equal to the infinite order generalized variance for the moving average process.     

Finite sample properties of estimators for autoregressive moving average models

We analyze by simulation the properties of three estimators frequently used in the analysis of autoregressive moving average time series models for both nonseasonal and seasonal data. The estimators considered are exact maximum likelihood, exact least squares and conditional least squares. For samples of the size commonly found in economic applications, the estimators are compared in terms of bias, mean squared error, and predictive ability. The reliability of the usually calculated confidence intervals is assessed for the maximum likelihood estimator.     

Problems with the estimation of moving average processes

As a consequence of the well-known underidentification of the moving average model unless the parameter space is restricted, Maximum Likelihood and other estimators possess properties which can pose problems for estimation when a root of the process is close to the unit circle. The behaviour of the estimators is studied both through the analytic properties of their criterion functions and by Monte Carlo simulation. Conclusions about the choice of estimator are drawn, in particular regarding the treatment of the pre-sample residuals.     

Testing for autoregressive against moving average errors in the linear regression model

This paper presents a new approach to hypotheses testing problems which are non-nested in the classical sense and which concern the covariance matrix of the disturbance vector of the linear regression model. In particular, the application of the approach to testing for AR(1) disturbances against MA(1) disturbances is explored in some detail. Practical difficulties are discussed and selected upper bounds for the test's five percent significance points are tabulated. The small sample power of four versions of the new test are compared empirically and a clear conclusion is made in regard to the best overall test.     

Estimation and forecasting in vector autoregressive moving average models for rich datasets

We address the issue of modelling and forecasting macroeconomic variables using rich datasets by adopting the class of Vector Autoregressive Moving Average (VARMA) models. We overcome the estimation issue that arises with this class of models by implementing an iterative ordinary least squares (IOLS) estimator. We establish the consistency and asymptotic distribution of the estimator for weak and strong VARMA(p,q) models. Monte Carlo results show that IOLS is consistent and feasible for large systems, outperforming the MLE and other linear regression based efficient estimators under alternative scenarios. Our empirical application shows that VARMA models are feasible alternatives when forecasting with many predictors. We show that VARMA models outperform the AR(1), ARMA(1,1), Bayesian VAR, and factor models, considering different model dimensions.     

Discriminating between autoregressive forms: A Monte Carlo comparison of Bayesian and ad hoc methods

The paper considers the problem of discriminating between the autoregressive forms of a Koyck distributed lag model and a regression model with autocorrelated distrubances. Several interpretations of an ad hoc rule-of-thumb suggested by Griliches are compared with Bayesian posterior odds analysis in a Monte Carlo experiment. The Bayesian analysis is generally superior to the rules-of-thumb, the latter exhibiting large probabilities of type I error, and low power. The rules-of-thumb excessively favour the distributed lag model, while the Bayesian method is free from such bias. All methods improve with increased sample size.     

Asymptotic properties of Monte Carlo estimators of diffusion processes

This paper studies the limit distributions of Monte Carlo estimators of diffusion processes. We examine two types of estimators based on the Euler scheme, one applied to the original processes, the other to a Doss transformation of the processes. We show that the transformation increases the speed of convergence of the Euler scheme. We also study estimators of conditional expectations of diffusions. After characterizing expected approximation errors, we construct second-order bias-corrected estimators. We also derive new convergence results for the Mihlstein scheme. Illustrations of the results are provided in the context of simulation-based estimation of diffusion processes.     

A Monte Carlo study of ranked efficiency estimates from frontier models

Parametric stochastic frontier models yield firm-level conditional distributions of inefficiency that are truncated normal. Given these distributions, how should one assess and rank firm-level efficiency? This study compares the techniques of estimating (a) the conditional mean of inefficiency and (b) probabilities that firms are most or least efficient. Monte Carlo experiments suggest that the efficiency probabilities are easier to estimate (less noisy) in terms of mean absolute percent error when inefficiency has large variation across firms. Along the way we tackle some interesting problems associated with simulating and assessing estimator performance in the stochastic frontier model.     

A Monte Carlo permutation test for co-occurrence data

Researchers commonly use co-occurrence counts to assess the similarity of objects. This paper illustrates how traditional association measures can lead to misguided significance tests of co-occurrence in settings where the usual multinomial sampling assumptions do not hold. I propose a Monte Carlo permutation test that preserves the original distributions of the co-occurrence data. I illustrate the test on a dataset of organizational categorization, in which I investigate the relations between organizational categories (such as “Argentine restaurants” and “Steakhouses”).     

A characterization of vector autoregressive processes with common cyclical features

This paper presents necessary and sufficient conditions for the existence of common cyclical features in Vector Auto Regressive (VAR) processes integrated of order 0, 1, 2, where the common cyclical features correspond to common serial correlation (CS), commonality in the final equations (CE) and co-dependence (CD). The results are based on local rank factorizations of the reversed AR polynomial around the poles of its inverse. All processes with CS structures are found to present also CE structures and vice versa. The presence of CD structures, instead, implies the presence of both CS and CE structures, but not vice versa. Characterizations of the CS, CE, CD linear combinations are given in terms of linear subspaces defined in the local rank factorizations.     

面板数据单位根检验的一个简明蒙特卡洛实验框架

本文考虑到构成面板数据之横截面时间序列扰动项之间的关联性和异质性,设计出一个简明的蒙特卡洛实验框架以生成面板数据单位根检验统计值之有限样本密度分布和对应临界值。我们设计的蒙特卡洛框架提供了一个简明的可操作平台,可以运用于涉及到面板数据单位根检验的相关实证研究。     

面板数据协整关系检验的一个简明蒙特卡洛实验框架

体现处于考察中的面板数据之问的样本关联性,本文设计出一个简明蒙特卡洛实验框架以生成单一方程式面板数据之间协整关系检验统计值之有限样本密度分布及对应临界值。本文的蒙特卡洛实验框架提供了一个简明的可操作平台,可以运用于涉及面板数据协整关系检验的相关实证研究。为检测所发展的计量分析方法的可操作性与适用性,本文给出了相关应用实例。     

The (mis)specification of discrete duration models with unobserved heterogeneity: A Monte Carlo study

Empirical researchers usually prefer statistical models that can be easily estimated with the help of commonly available software packages. Sequential binary models with or without normal random effects are an example of such models that can be adopted to estimate discrete duration models with unobserved heterogeneity. But an easy-to-implement estimation may incur a cost. In this paper we conduct a Monte Carlo simulation to evaluate the consequences of omitting or misspecifying the unobserved heterogeneity distribution in single-spell discrete duration models.     

A bootstrap theory for weakly integrated processes

This paper develops a bootstrap theory for models including autoregressive time series with roots approaching to unity as the sample size increases. In particular, we consider the processes with roots converging to unity with rates slower than n^-1$n^{-1}$. We call such processes weakly   integrated processes. It is established that the bootstrap relying on the estimated autoregressive model is generally consistent for the weakly integrated processes. Both the sample and bootstrap statistics of the weakly integrated processes are shown to yield the same normal asymptotics. Moreover, for the asymptotically pivotal statistics of the weakly integrated processes, the bootstrap is expected to provide an asymptotic refinement and give better approximations for the finite sample distributions than the first order asymptotic theory. For the weakly integrated processes, the magnitudes of potential refinements by the bootstrap are shown to be proportional to the rate at which the root of the underlying process converges to unity. The order of boostrap refinement can be as large as o(n^-1/2+?)$o(n^{-1/2+?})$ for any ?>0$?>0$. Our theory helps to explain the actual improvements observed by many practitioners, which are made by the use of the bootstrap in analyzing the models with roots close to unity.     

The standard error of moving average smoothed equipercentile equating

A very important aspect of virtually any kind of systematic investigation is to be able to identify whether two entities are different, and, almost equivalently, whether they are the same. We need to be sure that measurements made at different time in different places by different experimenters are equivalent. To do this in the social sciences, the procedure of equating is necessary to be able to compare measurements made using different instruments. Small sample sizes can lead to apparent jaggedness in the formulae for equating two quantities, and some kind of smoothing procedure is frequently necessary when dealing with relatively small samples. A large-sample formula is developed for the standard error of moving average smoothed equipercentile equating on a single sample. An example is given of the application in equating two versions of a reading test, and the results are verified using a bootstrap procedure. The large sample formula gives a result that is close to the bootstrap procedure, except at very sparse frequencies.     

Small-sample properties of dimensionality statistics for fitting VAR models to aggregate economic data: A Monte Carlo study

The analysis of aggregate economic phenomena by VAR's as suggested by Sims often results in a small sample relative to the number of estimated parameters. Since the model is identified by a dimensionality criterion, the small-sample properties of available criteria are important. This paper presents a study of small-sample properties for six criteria with Monte Carlo methods. It is found that no criterion performs well, and that underfitting of models may be quite common.     

Time and causality: A Monte Carlo assessment of the timing-of-events approach

We present new Monte Carlo evidence regarding the feasibility of separating causality from selection within non-experimental duration data, by means of the non-parametric maximum likelihood estimator (NPMLE). Key findings are: (i) the NPMLE is extremely reliable, and it accurately separates the causal effects of treatment and duration dependence from sorting effects, almost regardless of the true unobserved heterogeneity distribution; (ii) the NPMLE is normally distributed, and standard errors can be computed directly from the optimally selected model; and (iii) unjustified restrictions on the heterogeneity distribution, e.g., in terms of a pre-specified number of support points, may cause substantial bias.