Choice Of Lag Length Research Articles

Aggregate Hours and Local Projections with Long-Run Restrictions

I extend the local projections method to identify structural shocks using long-run restrictions. I show that the proposed estimator is substantially more robust than structural VARs (SVARs) to both the choice of lag length and the order of integration of the endogenous variables using data from a standard real business cycle (RBC) model. Benchmark simulations show that the proposed estimator can yield substantial reductions in both the bias and mean squared error of estimated impulse response functions relative to SVARs, particularly at short forecast horizons. In all cases, the proposed estimator correctly estimates the direction of the contemporaneous response and the shape of the full impulse response function, and can eliminate virtually all of the bias for some specification choices. Using my proposed estimator and data obtained from the Bureau of Labor Statistics, I then estimate the response of aggregate labor hours to productivity shocks. In contrast to much of the evidence based on SVARs, I find that labor hours rise in response to positive productivity shocks and subsequently follow a hump shaped profile. This result is robust to a number of specification choices and provides new evidence in support of the standard RBC model.

On inferences about lag effects using lag models in air pollution time-series studies

The choice of lag length is a matter of uncertainty in air pollution time-series studies. Lag models and model selections are widely used for inferences about lag effects, but there is lack of discussion on the integration of the two. We aimed to provide theoretical discussion on the performance of lag models, and the impact of model selections on inferences about lag effects. Bias and model selections based upon information criteria, statistical significance, effect size, and model averaging were discussed in the context of lag analysis. A simulation with eight of PM2.5-mortality relation scenarios was also conducted in order to explore the performances of lag models and to compare the model selections. The application of lag models with an insufficient lag interval taken into account (i.e. insufficient lag models) provides biased estimates. We provided features of the model selections and showed their pitfalls in lag analysis of air pollution time-series studies. We also discussed limitations of meta-analysis which fails to consider the application of different lag models in individual studies. To foster exploration on air pollution-lag-response relations with relevant tools, we encourage researchers to compare different lag models in terms of effect estimates and variance estimates, and to report their favored models and competing models together based upon scientific knowledge supporting lag-response relations.

Stationarity‐Based Approach for the Selection of Lag Length in Cointegration Analysis Used for Structural Damage Detection

AbstractCointegration has been recently brought to structural health monitoring (SHM) as a new methodology for dealing with the problem of environmental and/or operational variability in monitored structures. However, it is well known that the choice of lag length in cointegration analysis has a strong influence on damage detection results. The article presents a new approach for optimal lag length selection in cointegration analysis used for structural damage detection. This new method is based on stationarity analysis of data representing undamaged condition. The proposed method is validated using Lamb wave data under the effects of temperature variations and vibroacoustic data obtained from nonlinear vibroacoustic modulation experiments with different low‐frequency vibration (or modal) excitations. The results demonstrate the effectiveness of the method for structural damage detection based on SHM data heavily affected by environmental or operational conditions.

TU‐C‐351‐10: Inference of Hysteretic Respiratory Tumour Motion From External Surrogates: A State Augmentation Approach

Purpose: To infer internal respiration‐induced tumor motion from external surrogate. To systematically resolve mapping ambiguity caused by breathing hysteresis. Method and Materials: We propose a state‐augmentation approach to capture system dynamics. Concatenating real‐time surrogate observations with their time‐delayed records describes the state information in a higher‐dimensional state space. In such space, inhale and exhale “stages” are naturally separated due to the incorporated velocity contents. Any existing inference model migrates effortlessly into this framework. We illustrate the idea with simple polynomial inference models, and derive a closed‐form solution for optimal choice of model parameters. Choice of lag length is demonstrated empirically to be robust and may be chosen offline. This approach is tested on synchronized recordings of internal tumor trajectories and external fiducial marker readouts from eight lung patients (multiple fractions and readings) with a Mitsubishi real‐time radiotherapy (RTRT) system. Internal recording is obtained by fluoroscopic tracking of implanted 1.5mm‐diameter gold ball bearings around the tumor and external surrogates measure relative abdominal skin positions. Results: Examination of trajectories in the augmented state‐space suggests the existence of a consistent and unambiguous inference map. Empirical tests with clinical data show that using state augmentation decreases the 3D RMSE from 2.01mm to 1.74mm with the linear model and 1.93mm to 1.63 with the quadratic model. Paired student‐t tests with P‐values on the order of 10e‐13 indicate statistical significance of the improvement. Conclusion: We proposed a simple state‐augmentation approach to implicitly incorporate the hysteretic internal‐external response pattern into the estimation framework with any existing inference model. For the general class of correspondence models that are linear in their parameters, closed‐form solutions for the optimal parameter values and the error evaluations are derived. Tests with clinical data demonstrate statistically significant improvement over direct models.This work is sponsored by NIH P01‐CA59827 and Barbour Scholarship.

Cointegration analysis and the choice of lag length

This article investigates the effects of the choice of lag length on the estimation of long run cointegration relationships using the Johansen estimation procedure. This issue is of particular interest to applied researchers using time series data, see for example Awokuse (2005), Bacchiocchi et al . (2005), Gallegati (2005), Gomes and Paz (2005), Hasan (2005) and Pieroni and Ricciarelli (2005), among many others. An empirical example is used to demonstrate some of the issues that applied researchers face when they wish to use cointegration analysis. First, the number of lags to include in the model must be determined. However, different lag length selection criteria often lead to a different conclusion regarding the optimal lag order that should be used. Second, as demonstrated in this article, the choice of lag length can drastically affect the results of the cointegration analysis.

Lag length estimation in large dimensional systems

We study the impact of the system dimension on commonly used model selection criteria (AIC, BIC, HQ) and LR based general to specific testing strategies for lag length estimation in VARs. We show that AIC's well known overparameterization feature becomes quickly irrelevant as we move away from univariate models, with the criterion leading to consistent estimates under sufficiently large system dimensions. Unless the sample size is unrealistically small, all model selection criteria will tend to point towards low orders as the system dimension increases, with the AIC remaining by far the best performing criterion. This latter point is also illustrated via the use of an analytical power function for model selection criteria. The comparison between the model selection and general to specific testing strategy is discussed within the context of a new penalty term leading to the same choice of lag length under both approaches.

Money, prices and causality: monetarist versus structuralist explanations using pooled country evidence

The direction of causality between changes in money supply and aggregate prices has long been a matter of controversy between structuralists and monetarists. This paper addresses deficiencies in this literature in three ways. First, a large sample of countries with alternate measures of money and price variables is used to evaluate the evidence on money, inflation and causality. Second, combined data are tested for causality, with the combinations based on variables suggested by the literature - level of per capita income, magnitude of inflation, degree of financial market development, and independence of the central bank. Finally, because the choice of lag length is often arbitrary, results are generated with varying lags and consistency across different lag periods looked for. Two presentation methods are developed - categorical and graphical. Evidence of structural inflation, was found only in Chile and Sri Lanka. Evidence of money supply exogeneity on the other hand was found to be strongest in Kuwait, Paraguay and the USA. Most countries exhibited mixed evidence of money supply endogeneity, with bidirectional causation between money supply and aggregate prices a common result.

Fractional Bayesian Lag Length Inference in Multivariate Autoregressive Processes

The posterior distribution of the number of lags in a multivariate autoregression is derived under an improper prior for the model parameters. The fractional Bayes approach is used to handle the indeterminacy in the model selection caused by the improper prior. An asymptotic equivalence between the fractional approach and the Schwarz Bayesian Criterion (SBC) is proved. Several priors and three loss functions are entertained in a simulation study which focuses on the choice of lag length. The fractional Bayes approach performs very well compared to the three most widely used information criteria, and it seems to be reasonably robust to changes in the prior distribution for the lag length, especially under the zero‐one loss.

Lag-length selection in VAR-models using equal and unequal lag-length procedures

It is well known that inference in vector autoregressive models depends crucially on the choice of lag-length. Various lag-length selection procedures have been suggested and evaluated in the liter ...

REGIME-SENSITIVE COINTEGRATION WITH AN APPLICATION TO INTEREST-RATE PARITY

There exist a variety of reasons for the failure to find a unique cointegrating relationship between economic time series where one would normally be expected on the basis of economic theory. Among these are the testing procedure, the span of the data set, the choice of lag length in generating the test statistic, the presence of structural breaks, and the presence of cointegration only beyond some threshold. We propose the concept of regime-sensitive cointegration whereby the underlying series need not be cointegrated at all times. We show that cointegration can be switched off when a common stochastic trend is added. Alternatively, cointegration can be switched on or off because series normally believed to contain a unit actually do not. This implies that a linear combination of such variables need not be cointegrated. To illustrate the concept empirically, we test the hypothesis of interest-rate parity, and related hypotheses, using daily Eurorates for the United States and Canada.

POLICY INEFFECTIVENESS: TESTS WITH AUSTRALIAN DATA*

This paper tests, using Australian data, the proposition that only unanticipated monetary growth infl uences real variables. The methodology used is that of L. Leiderman ( 1980) and F. S. Mishkin (1982). In tests using the unemployment rate as a real variable, it is found that the data decisively reject the p olicy-ineffectiveness proposition and its subsidiary hypotheses of st ructural neutrality and rational expectations. This confirms results obtained for Australia by J. Horne and I. M. McDonald (1984) using a different approach. The results are found to be robust with respect t o choice of lag length and choice of monetary aggregate but not with respect to choice of real variable-the results are mixed when the une mployment rate is replaced by the rate of growth of real GDP. Copyright 1987 by Blackwell Publishers Ltd/University of Adelaide and Flinders University of South Australia

The Andersen-Jordan equation revisited

This paper deals with two common econometric criticisms of the Andersen and Jordan (1968)equation—the endogeneity of the right-hand-side variables and the ad hoc implementation of Almon's polynomial distributed lag estimation technique. Using the original Andersen-Jordan data, we found no support for either criticism. While we note that the PDL specification of their equation is highly unusual, we found that their policy conclusions do not depend their particular choice of lag length or polynomial degree or their imposition of the endpoint constraints. Furthermore, the right-hand-side variables were found to satisfy necessary conditions for statistical exogeneity.