Norman R. Swanson

Impulse Response Functions Based on a Causal Approach to Residual Orthogonalization in Vector Autoregressions

Abstract A data-determined method for testing structural models of the errors in vector autoregressions is discussed. The method can easily be combined with prior economic knowledge and a subjective analysis of data characteristics to yield valuable information concerning model selection and specification. In one dimension, it turns out that standard t statistics can be used to test the various overidentifying restrictions that are implied by a model. In another dimension, the method compares a priori knowledge of a structural model for the errors with the properties exhibited by the data. Thus this method may help to ensure that orderings of the errors for impulse response and forecast error variance decomposition analyses are sensible, given the data. Two economic examples are used to illustrate the method.

A Model Selection Approach to Real-Time Macroeconomic Forecasting Using Linear Models and Artificial Neural Networks

We take a model selection approach to the question of whether a class of adaptive prediction models (artificial neural networks) is useful for predicting future values of nine macroeconomic variables. We use a variety of out-of-sample forecast-based model selection criteria, including forecast error measures and forecast direction accuracy. Ex ante or real-time forecasting results based on rolling window prediction methods indicate that multivariate adaptive linear vector autoregression models often outperform a variety of (1) adaptive and nonadaptive univariate models, (2) nonadaptive multivariate models, (3) adaptive nonlinear models, and (4) professionally available survey predictions. Further, model selection based on the in-sample Schwarz information criterion apparently fails to offer a convenient shortcut to true out-of-sample performance measures.

A Model-Selection Approach to Assessing the Information in the Term Structure Using Linear Models and Artificial Neural Networks

We take a model-selection approach to the question of whether forward-interest rates are useful in predicting future spot rates, using a variety of out-of-sample forecast-based model-selection criteria—forecast mean squared error, forecast direction accuracy, and forecast-based trading-system profitability. We also examine the usefulness of a class of novel prediction models called artificial neural networks and investigate the issue of appropriate window sizes for rolling-window-based prediction methods. Results indicate that the premium of the forward rate over the spot rate helps to predict the sign of future changes in the interest rate. Furthermore, model selection based on an in-sample Schwarz information criterion (SIC) does not appear to be a reliable guide to out-of-sample performance in the case of short-term interest rates. Thus, the in-sample SIC apparently fails to offer a convenient shortcut to true out-of-sample performance measures.

An introduction to stochastic unit-root processes

A class of nonlinear processes which have a root that is not constant, but is stochastic, and varying around unity is introduced. Th eprocess can be stationary for some periods, and mildly explosive for others.

Money and output viewed through a rolling window

Abstract We examine the extent to which fluctuations in the money stock anticipate (or Granger cause) fluctuations in real output using a variety of rolling window and increasing window estimation techniques. Various models are considered using simple sum as well as Divisia measures of M 1 and M 2, income, prices, and both the T-bill rate and the commercial paper rate. Findings indicate that the relation between income, money, prices, and interest rates is stable, as long as sufficient data are used, and that there is cointegration among the variables considered, although cointegration spaces become very difficult to estimate precisely when smaller windows of data are used. Further, both M 1 and M 2 are shown to be important predictors of income for the entire period from 1960:2–1996:3, based on modified versions of what we term the ‘most damaging’ specifications from Friedman and Kuttner (1993) and Thoma (1994) . Our new evidence is based in part on a rather novel model selection approach to examining the relationship between money and income.

A consistent test for nonlinear out of sample predictive accuracy

In this paper, we draw on both the consistent specification testing and the predictive ability testing literatures and propose a test for predictive accuracy which is consistent against generic nonlinear alternatives. Broadly speaking, given a particular reference model, assume that the objective is to test whether there exists any alternative model, among an infinite number of alternatives, that has better predictive accuracy than the reference model, for a given loss function. A typical example is the case in which the reference model is a simple autoregressive model and the objective is to check whether a more accurate forecasting model can be constructed by including possibly unknown (non)linear functions of the past of the process or of the past of some other process(es). We propose a statistic which is similar in spirit to that of White (2000), although our approach differs from his as we allow for an infinite number of competing models that may be nested. In addition, we allow for non vanishing parameter estimation error. In order to construct valid asymptotic critical values, we implement a conditional p-value procedure which extends the work of Inoue (1999) by allowing for non vanishing parameter estimation error.

The real-time predictive content of money for output ☆

Data on monetary aggregates are subject to periodic redefinitions, presumably in part to improve their link to measures of output. Money data are also revised on a regular basis. Taking these data imperfections into account, we reassess the evidence on the marginal predictive content of M1 and m2 for real and nominal output. In particular, by first using the latest version of the data that is available, and then using sequences of historical time series that would have been available to forecasters in real-time, we are able to provide a comprehensive assessment of whether money is useful for predicting output. We conclude that the generally significant marginal predictive content of M1 and m2 for output that is found using a recently revised data set is not duplicated in a real-time setting, although M2 is shown to remain useful when 1-year ahead forecasts are constructed using fitted vector autoregressive models.

NONPARAMETRIC BOOTSTRAP PROCEDURES FOR PREDICTIVE INFERENCE BASED ON RECURSIVE ESTIMATION SCHEMES

Our objectives in this paper are twofold. First, we introduce block bootstrap techniques that are (first order) valid in recursive estimation frameworks. Thereafter, we present two examples where predictive accuracy tests are made operational using our new bootstrap procedures. In one application, we outline a consistent test for out-of-sample nonlinear Granger causality, and in the other we outline a test for selecting amongst multiple alternative forecasting models, all of which are possibly misspecified. More specifically, our examples extend the White (2000) reality check to the case of non vanishing parameter estimation error, and extend the integrated conditional moment tests of Bierens (1982, 1990) and Bierens and Ploberger (1997) to the case of out-of-sample prediction. In both examples, appropriate re-centering of the bootstrap score is required in order to ensure that the tests have asymptotically correct size, and the need for such re-centering is shown to arise quite naturally when testing hypotheses of predictive accuracy. In a Monte Carlo investigation, we compare the finite sample properties of our block bootstrap procedures with the parametric bootstrap due to Kilian (1999); all within the context of various encompassing and predictive accuracy tests. An empirical illustration is also discussed, in which it is found that unemployment appears to have nonlinear marginal predictive content for inflation.

Bootstrap Conditional Distribution Tests in the Presence of Dynamic Misspecification

In this paper, we show the first order validity of the block bootstrap in the context of Kolmogorov type conditional distribution tests when there is dynamic misspecification and parameter estimation error. Our approach di®ers from the literature to date because we construct a bootstrap statistic that allows for dynamic misspecification under both hypotheses. We consider two test statistics; one is the CK test of Andrews (1997), and the other is in the spirit of Diebold, Gunther and Tay (1998). The limiting distribution of both tests is a Gaussian process with a covariance kernel that reflects dynamic misspecification and parameter estimation error. In order to provide valid asymptotic critical values we suggest an extention of the empirical process version of the block bootstrap to the case of non vanishing parameter estimation error. The findings from Monte Carlo experiments show that both statistics have good finite sample properties for samples as small as 500 observations.

Are Statistical Reporting Agencies Getting It Right? Data Rationality and Business Cycle Asymmetry

This article provides new evidence on the rationality of early releases of industrial production (IP) and producer price index (PPI) data. Rather than following the usual practice of examining only first available and fully revised data, we examine the entire revision history for each variable. Thus we are able to assess, for example, whether earlier releases of data are in any sense “less” rational than later releases, and when data become rational. Our findings suggest that seasonally unadjusted IP and PPI become rational after approximately 3–4 months, whereas seasonally adjusted versions of these series remain irrational for at least 6–12 months after initial release. For all variables examined, we find evidence that the remaining revision is predictable from its own past or from publicly available information in other economic and financial variables. In addition, we find a clear increase in the volatility of revisions during recessions, suggesting that early data releases are less reliable in tougher economic times. Finally, we explore whether nonlinearities in economic behavior manifest themselves in the form of nonlinearities in the rationality of early releases of economic data, by separately analyzing expansionary and recessionary economic phases and by allowing for structural breaks. These types of nonlinearities are shown to be prevalent and in some cases to lead to incorrect inferences concerning data rationality when they are not taken into account.