Noncausal Bayesian Vector Autoregression

We consider Bayesian analysis of the noncausal vector autoregressive model that is capable of capturing nonlinearities and effects of missing variables. Specifically, we devise a fast and reliable posterior simulator that yields the predictive distribution as a by‐product. We apply the methods to postwar US inflation and GDP growth. The noncausal model is found superior in terms of both in‐sample fit and out‐of‐sample forecasting performance over its conventional causal counterpart. Economic shocks based on the noncausal model turn out to be highly anticipated in advance. We also find the GDP growth to have predictive power for future inflation, but not vice versa. Copyright © 2016 John Wiley & Sons, Ltd.     

Evaluating alternative models of trend inflation

With the concept of trend inflation now being widely understood to be important to the accuracy of longer-term inflation forecasts, this paper assesses alternative models of trend inflation. Reflecting the models which are common in reduced-form inflation modeling and forecasting, we specify a range of models of inflation that incorporate different trend specifications. We compare the models on the basis of their accuracies in out-of-sample forecasting, both point and density. Our results show that it is difficult to say that any one model of trend inflation is the best. Several different trend specifications seem to be about equally accurate, and the relative accuracy is somewhat prone to instabilities over time.     

Macroeconomic Forecasting Performance under Alternative Specifications of Time‐Varying Volatility

This paper compares alternative models of time‐varying volatility on the basis of the accuracy of real‐time point and density forecasts of key macroeconomic time series for the USA. We consider Bayesian autoregressive and vector autoregressive models that incorporate some form of time‐varying volatility, precisely random walk stochastic volatility, stochastic volatility following a stationary AR process, stochastic volatility coupled with fat tails, GARCH and mixture of innovation models. The results show that the AR and VAR specifications with conventional stochastic volatility dominate other volatility specifications, in terms of point forecasting to some degree and density forecasting to a greater degree. Copyright © 2014 John Wiley & Sons, Ltd.     

Mixed Causal–Noncausal Autoregressions: Bimodality Issues in Estimation and Unit Root Testing1

This paper stresses the bimodality of the likelihood function of the Mixed causal–noncausal AutoRegressions (MAR), and it is shown that the bimodality issue becomes more salient as the causal root approaches unity from below. The consequences are important as the roots of the local maxima are typically interchanged, attributing the noncausal component to the causal one and vice-versa. This severely changes the interpretation of the results, and the properties of unit root tests of the backward root are adversely affected. To circumvent the bimodality issue, this paper proposes an estimation strategy which (i) increases noticeably the probability of attaining the global MLE; and (ii) selects carefully the maximum used for the unit root test against a MAR stationary alternative.     

Mixed Causal–Noncausal Autoregressions: Bimodality Issues in Estimation and Unit Root Testing1

This paper stresses the bimodality of the likelihood function of the Mixed causal–noncausal AutoRegressions (MAR), and it is shown that the bimodality issue becomes more salient as the causal root approaches unity from below. The consequences are important as the roots of the local maxima are typically interchanged, attributing the noncausal component to the causal one and vice‐versa. This severely changes the interpretation of the results, and the properties of unit root tests of the backward root are adversely affected. To circumvent the bimodality issue, this paper proposes an estimation strategy which (i) increases noticeably the probability of attaining the global MLE; and (ii) selects carefully the maximum used for the unit root test against a MAR stationary alternative.     

Model identification for infinite variance autoregressive processes

We consider model identification for infinite variance autoregressive time series processes. It is shown that a consistent estimate of autoregressive model order can be obtained by minimizing Akaike’s information criterion, and we use all-pass models to identify noncausal autoregressive processes and estimate the order of noncausality (the number of roots of the autoregressive polynomial inside the unit circle in the complex plane). We examine the performance of the order selection procedures for finite samples via simulation, and use the techniques to fit a noncausal autoregressive model to stock market trading volume data.     

Asymmetric Quantile Persistence and Predictability: the Case of US Inflation

This article investigates the evidence of time‐variation and asymmetry in the persistence of US inflation. We compare the out‐of‐sample performance of different forecasting models and find that quantile forecasts from an Auto‐Regressive (AR) model with level‐dependent volatility are at least as accurate as the forecasts of the Quantile Auto‐Regressive model, in particular for the core inflation measures. Our results indicate that the persistence of core inflation has been relatively constant and high, but it declined for the headline inflation measures. We also find that the asymmetric persistence of inflation shocks can be mostly attributed to the positive relation between inflation level and its volatility.     

Mixed causal–noncausal autoregressions with exogenous regressors

Mixed causal–noncausal autoregressive (MAR) models have been proposed to model time series exhibiting nonlinear dynamics. Possible exogenous regressors are typically substituted into the error term to maintain the MAR structure of the dependent variable. We introduce a representation including these covariates called MARX to study their direct impact. The asymptotic distribution of the MARX parameters is derived for a class of non-Gaussian densities. For a Student likelihood, closed-form standard errors are provided. By simulations, we evaluate the MARX model selection procedure using information criteria. We examine the influence of the exchange rate and industrial production index on commodity prices.     

Transparency and inflation: What is the effect on the Brazilian economy?

This paper presents empirical evidence concerning the effect of central bank transparency on inflation considering the Brazilian case after the adoption of inflation targeting. Two indices for measuring transparency, based on forward-looking and backwardlooking views, are developed. Furthermore, empirical evidence is divided into three steps: (i) analysis of simple correlation through scatterplot diagrams; (ii) use of VAR models; and (iii) estimation of different specifications of the Phillips curve using OLS and GMM based on the structural model used by the Central Bank of Brazil (CBB). The findings allow one to conjecture that inflation expectations are well coordinated by the CBB. In short, the transparency of information by the CBB is a very important tool for guiding public expectations and thus contributes to maintain inflation under control.     

The use of monthly and quarterly data in an ARMA model

This paper deals with specification, prediction and length of interval between the observations in an ARMA model. An AR(1) model is found to be suitable for a specific monthly time series. From this series we construct two types of quarterly series and derive the corresponding ARMA models. The theoretical parameter values of the quarterly models, given the monthly model, are compared with the values found empirically when no monthly series exists. By using the variance of the predictor error, we assess the performance of all specifications in predicting up to one year ahead. We show that while the monthly model performs best in theory, the values computed directly from the estimates prove in our empirical example the quarterly models to be preferable in most cases where we are to predict more than one quarter ahead.     

New perspectives on forecasting inflation in emerging market economies: An empirical assessment

We use a broad-range set of inflation models and pseudo out-of-sample forecasts to assess their predictive ability among 14 emerging market economies (EMEs) at different horizons (1–12 quarters ahead) with quarterly data over the period 1980Q1-2016Q4. We find, in general, that a simple arithmetic average of the current and three previous observations (the RW-AO model) consistently outperforms its standard competitors—based on the root mean squared prediction error (RMSPE) and on the accuracy in predicting the direction of change. These include conventional models based on domestic factors, existing open-economy Phillips curve-based specifications, factor-augmented models, and time-varying parameter models. Often, the RMSPE and directional accuracy gains of the RW-AO model are shown to be statistically significant. Our results are robust to forecast combinations, intercept corrections, alternative transformations of the target variable, different lag structures, and additional tests of (conditional) predictability. We argue that the RW-AO model is successful among EMEs because it is a straightforward method to downweight later data, which is a useful strategy when there are unknown structural breaks and model misspecification.     

Beyond point forecasting: Evaluation of alternative prediction intervals for tourist arrivals

This paper evaluates the performances of prediction intervals generated from alternative time series models, in the context of tourism forecasting. The forecasting methods considered include the autoregressive (AR) model, the AR model using the bias-corrected bootstrap, seasonal ARIMA models, innovations state space models for exponential smoothing, and Harvey’s structural time series models. We use thirteen monthly time series for the number of tourist arrivals to Hong Kong and Australia. The mean coverage rates and widths of the alternative prediction intervals are evaluated in an empirical setting. It is found that all models produce satisfactory prediction intervals, except for the autoregressive model. In particular, those based on the bias-corrected bootstrap perform best in general, providing tight intervals with accurate coverage rates, especially when the forecast horizon is long.     

Inflation targeting and expectation anchoring: Evidence from developed and emerging market economies

Inflation expectations can be inferred from treasury yields data. Previous studies utilizing such data have found evidence for the role of inflation targeting in anchoring inflation expectations in a number of developed market economies. The goal of this paper is to extend the evidence for emerging market economies. We estimate inflation expectations from nominal treasury yields data and infer the anchoring of inflation expectations from the sensitivity of inflation expectations to current inflation rates. Our analysis shows that the effect of inflation targeting is statistically significant in emerging market economies as well as in developed market economies and that the magnitude is marginally greater in the former. Our results are robust to alternative specifications.     

Modelling Inflation Volatility

This paper discusses estimation of US inflation volatility using time‐varying parameter models, in particular whether it should be modelled as a stationary or random walk stochastic process. Specifying inflation volatility as an unbounded process, as implied by the random walk, conflicts with priors beliefs, yet a stationary process cannot capture the low‐frequency behaviour commonly observed in estimates of volatility. We therefore propose an alternative model with a change‐point process in the volatility that allows for switches between stationary models to capture changes in the level and dynamics over the past 40 years. To accommodate the stationarity restriction, we develop a new representation that is equivalent to our model but is computationally more efficient. All models produce effectively identical estimates of volatility, but the change‐point model provides more information on the level and persistence of volatility and the probabilities of changes. For example, we find a few well‐defined switches in the volatility process and, interestingly, these switches line up well with economic slowdowns or changes of the Federal Reserve Chair. Moreover, a decomposition of inflation shocks into permanent and transitory components shows that a spike in volatility in the late 2000s was entirely on the transitory side and characterized by a rise above its long‐run mean level during a period of higher persistence. Copyright © 2015 John Wiley & Sons, Ltd.     

A New Keynesian model with staggered price and wage setting under learning

This paper provides a study of the implications for economic dynamics when the central bank sets its nominal interest rate target in response to variations in wage inflation. I provide results on the existence, uniqueness, and stability under learning of rational expectations equilibrium for alternative specifications of the manner in which monetary policy responds to economic shocks when nominal rigidities are present. Monopolistically competitive producers set prices via staggered price contracts, and households set nominal wages in the same fashion. In this setting, the conditions for determinacy and learnability of rational expectations equilibrium differ from a model where only prices are sticky. I find that when the central bank responds to wage and price inflation and to the output gap, a Taylor principle for wage and price inflation arises that is related to stability under learning dynamics. In other words, a moderate reaction of the interest rate to wage inflation helps to avoid instability under learning and indeterminacy.     

Modelling the inflation process in transition economies: Empirical comparison of Poland, Hungary and Czech Republic

This paper starts from the observation that inflation in transition economies appears to be persistently high and volatile and attempts to provide some empirical characterisation of the inflation process in three such transition economies: Poland, Hungary and Czech Republic. We first consider the role of monetary growth as a major causal factor for inflation in these economies, and argue that the evidence provides rather weak support for the causal relationship. We then propose a transition economy cost-plus model and estimate this using the equilibrium-correction modelling (ECM) strategy augmented by introduction of a number of transitory factors and changes in the internal structure of the real economy which we believe may have had a significant impact on inflation in these economies. We show that this approach enables us to account for long-run inflation in these economies from the early 1980s to the present despite the turbulence of the latter part of the sample period. Our results support wage and exchange rate based inflation policies.     

USING A CGE MODEL TO IDENTIFY THE POLICY TRADE-OFF BETWEEN UNEMPLOYMENT AND INFLATION. THE EFFICIENT PHILLIPS CURVE

This paper provides a new reading of a classical economic relation: the short-run Phillips curve. Our point is that, when dealing with inflation and unemployment, policy-making can be understood as a multicriteria decision-making problem. Hence, we use so-called multiobjective programming in connection with a computable general equilibrium (CGE) model to determine the combinations of policy instruments that provide efficient combinations of inflation and unemployment. This approach results in an alternative version of the Phillips curve labelled as efficient Phillips curve. Our aim is to present an application of CGE models to a new area of research that can be especially useful when addressing policy exercises with real data. We apply our methodological proposal within a particular regional economy, Andalusia, in the south of Spain. This tool can give some keys for policy advice and policy implementation in the fight against unemployment and inflation.     

Causality and the independence phenomenon: The case of the demand for money

We examine the demand for money using causality results with data from two alternative policy regimes. For Spanish series of money and prices we obtain the same result of independence that Feige and others found with U.S. data. The result of the test for the German hyperinflation period reveals bidirectional causality. It is shown that the somehow striking results of widespread independence among economic time series do not disprove but rather confirm the existence of a true underlying causal relationship. Causality results, and independence in particular, give us testable restriction for the structural form. In the case of models for expectations in the rate of inflation, these restrictions allow us to revalidate the stability of the demand for money as postulated by the Quantity Theory.     

Multivariate subset autoregressive modelling with zero constraints for detecting ‘overall causality’

The necessary and sufficient condition to test for ‘overall causality’, i.e., the presence of Granger- causality and instantaneous causal relations, in a bivariate and trivariate autoregressive model with recursive form is discussed. It is argued that the conventional AR model (the reduced form AR) is a more straightforward and effective means of testing for ‘overall causality’. To detect instanta- neous causality it is proposed to select the best subset system in a residual regression system in conjunction with model selection criteria. The Canadian money-income-bank rate system is re-examined in this way and by using a previously proposed algorithm we identify the optimum multivariate subset AR with constraints to detect whether there is ‘overall causality’ in that system.     

Bayesian time series analysis of periodic behaviour and spectral structure

Analysis, model selection and forecasting in univariate time series models can be routinely carried out for models in which the model order is relatively small. Under an ARMA assumption, classical estimation, model selection and forecasting can be routinely implemented with the Box–Jenkins time domain representation. However, this approach becomes at best prohibitive and at worst impossible when the model order is high. In particular, the standard assumption of stationarity imposes constraints on the parameter space that are increasingly complex. One solution within the pure AR domain is the latent root factorization in which the characteristic polynomial of the AR model is factorized in the complex domain, and where inference questions of interest and their solution are expressed in terms of the implied (reciprocal) complex roots; by allowing for unit roots, this factorization can identify any sustained periodic components. In this paper, as an alternative to identifying periodic behaviour, we concentrate on frequency domain inference and parameterize the spectrum in terms of the reciprocal roots, and, in addition, incorporate Gegenbauer components. We discuss a Bayesian solution to the various inference problems associated with model selection involving a Markov chain Monte Carlo (MCMC) analysis. One key development presented is a new approach to forecasting that utilizes a Metropolis step to obtain predictions in the time domain even though inference is being carried out in the frequency domain. This approach provides a more complete Bayesian solution to forecasting for ARMA models than the traditional approach that truncates the infinite AR representation, and extends naturally to Gegenbauer ARMA and fractionally differenced models.