Charles S. Bos

Inflation, forecast intervals and long memory regression models

We examine recursive out-of-sample forecasting of monthly postwarU.S. core inflation and log price levels. We use theautoregressive fractionally integrated moving average model withexplanatory variables (ARFIMAX). Our analysis suggests asignificant explanatory power of leading indicators associatedwith macroeconomic activity and monetary conditions forforecasting horizons up to two years. Even after correcting forthe effect of explanatory variables, there is conclusive evidenceof both fractional integration and structural breaks in the meanand variance of inflation in the 1970s and 1980s and weincorporate these breaks in the forecasting model for the 1980sand 1990s. We compare the results of the fractionally integratedARFIMA(0,d,0) model with those for ARIMA(1,d,1) models withfixed order of d=0 and d=1 for inflation. Comparing meansquared forecast errors, we find that the ARMA(1,1) model performsworse than the other models over our evaluation period 1984-1999.The ARIMA(1,1,1) model provides the best forecasts, but itsmulti-step forecast intervals are too large.

Does the Canadian economy suffer from Dutch disease

We argue that the failure to disentangle the evolution of the Canadian currency from the U.S. currency leads to potentially incorrect conclusions regarding the case of Dutch disease in Canada. We propose a new approach that is aimed at extracting both currency components and energy- and commodity-price components from observed exchange rates and prices. We first analyze the separate influence of commodity prices on the Canadian and the U.S. currency components. We then estimate the separate impact of the two currency components on the shares of manufacturing employment in Canada. We show that between 33 and 39 per cent of the manufacturing employment loss that was due to exchange rate developments between 2002 and 2007 is related to the Dutch disease phenomenon. The remaining proportion of the employment loss can be ascribed to the weakness of the U.S.

A Comparison of Marginal Likelihood Computation Methods

In a Bayesian analysis, different models can be compared on the basis of theexpected or marginal likelihood they attain. Many methods have been devised to compute themarginal likelihood, but simplicity is not the strongest point of most methods. At the sametime, the precision of methods is often questionable.In this paper several methods are presented in a common framework. The explanation of thedifferences is followed by an application, in which the precision of the methods is testedon a simple regression model where a comparison with analytical results is possible.

State Space Models With a Common Stochastic Variance

This article considers a combination of the linear Gaussian state space model and the stochastic volatility model. The focus is on the simultaneous estimation of parameters related to the stochastic processes of both the mean and variance parts of the model. Kalman filter and Monte Carlo maximum likelihood methods lead to an elegant estimation procedure for which the simulation error can be made arbitrarily small. The standard asymptotic properties of maximum likelihood estimators apply as a result. A Monte Carlo simulation study is carried out to investigate the small-sample properties of the estimation procedure. The modeling and forecasting techniques within our new framework are illustrated for U.S. monthly inflation rates.

Long memory with stochastic variance model: A recursive analysis for US inflation

The time series characteristics of postwar US inflation have been found to vary over time. The changes are investigated in a model-based analysis where the time series of inflation is specified by a long memory autoregressive fractionally integrated moving average process with its variance modelled by a stochastic volatility process. Estimates of the parameters are obtained by a Monte Carlo maximum likelihood method. A long sample of monthly core inflation is considered in the analysis as well as subsamples of varying length. The empirical results reveal major changes in the variance, in the order of integration, in the short memory characteristics, and in the volatility of volatility. The findings provide further evidence that the time series properties of inflation are not stable over time.

Long Memory Modelling of Inflation with Stochastic Variance and Structural Breaks

We investigate changes in the time series characteristics of postwar U.S. inflation. In a model-based analysis the conditional mean of inflation is specified by a long memory autoregressive fractionally integrated moving average process and the conditional variance is modelled by a stochastic volatility process. We develop a Monte Carlo maximum likelihood method to obtain efficient estimates of the parameters using a monthly dataset of core inflation for which we consider different subsamples of varying size. Based on the new modelling framework and the associated estimation technique, we find remarkable changes in the variance, in the order of integration, in the short memory characteristics and in the volatility of volatility.

Relating Stochastic Volatility Estimation Methods

This discussion paper led to a chapter in: (L. Bauwens, C.M. Hafner & S. Laurent (Eds.)), Relating stochastic volatility estimation methods (pp. 147-174). New York: Wiley. Estimation of the volatility of time series has taken off since the introduction of the GARCH and stochastic volatility models. While variants of the GARCH model are applied in scores of articles, use of the stochastic volatility model is less widespread. In this article it is argued that one reason for this difference is the relative difficulty of estimating the unobserved stochastic volatility, and the varying approaches that have been taken for such estimation. In order to simplify the comprehension of these estimation methods, the main methods for estimating stochastic volatility are discussed, with focus on their commonalities. In this manner, the advantages of each method are investigated, resulting in a comparison of the methods for their efficiency, difficulty-of-implementation, and precision.

Time series models with a common stochastic variance for analysing economic time series

This discussion paper led to an article in Statistica Neerlandica (2003). Vol. 57, issue 4, pages 439-469. The linear Gaussian state space model for which the common variance istreated as a stochastic time-varying variable is considered for themodelling of economic time series. The focus of this paper is on thesimultaneous estimation of parameters related to the stochasticprocesses of the mean part and the variance part of the model. Theestimation method is based on maximum likelihood and it requires thesubsequent uses of the Kalman filter to treat the mean part andsampling techniques to treat the variance part. This approach leads tothe evaluation of the exact likelihood function of the model subject tosimulation error. The standard asymptotic properties of maximumlikelihood estimators apply as a result. A Monte Carlo study is carriedout to investigate the small-sample properties of the estimationprocedure. We present two illustrations which are concerned with themodelling and forecasting of two U.S. macroeconomic time series:inflation and industrial production.

A Quantile-based Realized Measure of Variation: New Tests for Outlying Observations in Financial Data

In this article we introduce a new class of test statistics designed to detect the occurrence of abnormal observations. It derives from the joint distribution of moment- and quantile-based estimators of power variation sigma^r, under the assumption of a normal distribution for the underlying data. Our novel tests can be applied to test for jumps and are found to be generally more powerful than widely used alternatives. An extensive empirical illustration for high-frequency equity data suggests that jumps can be more prevalent than inferred from existing tests on the second or third moment of the data.

Models with Time-Varying Mean and Variance: A Robust Analysis of U.S. Industrial Production

Many seasonal macroeconomic time series are subject to changes in their means and variances over a long time horizon. In this paper we propose a general treatment for the modelling of time-varying features in economic time series. We show that time series models with mean and variance functions depending on dynamic stochastic processes can be sufficiently robust against changes in their dynamic properties. We further show that the implementation of the treatment is relatively straightforward. An illustration is given for monthly U.S. Industrial Production. The empirical results including estimates of time-varying means and variances are discussed in detail.