Bayesian model averaging and identification of structural breaks in time series

Bayesian Model Averaging (BMA) is used for testing for multiple break points in univariate series using conjugate normal-gamma priors. This approach can test for the number of structural breaks and produce posterior probabilities for a break at each point in time. Results are averaged over specifications including: stationary; stationary around trend and unit root models, each containing different types and number of breaks and different lag lengths. The procedures are used to test for structural breaks on 14 annual macroeconomic series and 11 natural resource price series. The results indicate that there are structural breaks in all of the natural resource series and most of the macroeconomic series. Many of the series had multiple breaks. Our findings regarding the existence of unit roots, having allowed for structural breaks in the data, are largely consistent with previous work.     

TESTS OF UNIT ROOTS AND COINTEGRATION HYPOTHESES IN ECONOMETRIC MODELS*

A number of statistical procedures for testing the unit roots hypotheses and the cointegration hypothesis have been proposed by statisticians and econometricians. This paper unifies many of the previous studies on unit roots tests and cointegration tests in the framework of a multivariate regression model and develops some new test statistics. We give a convenient quadratic representation of the limiting distributions of test statistics using stochastic integrals with respect to Brownian motions. The test procedures in this paper include the statistics for testing the unit root, the double unit roots, the seasonal unit roots, and the cointegrating relations for special cases. We also discuss some useful generalizations of unit roots tests and cointegration tests for empirical studies.     

An application of a new seasonal unit root test to inflation

In this paper, we apply the modified seasonal unit root test with seasonal level shifts at unknown time proposed by Popp (2007) to the G7 inflation rate. We also study the power properties of this test and generate critical values for a range of different break points and sample sizes. We find that there is a non-seasonal unit root in Canada's inflation rate, a semi-annual unit root in Germany's inflation rate, and no seasonal unit root at the annual frequency for any of the G7 countries.     

Testing for a unit root in the presence of stochastic volatility and leverage effect

Previous studies have shown that the stationary and nonstationary time-varying volatilities have different implications on the unit root test. In this paper, we provide a Bayesian unit root test for an AR(1) model with stochastic volatility and leverage effect. Monte Carlo simulations show that the proposed Bayesian unit root test statistic achieves good finite sample properties and is robust to the stationarity of stochastic volatility.     

Stationarity and structural breaks — evidence from classical and Bayesian approaches

The purpose of this paper is to analyze and compare the results of applying classical and Bayesian methods to testing for a unit root in time series with a single endogenous structural break. We utilize a data set of macroeconomic time series for the Mexican economy similar to the Nelson–Plosser one. Under both approaches, we make use of innovational outlier models allowing for an unknown break in the trend function. Classical inference relies on bootstrapped critical values, in order to make inference comparable to the finite sample Bayesian one. Results from both approaches are discussed and compared.     

The behaviour of seasonal unit root tests under neglected local drifts

This paper analyses the limit distributions of the seasonal unit root test procedures proposed by Dickey, Hasza and Fuller (1984) and Hylleberg, Engle, Granger and Yoo (1990), when local trends at different frequencies are present in data generation processes, but ignored in the test regressions used. The findings presented explicitly show that neglected deterministic trends have negative effects on the distributions of the test statistics. Analytical observations and Monte Carlo simulations reveal that seasonal unit root test statistics become severely undersized as the values of standardized local trends increase. Hence, failure to consider local trends may often bear the undesirable effect of biasing decisions towards non-rejection of unit roots.Received: February 2001, Accepted: September 2001, JEL Classification: C12, C22Paulo M. M. Rodrigues: I am thankful to two anonymous referees for their detailed and useful comments and suggestions.     

Testing volatility persistence on Markov switching stochastic volatility models

In the literature, some researchers found that the high persistence of the volatility can be caused by Markov regime switching. This concern can be reflected as a unit root problem on the basis of Markov switching models. In this paper, our main purpose is to provide a Bayesian unit root testing approach for Markov switching stochastic volatility (MSSV) models. We illustrate the developed approach using S&P 500 daily return covering the subprime crisis started in 2008.     

On the Stationarity of Current Account Deficits in the European Union

In this paper, we test for the stationarity of EU current account deficits. Our testing strategy addresses two key concerns with regard to unit‐root panel data testing, namely (i) the identification of which panel members are stationary, and (ii) the presence of cross‐sectional dependence. For this purpose, we employ an AR‐based bootstrap approach to the Hadri (2000 ) test. While there is only mixed evidence that current account stationarity applies when examining individual countries, this does not appear to be the case when considering panels comprising both EU and non‐EU members.     

Assessing French inflation persistence with impulse saturation break tests and automatic general-to-specific modelling

This article has three different motivations. Firstly, we wish to contribute to the debate on whether French inflation has been persistent since the mid-eighties. Empirical evidence in this domain has been mixed. We use the standard method of testing for breaks in the mean of the inflation series to conclude whether possible unit root findings are the result of neglected breaks. Then, we build standard autoregressive representations of inflation, using an automatic general-to-specific approach. We conclude against inflation persistence in the sample period, and the point estimates of persistence we obtain are several percentage points below those achieved with other break tests and model selection methods. Moreover, our final model is congruent. Secondly, we provide the first empirical application of the new impulse saturation break test. The resulting estimates of the break dates are in line with other literature findings and have a sound economic meaning, confirming the good performance the test had revealed in theoretical and simulation studies. Finally, we also illustrate the shortcomings of the Bai–Perron test when applied to a small sample with high serial correlation. Indeed, we show the Bai–Perron break dates’ estimates would not allow us to build a congruent autoregressive representation of inflation.     

Instability in cointegration regressions: a brief review with an application to money demand in Portugal

This study addresses some modelling questions related to the possibility of structural change in models with nonstationary variables. Focusing on cointegration issues, some methodological aspects are discussed, attempting to integrate coherently the several steps of the modelling strategy. These range from unit root to cointegration testing and to testing for instability in the cointegration vector. An empirical example with Portuguese data tries to illustrate the usefulness of this approach, where a simple money demand function is estimated using an error-correction model (ECM). If a break is explicitly allowed in the cointegration vector the forecasting performance of the ECM improves.     

Searching for the Fed’s reaction function

There is still some doubt about those economic variables that really matter for the Fed’s decisions. In comparison with other estimations, this study uses the approach of Bayesian model averaging (BMA). The estimations show that over the long-run inflation, unemployment rates and long-term interest rates are the crucial variables in explaining the Federal Funds Rate. In the other two estimation samples, also the fiscal deficit and monetary aggregates were of relevance. There is also evidence for interest rate smoothing. In addition, we account for parameter instability by combining BMA with time-varying coefficient (TVC) modelling. We find strong evidence for structural breaks. Finally, a model average is constructed via an TVC-BMA approach.     

Testing for Seasonal Fractional Roots in German Real Output

Abstract. This paper examines the seasonal structure of German real GNP per capita by using a version of Robinson's (1994) tests which is suitable in the context of seasonality. This method has several advantages over alternative approaches when testing for seasonal unit roots. First, unlike standard tests, which are nested in AR alternatives, it is embedded in fractional alternatives. Second, it allows testing at the zero frequency and at each of the seasonal frequencies separately. Third, it makes it possible to test for different orders of integration at each of the frequencies simultaneously. The empirical analysis suggests that the real output series may have a unit root at the zero frequency, and fractional rather than unit roots at the seasonal ones. This is in contrast to the findings reported by Lutkepohl et al. (1999) in their study on German money demand, and shows the importance of modelling the seasonal features of the data in alternative ways.     

Bayesian Estimation and Unit Root Test for Logistic Smooth Transition Autoregressive Process

The paper considers nonlinear logistic smooth transition autoregressive (LSTAR) process and aims to detect the unit root under the null hypothesis of a random walk process against the alternative of a stationary LSTAR process and to estimate the parameters of the process in Bayesian framework using MCMC. The simulation study is carried out for investigating the performance of the Bayes estimators for parameters and Bayesian unit root test and it has been observed that the estimates of parameters of the LSTAR process are close to the true parameter values. It has been observed that the Bayesian unit root test performs well and the power of the test is high even for the boundary cases having root close to unity, at least when the sample size is large. Since the LSTAR models are widely applied for real exchange rate modeling, the theoretical results are illustrated empirically for the real exchange rates of ten OCED countries.

     

Model uncertainty and aggregated default probabilities: new evidence from Austria

Understanding the determinants of aggregated corporate default probabilities (PDs) has attracted substantial research interest over the past decades. This study addresses two major difficulties in understanding the determinants of aggregate PDs: model uncertainty and multicollinearity among the regressors. We present Bayesian model averaging (BMA) as a powerful tool that overcomes model uncertainty. Furthermore, we supplement BMA with ridge regression to mitigate multicollinearity. We apply our approach to an Austrian data set. Our findings suggest that factor prices like short-term interest rates (STIs) and energy prices constitute major drivers of default rates, while firms’ profits reduce the expected number of failures. Finally, we show that the results of our model are fairly robust with respect to the choice of the BMA parameters.     

Are business cycles stationary fluctuations around a deterministic trend? Empirical evidence from 79 developing countries

There is a large literature that tests the univariate time series properties of the real output series following the seminal work of Nelson and Plosser (1982). Whether or not real output is characterized by a unit root process has important implications. A unit root in real output, for instance, is inconsistent with the notion that business cycles are stationary fluctuations around a deterministic trend. In this paper, we investigate the univariate time series properties of real output for 79 developing countries using the conventional augmented Dickey and Fuller (1979) unit root test, the Zivot and Andrews’ (1992) one structural break unit root test, and the Lumsdaine and Papell (1997) two structural breaks unit root test. Our main finding is that, for 40 countries, real output is stationary around a trend. This indicates that business cycles are stationary fluctuations around a deterministic trend for only 51% of the developing countries in our sample.     

On predicting the semiconductor industry cycle: a Bayesian model averaging approach

This study considers the model uncertainty and utilizes the Bayesian model averaging (BMA) approach to identify useful predictors of the semiconductor industry cycle from a list of 70 potential predictors. The posterior inclusion probabilities, posterior means, and posterior standard deviations over the period of 1995:05–2012:10 are estimated and consequently used to identify the main determinants of the industry cycle. It is found that the Philadelphia Semiconductor Index and total inventories in various downstream industries have important roles in signaling the industry growth. The results from an out-of-sample forecasting exercise also reveal the predictive potential and usefulness of BMA for the long-term prediction.     

Forecasting economic activity by Bayesian bridge model averaging

This paper proposes the use of Bayesian model averaging (BMA) as an alternative tool to forecast GDP relative to simple bridge models and factor models. BMA is a computationally feasible method that allows us to explore the model space even in the presence of a large set of candidate predictors. We test the performance of BMA in now-casting by means of a recursive experiment for the euro area and the three largest countries. This method allows flexibility in selecting the information set month by month. We find that BMA-based forecasts produce smaller forecast errors than standard bridge model when forecasting GDP in Germany, France and Italy. At the same time, it also performs as well as medium-scale factor models when forecasting Eurozone GDP.     

The seasonal unit root structure in New Zealand Macroeconomic variables

ADF unit root tests are generally applied to macroeconomic data prior to testing theoritical models to ensure that all relevant variables are integrated of the same order. Not only is it important to test that these variables are integrated of the same order but also that a cointegrating relationship exists; failure to do so raise the specture of false inference associated with the spurious regression problem. The seasonal nature of quarterly data adds a further proplem which has generally been overcome by seasonally adjusting the data using procedure such as the census X-11 rather than suppressing it, have attempted to determine whether the seasonal component in each variable exhibits stochastic non-stationary. This paper analysisunit roots in a seasonal setting and compares the recently developed tests for seasonal unit roots as well as the standard augmented Dickey-Fuller zerop frequency unit root tests. Of the variables tested relatively few paper to be integrated at the seasonal frequenciues and, as other studies suggest,determinstic seasonal effects are typically more important than stochastic ones.     

Threshold,smooth transition and mean reversion in inflation: New evidence from European countries

Knowing the absence or presence of a unit root in inflation is helpful not only in distinguishing between different economic hypotheses but is also important to monetary authorities in implementing the policies of disinflation. Using data for fourteen European countries, this study investigates the issue of nonstationarity in inflation by considering the possibility of nonlinearity. In particular, we consider the properties of a threshold, smooth transition and structural break in testing for a unit root in the inflation rates. By and large, the results support the view that the inflation rates of the European countries are characterized by a unit root process based on the conventional linear unit root tests. However, the results of the nonlinear unit root tests show that the inflation rates are characterized by nonlinear mean reversion after considering the nonlinear properties of the threshold, smooth transition and structural break. The mean reversion in inflation favors the hypothesis of, for example, the natural rate of inflation and the sticky-price model and implies that shocks only have transitory effects.