Multivariate contemporaneous-threshold autoregressive models

This paper proposes a contemporaneous-threshold multivariate smooth transition autoregressive (C-MSTAR) model in which the regime weights depend on the ex ante probabilities that latent regime-specific variables exceed certain threshold values. A key feature of the model is that the transition function depends on all the parameters of the model as well as on the data. Since the mixing weights are also a function of the regime-specific innovation covariance matrix, the model can account for contemporaneous regime-specific co-movements of the variables. The stability and distributional properties of the proposed model are discussed, as well as issues of estimation, testing and forecasting. The practical usefulness of the C-MSTAR model is illustrated by examining the relationship between US stock prices and interest rates.

Subsampling inference in threshold autoregressive models

This paper discusses inference in self exciting threshold autoregressive (SETAR)models. Of main interest is inference for the threshold parameter. It iswell-known that the asymptotics of the corresponding estimator depend uponwhether the SETAR model is continuous or not. In the continuous case, thelimiting distribution is normal and standard inference is possible. Inthe discontinuous case, the limiting distribution is non-normal and cannotbe estimated consistently. We show valid inference can be drawn by theuse of the subsampling method. Moreover, the method can even be extendedto situations where the (dis)continuity of the model is unknown. In thiscase, also the inference for the regression parameters of the modelbecomes difficult and subsampling can be used advantageously there aswell. In addition, we consider an hypothesis test for the continuity ofthe SETAR model. A simulation study examines small sample performance.

Understanding sources of the change in international business cycles

Macroeconomic activity has become less volatile over the past three decades in most G7 economies. Current literature focuses on the characterization of the volatility reduction and explanations for this so called "moderation" in each G7 economy separately. In opposed to individual country analysis and individual variable analysis, this paper focuses on common characteristics of the reduction and common explanations for the moderation in G7 countries. In particular, we study three explanations: structural changes in the economy, changes in common international shocks and changes in domestic shocks. We study these explanations in a unified model structure. To this end, we propose a Bayesian factor structural vector autoregressive model. Using the proposed model, we investigate whether we can find common explanations for all G7 economies when information is pooled from multiple domestic and international sources. Our empirical analysis suggests that volatility reductions can largely be attributed to the decline in the magnitudes of the shocks in most G7 countries while only for the U.K., the U.S. and Italy they can partially be attributed to structural changes in the economy. Analyzing the components of the volatility, we also find that domestic shocks rather than common international shocks can account for a large part of the volatility reduction in most of the G7 countries. Finally, we find that after mid-1980s the structure of the economy changes substantially in five of the G7 countries: Germany, Italy, Japan, the U.K. and the U.S..

Heterogeneous dynamics, aggregation and the persistence of economic shocks

It has been recently emphasized that, if individuals have heterogeneous dynamics, estimates of shock persistence based on aggregate data are significatively higher than those derived from its disaggregate counterpart. However, a careful examination of the implications of this statement on the various tools routinely employed to measure persistence is missing in the literature. This paper formally examines this issue. We consider a disaggregate linear model with heterogeneous dynamics and compare the values of several measures of persistence across aggregation levels. Interestingly, we show that the average persistence of aggregate shocks, as measured by the impulse response function (IRF) of the aggregate model or by the average of the individual IRFs, is identical on all horizons. This result remains true even in situations where the units are (short-memory) stationary but the aggregate process is long-memory or even nonstationary. In contrast, other popular persistence measures, such as the sum of the autoregressive coefficients or the largest autoregressive root, tend to be higher the higher the aggregation level. We argue, however, that this should be seen more as an undesirable property of these measures than as evidence of different average persistence across aggregation levels. The results are illustrated in an application using U.S. inflation data.

State-dependent threshold STAR models

In this paper we consider extensions of smooth transition autoregressive (STAR) models to situations where the threshold is a time-varying function of variables that affect the separation of regimes of the time series under consideration. Our specification is motivated by the observation that unusually high/low values for an economic variable may sometimes be best thought of in relative terms. State-dependent logistic STAR and contemporaneous-threshold STAR models are introduced and discussed. These models are also used to investigate the dynamics of U.S. short-term interest rates, where the threshold is allowed to be a function of past output growth and inflation.

The determinants of YIc's R&D activity

This paper examines the determinants of young innovative companies’ (YICs) R&D activities taking into account the autoregressive nature of innovation. Using a large longitudinal dataset comprising Spanish manufacturing firms over the period 1990-2008, we find that previous R&D experience is a fundamental determinant for mature and young firms, albeit to a smaller extent in the case of the YICs, suggesting that their innovation behaviour is less persistent and more erratic. Moreover, our results suggest that firm and market characteristics play a distinct role in boosting the innovation activity of firms of different age. In particular, while market concentration and the degree of product diversification are found to be important in boosting R&D activities in the sub-sample of mature firms only, YICs’ spending on R&D appears to be more sensitive to demand-pull variables, suggesting the presence of credit constraints. These results have been obtained using a recently proposed dynamic type-2 tobit estimator, which accounts for individual effects and efficiently handles the initial conditions problem.

Priors about observables in vector autoregressions

Standard practice in Bayesian VARs is to formulate priors on the autoregressive parameters, but economists and policy makers actually have priors about the behavior of observable variables. We show how this kind of prior can be used in a VAR under strict probability theory principles. We state the inverse problem to be solved and we propose a numerical algorithm that works well in practical situations with a very large number of parameters. We prove various convergence theorems for the algorithm. As an application, we first show that the results in Christiano et al. (1999) are very sensitive to the introduction of various priors that are widely used. These priors turn out to be associated with undesirable priors on observables. But an empirical prior on observables helps clarify the relevance of these estimates: we find much higher persistence of output responses to monetary policy shocks than the one reported in Christiano et al. (1999) and a significantly larger total effect.

On prediction of individual sequences

Sequential randomized prediction of an arbitrary binary sequence isinvestigated. No assumption is made on the mechanism of generating the bit sequence. The goal of the predictor is to minimize its relative loss, i.e., to make (almost) as few mistakes as the best ``expert'' in a fixed, possibly infinite, set of experts. We point out a surprising connection between this prediction problem and empirical process theory. First, in the special case of static (memoryless) experts, we completely characterize the minimax relative loss in terms of the maximum of an associated Rademacher process. Then we show general upper and lower bounds on the minimaxrelative loss in terms of the geometry of the class of experts. As main examples, we determine the exact order of magnitude of the minimax relative loss for the class of autoregressive linear predictors and for the class of Markov experts.

Unemployment dynamics and NAIRU estimates for CEECs : a univariate approach

In this paper we test for the hysteresis versus the natural rate hypothesis on the unemployment rates of the EU new members using unit root tests that account for the presence of level shifts. As a by product, the analysis proceeds to the estimation of a NAIRU measure from a univariate point of view. The paper also focuses on the precision of these NAIRU estimates studying the two sources of inaccuracy that derive from the break points estimation and the autoregressive parameters estimation. The results point to the existence of up to four structural breaks in the transition countries NAIRU that can be associated with institutional changes implementing market-oriented reforms. Moreover, the degree of persistence in unemployment varies dramatically among the individual countries depending on the stage reached in the transition process

Unemployment dynamics and NAIRU estimates for CEECs : a univariate approach

In this paper we test for the hysteresis versus the natural rate hypothesis on the unemployment rates of the EU new members using unit root tests that account for the presence of level shifts. As a by product, the analysis proceeds to the estimation of a NAIRU measure from a univariate point of view. The paper also focuses on the precision of these NAIRU estimates studying the two sources of inaccuracy that derive from the break points estimation and the autoregressive parameters estimation. The results point to the existence of up to four structural breaks in the transition countries NAIRU that can be associated with institutional changes implementing market-oriented reforms. Moreover, the degree of persistence in unemployment varies dramatically among the individual countries depending on the stage reached in the transition process

Monitoring mortality as an indicator of influenza in Catalonia, Spain.

This study aimed to investigate the behaviour of two indicators of influenza activity in the area of Barcelona and to evaluate the usefulness of modelling them to improve the detection of influenza epidemics. DESIGN: Descriptive time series study using the number of deaths due to all causes registered by funeral services and reported cases of influenza-like illness. The study concentrated on five influenza seasons, from week 45 of 1988 to week 44 of 1993. The weekly number of deaths and cases of influenza-like illness registered were processed using identification of a time series ARIMA model. SETTING: Six large towns in the Barcelona province which have more than 60,000 inhabitants and funeral services in all of them. MAIN RESULTS: For mortality, the proposed model was an autoregressive one of order 2 (ARIMA (2,0,0)) and for morbidity it was one of order 3 (ARIMA (3,0,0)). Finally, the two time series were analysed together to facilitate the detection of possible implications between them. The joint study of the two series shows that the mortality series can be modelled separately from the reported morbidity series, but the morbidity series is influenced as much by the number of previous cases of influenza reported as by the previous mortality registered. CONCLUSIONS: The model based on general mortality is useful for detecting epidemic activity of influenza. However, because there is not an absolute gold standard that allows definition of the beginning of the epidemic, the final decision of when it is considered an epidemic and control measures recommended should be taken after evaluating all the indicators included in the influenza surveillance programme.

Lag-one autocorrelation in short series: Estimation and hypothesis testing

In the first part of the study, nine estimators of the first-order autoregressive parameter are reviewed and a new estimator is proposed. The relationships and discrepancies between the estimators are discussed in order to achieve a clear differentiation. In the second part of the study, the precision in the estimation of autocorrelation is studied. The performance of the ten lag-one autocorrelation estimators is compared in terms of Mean Square Error (combining bias and variance) using data series generated by Monte Carlo simulation. The results show that there is not a single optimal estimator for all conditions, suggesting that the estimator ought to be chosen according to sample size and to the information available of the possible direction of the serial dependence. Additionally, the probability of labelling an actually existing autocorrelation as statistically significant is explored using Monte Carlo sampling. The power estimates obtained are quite similar among the tests associated with the different estimators. These estimates evidence the small probability of detecting autocorrelation in series with less than 20 measurement times.

The effects of monetary policy on stock market bubbles: Some evidence

We estimate the response of stock prices to exogenous monetary policy shocks usinga vector-autoregressive model with time-varying parameters. Our evidence points toprotracted episodes in which, after a a short-run decline, stock prices increase persistently in response to an exogenous tightening of monetary policy. That responseis clearly at odds with the "conventional" view on the effects of monetary policy onbubbles, as well as with the predictions of bubbleless models. We also argue that it isunlikely that such evidence be accounted for by an endogenous response of the equitypremium to the monetary policy shocks.

Monitoring the decreasing trend of testicular cancer mortality in Spain during 2005-2019 through a Bayesian approach

Purpose : To assess time trends of testicular cancer (TC) mortality in Spain for period 1985-2019 for age groups 15-74 years old through a Bayesian age-period-cohort (APC) analysis. Methods: A Bayesian age-drift model has been fitted to describe trends. Projections for 2005-2019 have been calculated by means of an autoregressive APC model. Prior precision for these parameters has been selected through evaluation of an adaptive precision parameter and 95% credible intervals (95% CRI) have been obtained for each model parameter. Results: A decrease of -2.41% (95% CRI: -3.65%; -1.13%) per year has been found for TC mortality rates in age groups 15-74 during 1985-2004, whereas mortality showed a lower annual decrease when data was restricted to age groups 15-54 (-1.18%; 95% CRI: -2.60%; -0.31%). During 2005-2019 is expected a decrease of TC mortality of 2.30% per year for men younger than 35, whereas a leveling off for TC mortality rates is expected for men older than 35. Conclusions: A Bayesian approach should be recommended to describe and project time trends for those diseases with low number of cases. Through this model it has been assessed that management of TC and advances in therapy led to decreasing trend of TC mortality during the period 1985-2004, whereas a leveling off for these trends can be considered during 2005-2019 among men older than 35.

Monitoring the decreasing trend of testicular cancer mortality in Spain during 2005-2019 through a Bayesian approach

Purpose : To assess time trends of testicular cancer (TC) mortality in Spain for period 1985-2019 for age groups 15-74 years old through a Bayesian age-period-cohort (APC) analysis. Methods: A Bayesian age-drift model has been fitted to describe trends. Projections for 2005-2019 have been calculated by means of an autoregressive APC model. Prior precision for these parameters has been selected through evaluation of an adaptive precision parameter and 95% credible intervals (95% CRI) have been obtained for each model parameter. Results: A decrease of -2.41% (95% CRI: -3.65%; -1.13%) per year has been found for TC mortality rates in age groups 15-74 during 1985-2004, whereas mortality showed a lower annual decrease when data was restricted to age groups 15-54 (-1.18%; 95% CRI: -2.60%; -0.31%). During 2005-2019 is expected a decrease of TC mortality of 2.30% per year for men younger than 35, whereas a leveling off for TC mortality rates is expected for men older than 35. Conclusions: A Bayesian approach should be recommended to describe and project time trends for those diseases with low number of cases. Through this model it has been assessed that management of TC and advances in therapy led to decreasing trend of TC mortality during the period 1985-2004, whereas a leveling off for these trends can be considered during 2005-2019 among men older than 35.