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Abstract:
The measurement of core inflation can be carried out by optimal signal extraction techniques based on the multivariate local level model, by imposing suitable restrictions on its parameters. The various restrictions correspond to several specialisations of the model: the core inflation measure becomes the optimal estimate of the common trend in a multivariate time series of inflation rates for a variety of goods and services, or it becomes a minimum variance linear combination of the inflation rates, or it represents the component generated by the common disturbances in a dynamic error component formulation of the multivariate local level model. Particular attention is given to the characterisation of the optimal weighting functions and to the design of signal extraction filters that can be viewed as two sided exponentially weighted moving averages applied to a cross-sectional average of individual inflation rates. An empirical application relative to U.S. monthly inflation rates for 8 expenditure categories is proposed.

common trends, dynamic factor analysis, homogeneity, exponential smoothing

Abstract:
The chapter deals with parametric models for the measurement of the business cycle in economic time series. It presents univariate methods based on parametric trend - cycle decompositions and multivariate models featuring a Phillips type relationship between the output gap and inflation and the estimation of the gap using mixed frequency data. We finally address the issue of assessing the accuracy of the output gap estimates.

State Space Models, Kalman Filter and Smoother, Bayesian Estimation

Abstract:
In this paper we compare alternative approaches for dating the Euro area business cycle and analyzing its characteristics. First, we extend a commonly used dating procedure to allow for length, size and amplitude restrictions, and to compute the probability of a phase change. Second, we apply the modified algorithm for dating both the classical Euro area cycle and the deviation cycle, where the latter is obtained by a variety of methods, including a modified HP filter that reproduces the features of the BK filter but avoids end-point problems, and a production function based approach. Third, we repeat the dating exercise for the main Euro area countries, evaluate the degree of syncronization, and compare the results with the UK and the US. Fourth, we construct indices of business cycle diffusion, and assess how spread are cyclical movements throughout the economy. Finally, we repeat the dating exercise using monthly industrial production data, to evaluate whether the higher sampling frequency can compensate the higher variability of the series and produce a more accurate dating.

Business cycle, Euro area, cycle dating, cycle synchronization

Abstract:
In this paper we deal with several issues related to the quantification of business surveys. In particular, we propose and compare new ways of scoring the ordinal responses concerning the qualitative assessment of the state of the economy, such as the spectral envelope and cumulative logit unobserved components models, and investigate the nature of seasonality in the series. We conclude with an evaluation of the type of business cycle fluctuations that is captured by the qualitative surveys.

Spectral envelope, Seasonality, Deviation cycles, Cumulative Logit

Abstract:
We analyse the evolution of the business cycle in the accession countries, after a careful examination of the seasonal properties of the available series and the required modification of the cycle dating procedures. We then focus on the degree of cyclical concordance within the group of accession countries, which turns out to be in general lower than that between the existing EU countries (the Baltic countries constitute an exception). With respect to the Eurozone, the indications of synchronization are also generally low and lower relative to the position obtaining for countries taking part in previous enlargements (with the exceptions of Poland, Slovenia and Hungary). In the light of the optimal currency area literature, these results cast doubts on the usefulness of adopting the euro in the near future for most accession countries, though other criteria such as the extent of trade and the gains in credibility may point in a different direction.

Business cycles, dating algorithms, cycle synchronization, EU enlargement, seasonal adjustment

Abstract:
The paper explores and illustrates some of the typical trade-offs which arise in designing filters for the measurement of trends and cycles in economic time series, focusing, in particular, on the fundamental trade-off between the reliability of the estimates and the magnitude of the revisions as new observations become available. This assessment is available through a novel model based approach, according to which an important class of highpass and bandpass filters, encompassing the Hodrick-Prescott filter, are adapted to the particular time series under investigation. Via a suitable decomposition of the innovation process, it is shown that any linear time series with ARIMA representation can be broken down into orthogonal trend and cycle components, for which the class of filters is optimal. The main results then follow from Wiener-Kolmogorov signal extraction theory, whereas exact finite sample inferences are provided by the Kalman filter and smoother for the relevant state space representation of the decomposition.

Signal Extraction, Revisions, Kalman filter and Smoother, Bandpass

Abstract:
The paper focuses on the adaptation of local polynomial filters at the end of the sample period. We show that for real time estimation of signals (i.e. exactly at the boundary of the time support) we cannot rely on the automatic adaptation of the local polynomial smoothers, since the direct real time filter turns out to be strongly localised, and thereby yields extremely volatile estimates. As an alternative we evaluate a general family of asymmetric filters that minimises the mean square revision error subject to polynomial reproduction constraints; in the case of the Henderson filter it nests the well known Musgrave's surrogate filters. The class of filters depends on unknown features of the series such as the slope and the curvature of the underlying signal, which can be estimated from the data. Several empirical examples illustrate the effectiveness of our proposal. We also discuss the merits of using a nearest neighbour bandwidth as opposed to a fixed bandwidth for improving the quality of the approximation.

Henderson filter, Trend estimation, Nearest Neighbour Bandwidth, Musgrave asymmetric

Abstract:
This paper is concerned with the estimation of euro area potential output growth and its decomposition according to the sources of growth. The growth accounting exercise is based on a multivariate structural time series model which combines the decomposition of total output according to the production function approach with price and wage equations that embody Phillips type relationships linking inflation and nominal wage dynamics to the output gap and cyclical unemployment, respectively. Assuming a Cobb-Douglas technology with constant returns to scale, potential output results from the combination of the trend levels of total factor productivity and factor inputs, capital and labour (hours worked), which is decomposed into labour intensity (average hours worked), the employment rate, the participation rate, and population of working age. The nominal variables (prices and wages)play an essential role in defining the trend levels of the components of potential output, as the latter should pose no inflationary pressures on prices and wages. The structural model is further extended to allow for the estimation of potential output growth and the decomposition according to the sources of growth at different horizons (long-run, medium run and short run); in particular, we propose and evaluate a model-based approach to the extraction of the low-pass component of potential output growth at different cutoff frequencies. The approach has two important advantages: the signal extraction filters have an automatic adaptation property at the boundaries of the sample period, so that the real time estimates do not suffer from what is often referred to as the "end-of-sample bias". Secondly, it is possible to assess the uncertainty of potential output growth estimates with different degrees of smoothness.

Potential output, Output gap, Euro area, Unobserved components, Production function approach, Low-pass filters.

Abstract:
The paper evaluates the potential of band spectral estimation for extracting signals in economic time series. Two situations are considered. The first deals with trend extraction when the original data have been permanently altered by routine operations, such as prefiltering, temporal aggregation and disaggregation, and seasonal adjustment, which modify the high frequencies properties of economic time series. The second is when the measurement model is only partially specified, in that it aims at fitting the series in a particular frequency range, e.g. at interpreting the long run behaviour. These issues are illustrated with reference to a simple structural model, namely the random walk plus noise model.

Temporal Aggregation, Seasonal Adjustment, Trend Component, Frequency Domain

Abstract:
The paper advocates the use of state space methods to deal with the problem of temporal disaggregation by dynamic regression models, which encompass the most popular techniques for the distribution of economic flow variables, such as Chow-Lin, Fernandez and Litterman. The state space methodology offers the generality that is required to address a variety of inferential issues that have not been dealt with previously. The paper contributes to the available literature in three ways: (i) it concentrates on the exact initialization of the different models, showing that this issue is of fundamental importance for the properties of the maximum likelihood estimates and for deriving encompassing autoregressive distributed lag models that nest exactly the traditional disaggregation models; (ii) it points out the role of diagnostics and revisions histories in judging the quality of the disaggregated estimates and (iii) it provides a thorough treatment of the Litterman model, explaining the difficulties commonly encountered in practice when estimating this model.

Abstract:
This paper examines the convergence of regional business cycles in the decades that followed Italy's Unification. The aggregate construction series point to cyclical convergence, but a sectorlevel analysis traces this result to the decline in differentiated "regional-policy" shocks. The regional market cycles diverged, as the regions specialized in different sectors of production; market-cycle convergence is observed only within the "industrial triangle," the regions of which also developed different specializations. This suggests that the balance between growing interdependence and growing differentiation is not general, as the current literature presumes, but specialization-specific.

Abstract:
In this Paper we compare alternative approaches for dating the euro area business cycle and analysing its characteristics. First, we extend a commonly used dating procedure to allow for length, size and amplitude restrictions, and to compute the probability of a phase change. Second, we apply the modified algorithm for dating both the classical euro area cycle and the deviation cycle, where the latter is obtained by a variety of methods, including a modified HP filter that reproduces the features of the BK filter but avoids end-point problems, and a production function based approach. Third, we repeat the dating exercise for the main euro area countries, evaluate the degree of synchronization, and compare the results with the UK and the US. Fourth, we construct indices of business cycle diffusion, and assess how widespread are cyclical movements throughout the economy. Finally we repeat the dating exercise using monthly industrial production data, to evaluate whether the higher sampling frequency can compensate the higher variability of the series and produce a more accurate dating.

Business cycle, euro area, cycle dating, cycle synchronization

Abstract:
In this paper we propose a monthly measure for the euro area Gross Domestic Product (GDP) based on a small scale factor model for mixed frequency data, featuring two factors: the first is driven by hard data, whereas the second captures the contribution of survey variables as coincident indicators. Within this framework we evaluate both the in-sample contribution of the second survey-based factor, and the short term forecasting performance of the model in a pseudo-real time experiment. We find that the survey-based factor plays a significant role for two components of GDP: Industrial Value Added and Exports. Moreover, the two factor model outperforms in terms of out of sample forecasting accuracy the traditional autoregressive distributed lags (ADL) specifications and the single factor model, with few exceptions for Exports and in growth rates.

Survey data, Forecasting, Temporal Disaggregation, Dynamic factor modes, Kalman Filter and smoother

Abstract:
This paper proposes a dating algorithm based on an appropriately defined Markov chain that enforces alternation of peaks and troughs, and duration constraints concerning the phases and the full cycle. The algorithm, which implements Harding and Pagan's non-parametric dating methodology, allows an assessment of the uncertainty of the estimated turning points caused by filtering and can be used to construct indices of business cycle diffusion, aiming at assessing how widespread are cyclical movements throughout the economy. Its adaptation to the notion of a deviation cycle and the imposition of depth constraints are also discussed. We illustrate the algorithm with reference to the issue of dating the euro-area business cycle and analysing its characteristics, both from the classical and the growth cycle perspectives.

Abstract:
We analyse the evolution of the business cycle in the accession countries, after a careful examination of the seasonal properties of the available series and the required modification of the cycle dating procedures. We then focus on the degree of cyclical concordance within the group of accession countries, which turns out to be in general lower than that between the existing EU countries (the Baltic countries constitute an exception). With respect to the euro zone, the indications of synchronization are also generally low and lower relative to the position obtaining for countries taking part in previous enlargements (with the exceptions of Poland, Slovenia and Hungary). In the light of the optimal currency area literature, these results cast doubts on the usefulness of adopting the euro in the near future for most accession countries, though other criteria, such as the extent of trade and the gains in credibility, may point in a different direction.

Business cycles, dating algorithms, cycle synchronization, EU enlargement, seasonal adjustment

Abstract:
A continuous monitoring of the evolution of the economy is fundamental for the decisions of public and private decision makers. This paper proposes a new monthly indicator of the euro area real Gross Domestic Product (GDP), with several original features. First, it considers both the output side (six branches of the NACE classification) and the expenditure side (the main GDP components) and combines the two estimates with optimal weights reflecting their relative precision. Second, the indicator is based on information at both the monthly and quarterly level, modelled with a dynamic factor specification cast in state-space form. Third, since estimation of the multivariate dynamic factor model can be numerically complex, computational efficiency is achieved by implementing univariate filtering and smoothing procedures. Finally, special attention is paid to chain-linking and its implications, via a multistep procedure that exploits the additivity of the volume measures expressed at the prices of the previous year.

Chain-linking, Dynamic factor Models, euro area GDP, Kalman filter and smoother, Multivariate State Space Models, Temporal Disaggregation

Abstract:
We address the problem of seasonal adjustment of a nonlinear transformation of the original time series, measured on a ratio scale, which aims at enforcing two essential features: additivity and orthogonality of the components. The posterior mean and variance of the seasonally adjusted series admit an analytic finite representation only for particular values of the transformation parameter, e.g. for a fractional BoxCox transformation parameter. Even if available, the analytical derivation can be tedious and difficult. As an alternative we propose to compute the two conditional moments of the seasonally adjusted series by means of numerical and Monte Carlo integration. The former is both fast and reliable in univariate applications. The latter uses the algorithm known as the simulation smoother and it is most useful in multivariate applications. We present two case studies dealing with robust seasonal adjustment under the square root and the fourth root transformation. Our overall conclusion is that robust seasonal adjustment under transformations is feasible from the computational standpoint and that the possibility of transforming the scale ought to be considered as a further option for improving the quality of seasonal adjustment.

Abstract:
The class of periodic autoregressive (PAR) models, suitably extended so as to allow for 'periodic integration', has recently found widespread application to economic time series as an alternative to the time-invariant models available in the literature. An elaborate modelling strategy has been proposed, and new tests for periodic integration have been envisaged, whose empirical performance tends to support the notion that the kind of non-stationary stochastic dynamics observed in time series arises as a consequence of periodic integration. This paper aims at challenging this view by means of a Monte Carlo experiment: we generate data according to a trend with a seasonality model such that the trend is a random walk with drift and the seasonal component is generated according to a stochastic trigonometric model. It is found that all the fundamental tools of PAR modelling will tend to provide spurious evidence in favour of a periodic model, and conclude that, as long as macroeconomic time series are concerned, PAR models are an overelaborate way of capturing essential features, such as indeterministic trends and seasonals, that are more parsimoniously accommodated by a time-invariant model.