A Wavelet Approach for Factor-Augmented Forecasting

It has been acknowledged that wavelets can constitute a useful tool for forecasting in economics. Through a wavelet multiresolution analysis, a time series can be decomposed into different time-scale components and a model can be fitted to each component to improve the forecast accuracy of the series as a whole. Up to now, the literature on forecasting with wavelets has mainly focused on univariate modelling. On the other hand, in a context of growing data availability, a line of research has emerged on forecasting with large datasets. In particular, the use of factor-augmented models have become quite widespread in the literature and among practitioners. The aim of this paper is to bridge the two strands of the literature. A wavelet approach for factor-augmented forecasting is proposed and put to test for forecasting GDP growth for the major euro area countries. The results show that the forecasting performance is enhanced when wavelets and factor-augmented models are used together.

Measuring comovement in the time-frequency space

The measurement of comovement among variables has a long tradition in the economic and financial literature. Traditionally, comovement is assessed in the time domain through the well-known correlation coefficient while the evolving properties are investigated either through a rolling window or by considering non-overlapping periods. More recently, Croux, Forni and Reichlin [Review of Economics and Statistics 83 (2001)] have proposed a measure of comovement in the frequency domain. While it allows to quantify the comovement at the frequency level, such a measure disregards the fact that the strength of the comovement may vary over time. Herein, it is proposed a new measure of comovement resorting to wavelet analysis. This wavelet-based measure allows one to assess simultaneously the comovement at the frequency level and over time. In this way, it is possible to capture the time and frequency varying features of comovement within a unified framework which constitutes a refinement to previous approaches.

Forecasting Inflation Through a Bottom-Up Approach: The Portuguese Case

The aim of this paper is to assess inflation forecasting acurracy over the short-term horizon using Consumer Price Index (CPI) disaggregated data. That is, aggregating forecasts is compared with aggregate forecasting. In particular, three questions are addressed: i) one should bottom-up or not, ii) how bottom one should go and iii) how one should model at the bottom. In contrast with the literature, di erent levels of data dis-aggregation are allowed, namely a higher disaggregation level than the one considered up to now. Moreover, both univariate and multivariate models are considered, such as SARIMA and SARIMAX models with dynamic common factors. An out-of-sample forecast comparison (up to twelve months ahead) is done using Portuguese CPI dataset. Aggregating the forecasts seems to be better than aggregate forecasting up to a five-months ahead horizon. Moreover, this improvement increases with the disaggregation level and the multivariate modelling outperforms the univariate one in the very short-run.

Extremal Dependence in International Output Growth: Tales from the Tails

The statistical modelling of extreme values has recently received substantial attention in a broad spectrum of sciences. Given that in a wide variety of scenarios, one is mostly concerned with explaining tail events (say, an economic recession) than central ones, the need to rely on statistical methods well qualified for modelling extremes arises. Unfortunately, several classical tools regularly applied in the analysis of central events, are simply innapropriate for the analysis of extreme values. In particular, Pearson correlation is not a proper measure for assessing the level of agreement of two variables when one is concerned with tail events. This paper explores the comovement of the economic activity of several OECD countries during periods of large positive and negative growth (right and left tails, respectively). Extremal measures are here applied as means to assess the degree of cross-country tail dependence of output growth rates. Our main empirical findings are: (i) the comovement is much stronger in left tails than in right tails; (ii) asymptotic independence is claimed by the data; (iii) the dependence in the tails is considerably stronger than the one arising from a Gaussian dependence model. In addition, our results suggest that, among the typical determinants for explaining international output growth synchronization, only economic specialization similarity seems to play a role at extreme events.

An input-output analysis: linkages vs leakages

Resorting to input-output analysis, intersectoral linkages are investigated. For such assessment, the distinction between imported and domestically supplied inputs, which has been disregarded so far in empirical analysis, is crucial. Besides improving the measurement of domestic linkages, it also allows to evaluate the importance of international trade in the production process. Moreover, the interaction between domestic linkages and leakages resulting from international trade can also be analysed. Using as case study a small open economy, the Portuguese one, we assess sectoral interdependence and trade effects for individual sectors as well as for the economy as a whole.

International comovement of stock market returns: a wavelet analysis

The assessment of the comovement among international stock markets is of key interest, for example, for the international portfolio diversification literature. In this paper, we re-examine such comovement by resorting to a novel approach, wavelet analysis. Wavelet analysis allows one to measure the comovement in the time-frequency space. In this way, one can characterize how international stock returns relate in the time and frequency domains simultaneously, which allows one to provide a richer analysis of the comovement. We focus on Germany, Japan, UK and US and the analysis is done at both the aggregate and sectoral levels.

Coincident and Leading Indicators for the Euro Area: A Frequency Band Approach

In the context of a common monetary policy, tracking euro area economic developments becomes essential. The aim of this paper is to build monthly coincident and leading composite indicators for the euro area business cycle. However, instead of looking at the overall comovement between the variables as it is standard in the literature, we show how one can resort to both time and frequency domain analysis to achieve additional insight about their relationship. We find that, in general, the lead/lag properties of economic indicators depend on the cycles periodicity. Following a frequency band approach, we take advantage of this in the construction of the coincident and leading composite indicators. The resulting indicators are analysed and a comparison with other composite indicators proposed in the literature is made.

Money growth and inflation in the euro area: a time-frequency view

This paper provides new insights on the relationship between money growth and inflation in the euro area over the last forty years. This highly relevant link for the European Central Bank monetary policy strategy is assessed using wavelet analysis. In particular, wavelet analysis allows to study simultaneously the relationship between money growth and inflation in the euro area at the frequency level and assess how it has changed over time. The findings indicate a stronger link between inflation and money growth at low frequencies over the whole sample period. At the typical business cycle frequency range the link is only present until the beginning of the 1980’s. Moreover, there seems to be a recent deterioration of the leading properties of money growth with respect to inflation in the euro area. These results highlight the importance of a regular assessment of the role of money growth in tracking inflation developments in the euro area since such relationship varies across frequencies and over time.

Determining the number of factors in approximate factor models with global and group-specific factors

For an approximate factor model, in a static representation, with a common component comprising global factors and factors specific to groups of variables, the consistency of the principal components estimator is discussed. An extension of the well known Bai and Ng criteria is proposed for determining the number of global and group-specific factors. The consistency of the suggested criteria is established and the small sample properties are assessed through Monte Carlo simulations. As an empirical illustration, the proposed criteria is applied to estimate the number of global and country-specific macroeconomic factors for the major euro area countries.