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This thesis includes two essays that are focused on developing multivariate filter approaches to be used for extracting common cyclical components where the common components can be used as an estimator of a business cycle. The first chapter aims to develop an optimal multivariate filter in order to extract common cyclical components of macroeconomic indicators. The filter allows macroeconomic series to be modeled as a phase shifted version of a coinciding business cycle (BC) while keeping other time series components such as the stochastic trend and idiosyncratic shocks intact (i.e. they are individually specified for each series). Earlier studies of Rünstler (2004), Valle e Azevedo et al. (2006) have applied phase shift in the form of a delay parameter when specifying lead-lag cycles. However, the lead-lag relationship is defined by rotating the baseline cycle which leads to loss of information. This deficiency is especially important if one considers working in continuous time. Therefore, this paper improves on the former technique by allowing a more flexible phase shift mechanism on the original BC. This in turn should lead to more realistic estimates and filters considering that the underlying data is generated through a continuous time framework. The study starts by presenting a structure for bi-variate time series system and then extends to model to incorporate a structure for three time series and beyond. Kalman filter and smoothing recursions are applied to compute the smoothed cycle estimates and to construct the likelihood function. Using simulated data, we test both model specifications by carrying out a grid search of the initial delay parameter to see the likelihood behavior as the parameter moves into fractional neighborhoods. Afterwards, applying the methodology to a set of EU countries and macroeconomic indicators; the study aims to shed light to the presence of cyclical heterogeneity at country level economic activity for major EU member states. A second empirical study provides analysis on how the model can be implemented for assigning a lead/lag ordering to three main economic indicators of a single country. The second chapter implements a multivariate non-parametric filtering approach; the Vertical Multivariate Singular Spectrum Analysis (V-MSSA) of Hassani and Mahmoudvand (2013) and Golyandina et al. (2013). to be applied for identifying a common economic cycle indicator. The methodology is a data-driven procedure that can decompose a time series into many sub components. By exploiting this ability of the SSA, the paper aims to first extract cyclical components based on frequency characteristics and then follow by choosing only common cyclical component pairs with-in the business cycle frequency spectrum. These components will then be aggregated for constructing an EU region wide Business cycle indicator. The chapter outlines each steps of the algorithm that will eventually identify the SSA filter to act as a band-pass filter. The study then proceeds with simulation based data where the common cycle can be controlled and extracted a priori as a benchmark to the SSA-based filter estimates. The study follows with an empirical analysis similar to the framework set in Valle e Azevedo et al. (2006) with the aim to identify a Euro region business cycle indicator. The SSA based filter estimate is compared with Euro region economic activity indicators; the EuroCoin and the quarterly GDP growth rate of the EU area. Our results presents evidence of a successful alternative for tracing the cyclical position of the EU economy from a much smaller data set. Moreover, the constructed indicator also could serve as an unobserved proxy for a monthly growth cycle. A further analysis is also conducted to reveal whether the SSA based approach can be considered as an alternative to parametric filtering methods by providing results of common cycle extraction using Unobserved component model alternatives. This thesis includes two essays that are focused on developing multivariate filter approaches to be used for extracting common cyclical components where the common components can be used as an estimator of a business cycle. The first chapter aims to develop an optimal multivariate filter in order to extract common cyclical components of macroeconomic indicators. The filter allows macroeconomic series to be modeled as a phase shifted version of a coinciding business cycle (BC) while keeping other time series components such as the stochastic trend and idiosyncratic shocks intact (i.e. they are individually specified for each series). Earlier studies of Rünstler (2004), Valle e Azevedo et al. (2006) have applied phase shift in the form of a delay parameter when specifying lead-lag cycles. However, the lead-lag relationship is defined by rotating the baseline cycle which leads to loss of information. This deficiency is especially important if one considers working in continuous time. Therefore, this paper improves on the former technique by allowing a more flexible phase shift mechanism on the original BC. This in turn should lead to more realistic estimates and filters considering that the underlying data is generated through a continuous time framework. The study starts by presenting a structure for bi-variate time series system and then extends to model to incorporate a structure for three time series and beyond. Kalman filter and smoothing recursions are applied to compute the smoothed cycle estimates and to construct the likelihood function. Using simulated data, we test both model specifications by carrying out a grid search of the initial delay parameter to see the likelihood behavior as the parameter moves into fractional neighborhoods. Afterwards, applying the methodology to a set of EU countries and macroeconomic indicators; the study aims to shed light to the presence of cyclical heterogeneity at country level economic activity for major EU member states. A second empirical study provides analysis on how the model can be implemented for assigning a lead/lag ordering to three main economic indicators of a single country. The second chapter implements a multivariate non-parametric filtering approach; the Vertical Multivariate Singular Spectrum Analysis (V-MSSA) of Hassani and Mahmoudvand (2013) and Golyandina et al. (2013). to be applied for identifying a common economic cycle indicator. The methodology is a data-driven procedure that can decompose a time series into many sub components. By exploiting this ability of the SSA, the paper aims to first extract cyclical components based on frequency characteristics and then follow by choosing only common cyclical component pairs with-in the business cycle frequency spectrum. These components will then be aggregated for constructing an EU region wide Business cycle indicator. The chapter outlines each steps of the algorithm that will eventually identify the SSA filter to act as a band-pass filter. The study then proceeds with simulation based data where the common cycle can be controlled and extracted a priori as a benchmark to the SSA-based filter estimates. The study follows with an empirical analysis similar to the framework set in Valle e Azevedo et al. (2006) with the aim to identify a Euro region business cycle indicator. The SSA based filter estimate is compared with Euro region economic activity indicators; the EuroCoin and the quarterly GDP growth rate of the EU area. Our results presents evidence of a successful alternative for tracing the cyclical position of the EU economy from a much smaller data set. Moreover, the constructed indicator also could serve as an unobserved proxy for a monthly growth cycle. A further analysis is also conducted to reveal whether the SSA based approach can be considered as an alternative to parametric filtering methods by providing results of common cycle extraction using Unobserved component model alternatives. |
