24 research outputs found
Measuring business cycles with structural breaks and outliers: Applications to international data
This paper first generalizes the trend-cycle decomposition framework of Perron and Wada (2009) based on unobserved components models with innovations having a mixture of normals distribution, which is able to handle sudden level and slope changes to the trend function as well as outliers. We investigate how important are the differences in the implied trend and cycle compared to the popular decomposition based on the Hodrick and Prescott (HP) (1997) filter. Our results show important qualitative and quantitative differences in the implied cycles for both real GDP and consumption series for the G7 countries. Most of the differences can be ascribed to the fact that the HP filter does not handle well slope changes, level shifts and outliers, while our method does so. Then, we reassess how such different cycles affect some so-called āstylized factsā about the relative variability of consumption and output across countries
Trend and Cycles: A New Approach and Explanations of Some Old Puzzles
Recent work on trend-cycle decompositions for US real GDP yields the following puzzling features: method based on Unobserved Components models, the Beveridge-Nelson decomposition, the Hodrick-Prescott filter and others yield very different cycles which bears little resemblance to the NBER chronology, ascribes much movements to the trend leaving little to the cycles, and some imply a negative correlation between the noise to the cycle and the trend. We argue that these features are artifacts created by the neglect of the presence of a change in the slope of the trend function in real GDP in 1973. Once this is properly accounted for, the results show all methods to yield the same cycle with a trend that is non-stochastic except for a few periods around 1973. This cycle is more important in magnitude than previously reported, it accords very well with the NBER chronology and imply no correlation between the trend and cycle, since the former is non-stochastic. We propose a new approach to univariate trend-cycle decompositions using a generalized Unobserved Components models with errors having a mixture of Normals distribution for both the slope of the trend function and the cycle components. It can account endogenously for infrequent changes such as level shifts and change in slope, as well as different variances for expansions and recessions. It yields a decomposition that accords very well with common notions of the business cyclesTrend-Cycle Decomposition, Structural Change, Non Gaussian Filtering, Unobserved Components Model, Beveridge-Nelson Decomposition
The Real Exchange Rate and Real Interest Differentials: The Role of the Trend-Cycle Decomposition
We propose an alternative model and method to reconcile the puzzling feature in
the relationship between the real exchange rate and real interest rate differentials. Our
simple two-country model with preset prices, along with firmsā misperception about
the future exchange rate, implies that the real exchange rate follows an ARIMA(0,1,p)
process. This allows us to compute the exact Beveridge-Nelson decomposition, which is
a model-consistent decomposition. In accordance with our model, unit roots in the real
exchange rates are found; and statistical inference is partially found to be affirmative
regarding the link between the real exchange rate detrended by the Beveridge-Nelson
decomposition and corresponding real interest differentials
On the Correlations of Trend-Cycle Errors
This note provides explanations for an unexpected result, namely, the estimated parameter of the
correlation coefficient of the trend shock and cycle shock in the stateāspace model is almost always
(positive or negative) unity, even when the true variance of the trend shock is zero. It is shown that the
set of the true parameter values lies on the restriction that requires the varianceācovariance matrix of
the errors to be nonsingular, therefore, almost always the likelihood function has its (constrained) global
maximum on the boundary where the correlation coefficient implies perfect correlation
On the Correlations of Trend-Cycle Errors
This note provides explanations for an unexpected result, namely, the estimated parameter of the
correlation coefficient of the trend shock and cycle shock in the stateāspace model is almost always
(positive or negative) unity, even when the true variance of the trend shock is zero. It is shown that the
set of the true parameter values lies on the restriction that requires the varianceācovariance matrix of
the errors to be nonsingular, therefore, almost always the likelihood function has its (constrained) global
maximum on the boundary where the correlation coefficient implies perfect correlation
International Stock Market Efficiency: A Non-Bayesian Time-Varying Model Approach
This paper develops a non-Bayesian methodology to analyze the time-varying
structure of international linkages and market efficiency in G7 countries. We
consider a non-Bayesian time-varying vector autoregressive (TV-VAR) model, and
apply it to estimate the joint degree of market efficiency in the sense of Fama
(1970, 1991). Our empirical results provide a new perspective that the
international linkages and market efficiency change over time and that their
behaviors correspond well to historical events of the international financial
system.Comment: 21 pages, 2 tables, 6 figure
Let's take a break: Trends and cycles in US real GDP
Trend-cycle decompositions for US real GDP such as the unobserved components models, the Beveridge-Nelson decomposition, the Hodrick-Prescott filter and others yield very different cycles which bear little resemblance to the NBER chronology, ascribes much movements to the trend leaving little to the cycle, and some imply a negative correlation between the noise to the cycle and the trend. We argue that these features are artifacts created by the neglect of a change in the slope of the trend function. Once this is accounted for, all methods yield the same cycle with a trend that is non-stochastic except for a few periods around 1973. The cycle is more important in magnitude than previously reported and it accords well with the NBER chronology. Our results are corroborated using an alternative trend-cycle decomposition based on a generalized unobserved components models with errors having a mixture of normals distribution for both the slope of the trend function and the cyclical component.Trend-cycle decomposition Structural change Non-Gaussian filtering Unobserved components model Beveridge-Nelson decomposition