bssa: Singular Spectrum Business Cycle Indicator

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/bssa.R


Computes a business cycle indicator using singular spectrum analysis.


bssa(y, l = 32)



time series of economic activity data from which the cycle is to be extracted.


window length; by default, l = 32.


The business cycle indicator produced using this routine is based on methods proposed in de Carvalho et al (2012) and de Carvalho and Rua (2017). A quick summary of the method is as follows: Singular spectrum analysis is used to decompose a GDP time series (y) into principal components, and a Fisher g statistic automatically selects elementary reconstructed components (erc) within business cycle frequencies. The indicator results from adding principal components within business cycle frequencies. The plot method depicts the resulting business cycle indicator, and the print method reports the business cycle indicator along with the components selected by the Fisher g statistic.



time series with the business cycle indicator.


vector with indices of principal components selected with Fisher g statistic; see details.


time series with elementary reconstructed components resulting from targeted grouping based on a Fisher g statistic.


window length.


Miguel de Carvalho.


de Carvalho, M., Rodrigues, P., and Rua, A. (2012) Tracking the US business cycle with a singular spectrum analysis. Economics Letters, 114, 32–35.

de Carvalho, M. and Rua, A. (2017) Real-time nowcasting the US output gap: Singular spectrum analysis at work. International Journal of Forecasting, 33, 185–198.

See Also

See combplot for a chart of the selected elementary reconstructed components from which the business cycle indicator results. See bmssa for a multivariate version of the method.


## Tracking the US Business Cycle (de Carvalho et al, 2017; Fig. 6) 
fit <- bssa(log(GDPIP[, 1]))

Example output

## ============================================== ##
## ASSA 1.0                                       ##
## ---------------------------------------------- ##
##  Copyright (C) 2018                            ##
##  M. de Carvalho and G. Martos                  ##
## ============================================== ##

 Singular Spectrum Business Cycle Analysis:
 bssa.default(y = log(GDPIP[, 1]))

 Business cycle indicator:

              Qtr1          Qtr2          Qtr3          Qtr4
1947  1.554288e-02  5.608885e-03  1.981290e-03  5.929933e-03
1948  1.183468e-02  1.451144e-02  9.698122e-03 -2.934166e-03
1949 -2.050815e-02 -3.686477e-02 -4.694418e-02 -4.809368e-02
1950 -3.832702e-02 -2.169488e-02 -3.132920e-03  1.200064e-02
1951  2.088902e-02  2.282218e-02  1.882552e-02  1.178704e-02
1952  6.498018e-03  6.538789e-03  1.295639e-02  2.262662e-02
1953  2.880704e-02  2.602349e-02  1.312687e-02 -5.593969e-03
1954 -2.242972e-02 -3.056578e-02 -2.716107e-02 -1.461554e-02
1955  1.625559e-03  1.405256e-02  1.872893e-02  1.611874e-02
1956  1.038416e-02  6.705517e-03  7.328220e-03  1.121800e-02
1957  1.373333e-02  1.060833e-02  6.659882e-04 -1.389873e-02
1958 -2.695652e-02 -3.169303e-02 -2.615352e-02 -1.330392e-02
1959  1.507732e-03  1.330981e-02  1.880255e-02  1.814801e-02
1960  1.256720e-02  3.068371e-03 -7.377966e-03 -1.572859e-02
1961 -1.884021e-02 -1.613981e-02 -9.515974e-03 -2.012047e-03
1962  3.133905e-03  4.019848e-03  9.792231e-04 -3.960354e-03
1963 -7.898353e-03 -9.086850e-03 -7.518766e-03 -4.961177e-03
1964 -3.106106e-03 -3.654688e-03 -6.108438e-03 -8.330907e-03
1965 -7.298422e-03 -2.229575e-03  6.099433e-03  1.479460e-02
1966  2.046867e-02  2.095289e-02  1.705482e-02  1.082682e-02
1967  4.577117e-03  5.551763e-05 -1.454158e-03  6.911446e-05
1968  3.957673e-03  8.485643e-03  1.210496e-02  1.401569e-02
1969  1.377241e-02  1.060382e-02  4.811162e-03 -2.786327e-03
1970 -1.038474e-02 -1.640511e-02 -2.007744e-02 -2.158642e-02
1971 -2.059466e-02 -1.871827e-02 -1.616360e-02 -1.248837e-02
1972 -6.599675e-03  1.576581e-03  1.120639e-02  2.131729e-02
1973  2.991276e-02  3.456190e-02  3.409153e-02  2.879381e-02
1974  1.872734e-02  5.454474e-03 -9.225011e-03 -2.227416e-02
1975 -3.090435e-02 -3.303291e-02 -2.942249e-02 -2.286168e-02
1976 -1.637063e-02 -1.242661e-02 -1.093847e-02 -1.033837e-02
1977 -8.966382e-03 -6.048834e-03 -1.906582e-03  3.093993e-03
1978  9.555691e-03  1.755788e-02  2.480381e-02  3.015971e-02
1979  3.241842e-02  3.109746e-02  2.612883e-02  1.800406e-02
1980  8.615125e-03  7.679112e-04 -1.915973e-03  1.006631e-03
1981  6.072686e-03  8.239626e-03  4.723848e-03 -5.653455e-03
1982 -2.004501e-02 -3.360385e-02 -4.268025e-02 -4.455674e-02
1983 -3.875377e-02 -2.735033e-02 -1.399894e-02 -1.943482e-03
1984  6.633733e-03  1.104533e-02  1.203887e-02  1.139201e-02
1985  1.072660e-02  1.063463e-02  1.076828e-02  1.003064e-02
1986  8.032045e-03  4.869072e-03  1.303420e-03 -1.938360e-03
1987 -3.893904e-03 -3.979668e-03 -2.355276e-03  3.801916e-04
1988  3.027548e-03  5.223631e-03  6.808078e-03  8.348318e-03
1989  1.004332e-02  1.198930e-02  1.392912e-02  1.509074e-02
1990  1.461577e-02  1.125466e-02  4.796540e-03 -3.589310e-03
1991 -1.135478e-02 -1.613140e-02 -1.706951e-02 -1.443581e-02
1992 -9.577274e-03 -4.707880e-03 -1.705277e-03 -1.295389e-03
1993 -2.886710e-03 -4.581393e-03 -4.726468e-03 -2.553792e-03
1994  1.032576e-03  4.442962e-03  5.919838e-03  4.836687e-03
1995  1.386424e-03 -2.978334e-03 -6.583769e-03 -8.459456e-03
1996 -8.366728e-03 -6.782908e-03 -5.077503e-03 -3.944329e-03
1997 -3.548520e-03 -3.425605e-03 -3.304537e-03 -2.871631e-03
1998 -1.839077e-03 -3.217540e-04  1.471795e-03  3.339168e-03
1999  5.257705e-03  7.786466e-03  1.129619e-02  1.527622e-02
2000  1.835635e-02  1.964968e-02  1.782251e-02  1.323392e-02
2001  6.936796e-03  6.746628e-04 -4.580642e-03 -8.182956e-03
2002 -1.051967e-02 -1.261301e-02 -1.486251e-02 -1.682569e-02
2003 -1.732109e-02 -1.556528e-02 -1.182576e-02 -7.515987e-03
2004 -3.903145e-03 -1.475499e-03 -1.021809e-04  8.716467e-04
2005  2.280652e-03  4.526355e-03  7.602747e-03  1.073727e-02
2006  1.300230e-02  1.291618e-02  1.159875e-02  1.043904e-02
2007  1.068880e-02  1.294337e-02  1.617224e-02  1.812252e-02
2008  1.639909e-02  9.864312e-03 -1.321350e-03 -1.478001e-02
2009 -2.636938e-02 -3.264083e-02 -3.239340e-02 -2.675809e-02
2010 -1.864904e-02 -1.102570e-02 -6.118116e-03 -4.239615e-03
2011 -4.026840e-03 -2.783366e-03  7.933413e-04  6.557145e-03
2012  1.216516e-02  1.525314e-02  1.523746e-02  1.279048e-02
2013  1.049569e-02  1.068693e-02  1.414140e-02  1.913012e-02

 Principal components selected by the Fisher g statistic 

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ASSA documentation built on Nov. 20, 2020, 5:10 p.m.

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