factor.number {fnets}

Factor number selection methods

Description

Methods to estimate the number of factor. When method = 'er', the factor number is estimated by maximising the ration of successive eigenvalues. When method = 'ic', the information criterion-methods discussed in Hallin and Liška (2007) (when fm.restricted = FALSE) and Alessi, Barigozzi and Capasso (2010) (when fm.restricted = TRUE) are implemented. The information criterion called by ic.op = 5 (as an argument to fnets or fnets.factor.model) is recommended by default.

Usage

factor.number(
  x,
  fm.restricted = FALSE,
  method = c("ic", "er"),
  q.max = NULL,
  center = TRUE
)

Arguments

x

input time series each column representing a time series variable; it is coerced into a ts object

fm.restricted

whether to estimate the number of restricted or unrestricted factors

method

A string specifying the factor number selection method; possible values are:

"ic"

information criteria-based methods of Alessi, Barigozzi & Capasso (2010) when fm.restricted = TRUE or Hallin and Liška (2007) when fm.restricted = FALSE

"er"

eigenvalue ratio of Ahn and Horenstein (2013) when fm.restricted = TRUE or Avarucci et al. (2022) when fm.restricted = FALSE

q.max

maximum number of factors; if q.max = NULL, a default value is selected as min(50, floor(sqrt(min(dim(x)[2] - 1, dim(x)[1]))))

center

whether to de-mean the input x

Details

For further details, see references.

Value

S3 object of class factor.number. If method = "ic", a vector containing minimisers of the six information criteria, otherwise, the maximiser of the eigenvalue ratio

References

Ahn, S. C. & Horenstein, A. R. (2013) Eigenvalue ratio test for the number of factors. Econometrica, 81(3), 1203–1227.

Alessi, L., Barigozzi, M., and Capasso, M. (2010) Improved penalization for determining the number of factors in approximate factor models. Statistics & Probability Letters, 80(23-24):1806–1813.

Avarucci, M., Cavicchioli, M., Forni, M., & Zaffaroni, P. (2022) The main business cycle shock(s): Frequency-band estimation of the number of dynamic factors.

Hallin, M. & Liška, R. (2007) Determining the number of factors in the general dynamic factor model. Journal of the American Statistical Association, 102(478), 603–617.

Owens, D., Cho, H. & Barigozzi, M. (2024+) fnets: An R Package for Network Estimation and Forecasting via Factor-Adjusted VAR Modelling. The R Journal (to appear).

See Also

plot.factor.number, print.factor.number

Examples

library(fnets)
## Alessi, Barigozzi, and Capasso method for restricted models
abc <- factor.number(data.restricted, fm.restricted = TRUE)
print(abc)
plot(abc)

## Eigenvalue ratio method
er <- factor.number(data.restricted, method = "er", fm.restricted = TRUE)
print(er)
plot(er)

## Hallin and Liška method for unrestricted models
hl <- factor.number(data.unrestricted, fm.restricted = FALSE)
print(hl)
plot(hl)