dfmpc: Dynamic Factor Model by Principal Components

In SLBDD: Statistical Learning for Big Dependent Data

Dynamic Factor Model by Principal Components

Description

The function estimates the Dynamic Factor Model by Principal Components and by the estimator of Lam et al. (2011).

Usage

dfmpc(x, stand = 0, mth = 4, r, lagk = 0)

Arguments

x	T by k data matrix: T data points in rows with each row being data at a given time point, and k time series in columns.
stand	Data standardization. The default is stand = 0 and x is not transformed, if stand = 1 each column of x has zero mean an if stand=2 also unit variance.
mth	Method to estimate the number of factors and the common component (factors and loadings): mth = 0 - the number of factors must be given by the user and the model is estimated by Principal Components. mth = 1 - the number of factors must be given by the user and the model is estimated using Lam et al. (2011) methodology. mth = 2 - the number of factors is estimated using Bai and Ng (2002) ICP1 criterion and the model is estimated by Principal Components. mth = 3 - the number of factors is estimated using Bai and Ng (2002) ICP1 criterion and the model is estimated using Lam et al. (2011) methodology. mth = 4 - the number of factors is estimated by applying once the Lam and Yao (2012) criterion and the model is estimated using Lam et al. (2011) methodology (default method). mth = 5 - the number of factors is estimated using Ahn and Horenstein (2013) test and the model is estimated by Principal Components. mth = 6 - the number of factors is estimated using Caro and Peña (2020) test and the model is estimated using Lam et al. (2011) methodology with the combined correlation matrix.
r	Number of factors, default value is estimated by Lam and Yao (2012) criterion.
lagk	Maximum number of lags considered in the combined matrix. The default is lagk = 3.

Value

A list with the following items:

• r - Estimated number of common factors, if mth=0, r is given by the user.

• F - Estimated common factor matrix (T x r).

• L - Estimated loading matrix (k x r).

• E - Estimated noise matrix (T x k).

• VarF - Proportion of variability explained by the factor and the accumulated sum.

• MarmaF - Matrix giving the number of AR, MA, seasonal AR and seasonal MA coefficients for the Factors, plus the seasonal period and the number of non-seasonal and seasonal differences.

• MarmaE - Matrix giving the number of AR, MA, seasonal AR and seasonal MA coefficients for the noises, plus the seasonal period and the number of non-seasonal and seasonal differences.

References

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

Bai, J. and Ng, S. (2002). Determining the number of factors in approximate factor models. Econometrica, 70(1):191–221.

Caro, A. and Peña, D. (2020). A test for the number of factors in dynamic factor models. UC3M Working papers. Statistics and Econometrics.

Lam, C. and Yao, Q. (2012). Factor modeling for high-dimensional time series: inference for the number of factors. The Annals of Statistics, 40(2):694–726.

Lam, C., Yao, Q., and Bathia, N. (2011). Estimation of latent factors for high-dimensional time series. Biometrika, 98(4):901–918.

Examples

data(TaiwanAirBox032017)
dfm1 <- dfmpc(as.matrix(TaiwanAirBox032017[1:100,1:30]), mth=4)

SLBDD documentation built on April 27, 2022, 5:08 p.m.