dfmpc {SLBDD}

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)