The function estimates the Dynamic Factor Model by Principal Components and by the estimator of Lam et al. (2011).
dfmpc(x, stand = 0, mth = 4, r, lagk = 0)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.
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.
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 Pe<U+00F1>a (2020) test and the model is estimated using Lam et al. (2011) methodology with the combined correlation matrix.
Number of factors, default value is estimated by Lam and Yao (2012) criterion.
Maximum number of lags considered in the combined matrix. The default is lagk = 3.
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.
Ahn, S. C. and Horenstein, A. R. (2013). Eigenvalue ratio test for the number of factors. Econometrica, 81(3):1203<U+2013>1227.
Bai, J. and Ng, S. (2002). Determining the number of factors in approximate factor models. Econometrica, 70(1):191<U+2013>221.
Caro, A. and Pe<U+00F1>a, 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<U+2013>726.
Lam, C., Yao, Q., and Bathia, N. (2011). Estimation of latent factors for high-dimensional time series. Biometrika, 98(4):901<U+2013>918.
# NOT RUN {
data(TaiwanAirBox032017)
dfm1 <- dfmpc(as.matrix(TaiwanAirBox032017[1:100,1:30]), mth=4)
# }
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