factors | R Documentation |
factors()
deals with factor modeling for high-dimensional
time series proposed in Lam and Yao (2012):
{\bf y}_t = {\bf Ax}_t + {\boldsymbol{ε}}_t,
where {\bf x}_t is an r \times 1 latent process with (unknown) r ≤q p, {\bf A} is a p \times r unknown constant matrix, and {\boldsymbol{ε}}_t \sim \mathrm{WN}({\boldsymbol{μ}}_{ε}, {\bf Σ}_{ε}) is a vector white noise process. The number of factors r and the factor loadings {\bf A} can be estimated in terms of an eigenanalysis for a nonnegative definite matrix, and is therefore applicable when the dimension of {\bf y}_t is on the order of a few thousands. This function aims to estimate the number of factors r and the factor loading matrix {\bf A}.
factors(Y, lag.k = 5, twostep = FALSE)
Y |
{\bf Y} = \{{\bf y}_1, … , {\bf y}_n \}', a data matrix with n rows and p columns, where n is the sample size and p is the dimension of {\bf y}_t. |
lag.k |
Time lag k_0 used to calculate the nonnegative definte matrix \widehat{\mathbf{M}}: \widehat{\mathbf{M}}\ =\ ∑_{k=1}^{k_0}\widehat{\mathbf{Σ}}_y(k)\widehat{\mathbf{Σ}}_y(k)', where \widehat{\bf Σ}_y(k) is the sample autocovariance of {\bf y}_t at lag k. |
twostep |
Logical. If |
An object of class "factors" is a list containing the following components:
factor_num |
The estimated number of factors \hat{r}. |
loading.mat |
The estimated p \times r factor loading matrix \widehat{\bf A}. |
Lam, C. & Yao, Q. (2012). Factor modelling for high-dimensional time series: Inference for the number of factors, The Annals of Statistics, Vol. 40, pp. 694–726.
## Generate x_t p <- 400 n <- 400 r <- 3 X <- mat.or.vec(n, r) A <- matrix(runif(p*r, -1, 1), ncol=r) x1 <- arima.sim(model=list(ar=c(0.6)), n=n) x2 <- arima.sim(model=list(ar=c(-0.5)), n=n) x3 <- arima.sim(model=list(ar=c(0.3)), n=n) eps <- matrix(rnorm(n*p), p, n) X <- t(cbind(x1, x2, x3)) Y <- A %*% X + eps Y <- t(Y) fac <- factors(Y,lag.k=2) r_hat <- fac$factor_num loading_Mat <- fac$loading.mat
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