Coint: Identifying cointegration rank of given time series

In HDTSA: High Dimensional Time Series Analysis Tools

Identifying cointegration rank of given time series

Description

Coint seeks for a contemporaneous linear transformation for a multivariate time series such that we can identifying cointegration rank from the transformed series.

Usage

Coint(
  Y,
  lag.k = 5,
  type = c("acf", "pptest", "Chang", "all"),
  c0 = 0.3,
  m = 20,
  alpha = 0.01
)

Arguments

Y	{\bf Y} = \{{\bf y}_1, \dots , {\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{{\bf W}}_y: \widehat{\mathbf{W}}_y\ =\ \sum_{k=0}^{k_0}\widehat{\mathbf{\Sigma}}_y(k)\widehat{\mathbf{\Sigma}}_y(k)' where \widehat{\bf \Sigma}_y(k) is the sample autocovariance of \widehat{{\bf y}_t} at lag k.
type	The method of identifying cointegration rank after segment procedure. Option is 'acf', 'all', 'chang' or 'pptest' , the latter two methods use the unit-root test method to identify the cointegration rank, and the option type = 'all' means use all three methods to identify the cointegration rank. Default is type = 'acf'. See Sections 2.3 in Zhang, Robinson and Yao (2019) for more information.
c0	The prescribed constant for identifying cointegration rank using "acf" method. Default is 0.3.[See (2.3) in Zhang, Robinson and Yao (2019)].
m	The prescribed constant for identifying cointegration rank using "acf" method. Default is 20. [See (2.3) in Zhang, Robinson and Yao (2019)].
alpha	The prescribed significance level for identifying cointegration rank using "pptest","chang" method. Default is 0.01. [See (2.3) in Zhang, Robinson and Yao (2019)].

Value

An object of class "coint" is a list containing the following components:

Z	The transformed series with n rows and p columns.
coint_rank	A 1 \times 1 matrix representing the cointegration rank. If type = 'all', then return a 1 \times 3 matrix representing the cointegration rank of all three methods.
lag.k	a prescribed positive integer which means the time lags used to calculate the statistic.
method	a character string indicating which method was performed.

References

Zhang, R., Robinson, P. & Yao, Q. (2019). Identifying Cointegration by Eigenanalysis. Journal of the American Statistical Association, Vol. 114, pp. 916–927

Examples

p <- 10
n <- 1000
r <- 3
d <- 1
X <- mat.or.vec(p, n)
X[1,] <- arima.sim(n-d, model = list(order=c(0, d, 0)))
for(i in 2:3)X[i,] <- rnorm(n)
for(i in 4:(r+1)) X[i, ] <- arima.sim(model = list(ar = 0.5), n)
for(i in (r+2):p) X[i, ] <- arima.sim(n = (n-d), model = list(order=c(1, d, 1), ar=0.6, ma=0.8))
M1 <- matrix(c(1, 1, 0, 1/2, 0, 1, 0, 1, 0), ncol = 3, byrow = TRUE)
A <- matrix(runif(p*p, -3, 3), ncol = p)
A[1:3,1:3] <- M1
Y <- t(A%*%X)
Coint(Y, type = "all")

HDTSA documentation built on Sept. 11, 2024, 5:49 p.m.