Implements the cross-sectionally augmented IPS (CIPS) panel unit root test of Pesaran (2007), which allows for cross-sectional dependence through a single unobserved common factor. For each unit, a cross-sectionally augmented Dickey-Fuller (CADF) regression is run:
cips_test(x, ...)# S3 method for matrix
cips_test(x, ..., lags = 0L, trend = FALSE)
# S3 method for dcce_fit
cips_test(x, ..., lags = 0L, trend = FALSE)
# S3 method for default
cips_test(
x,
...,
data = NULL,
unit_index = NULL,
time_index = NULL,
lags = 0L,
trend = FALSE
)
An object of class dcce_cips with elements:
The CIPS statistic (truncated cross-sectional average).
Approximate p-value from Pesaran (2007) critical values.
Per-unit truncated CADF t-statistics.
Number of units.
Time dimension.
Number of augmentation lags.
Whether a trend was included.
A numeric vector, numeric matrix (N x T), data.frame, or
dcce_fit object. If a vector, data, unit_index, and time_index
must also be supplied.
Additional arguments passed to methods.
Integer: number of lags of \(\Delta y\) to include in the CADF regression. Default 0 (pure CADF without augmentation).
Logical: include a linear time trend? Default FALSE.
A data.frame containing the panel structure (when x is
a vector).
Character: name of the unit variable in data.
Character: name of the time variable in data.
$$\Delta y_{it} = a_i + b_i y_{i,t-1} + c_i \bar{y}_{t-1} + d_i \Delta \bar{y}_t + \sum_{j=1}^{p} \rho_{ij} \Delta y_{i,t-j} + \sum_{j=0}^{p} \delta_{ij} \Delta \bar{y}_{t-j} + u_{it}.$$
The CIPS statistic is the cross-sectional average of the unit-level t-statistics for \(b_i = 0\) (the CADF statistic). Critical values come from Pesaran (2007, Table II(b), constant case) and Pesaran (2007, Table II(c), constant + trend case). The null hypothesis is that all series contain a unit root.
Pesaran, M. H. (2007). A simple panel unit root test in the presence of cross-section dependence. Journal of Applied Econometrics, 22(2), 265-312.
set.seed(1)
N <- 20; T <- 30
f <- cumsum(rnorm(T))
X <- matrix(NA, N, T)
for (i in seq_len(N)) X[i, ] <- cumsum(rnorm(T)) + 0.5 * f
cips_test(X)
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