Generates a random instance of a partial cointegration model
rpci(n, beta, sigma_C, rho, sigma_M, sigma_R,
include.state = FALSE, robust = FALSE, nu = 5)Number of observations to generate
A vector of factor loadings
A vector of standard deviations
The coefficient of mean reversion
The standard deviation of the innovations of the random walk portion of the residual series
The standard deviation of the innovations of the mean-reverting portion of the residual series
If TRUE, then the output data.frame contains the innovations to the factors and residual series, as well as the state of the residual series. Default: FALSE
If TRUE, then a t-distribution is used to generate the innovations. Otherwise, the innovations are normally distributed. Default: FALSE.
The degrees of freedom parameter used for t-distributed innovations. Default: 5.
A data.frame of n rows representing the realization of the partially
cointegrated sequence.
If include.state is FALSE, returns an n x (k+1) matrix whose columns
are y, F_1, F_2, ..., F_k. If include.state is TRUE, returns an
n x (2k + 6) matrix whose columns are
y, F_1, F_2, ..., F_k, x, M, R, delta_1, delta_2, ..., delta_k, epsilon_M, epsilon_R.
Generates a random set of partially cointegrated vectors. On input, n is the
length of the sequence to be generated. beta is a vector of length k
representing the coefficients of the factor loadings, and sigma_C is a
vector of length k representing the standard deviations of the increments
of the factor loadings.
Generates a random realization of the sequence $$Y_t = \beta_1 F_{1,t} + \beta_2 F_{2,t} + ... + \beta_k F_{k,t} + M_t + R_t$$ $$F_{i,j} = F_{i,j-1} + \delta_{i,j}$$ $$M_t = \rho m_{t-1} + \epsilon_{M,t}$$ $$R_t = r_{t-1} + \epsilon_{R,t}$$ $$\delta_{i,j} ~ N(0, \sigma_{C,i}^2)$$ $$\epsilon_{M,t} ~ N(0, \sigma_M^2)$$ $$\epsilon_{R,t} ~ N(0, \sigma_R^2)$$
# NOT RUN {
rpci(10, beta=1, sigma_C=1, rho=0.9, sigma_R=1, sigma_M=1)
# }
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