Description Usage Arguments Details Value Examples
The response (univariate) is generated by the formula
y^{(t)} = X^{(t)}β^{(0)} + X^{(t-1)}β^{(1)} + ... + ε_t
where each X is a vector of covariates at a certain time point, with corresponding regression coefficients. Also automatically prepares the necessary lagged response matrix for second step (residual fitting)
1 |
beta |
a list. Default number of list is 5, corresponding to the furthest lag x^{t-4}. Each list is a vector of regression coefficients, corresponding to all covariates at that time stamp. |
sigmay |
a number. Standard deviation of noise for response. |
X |
a matrix. Covariate matrix, each column being one x. This corresponds to the output X from |
lagx |
a number. Number of lags for covarites, default is 5, meaning that the furthest covariate is x^{(t-4)}. |
lagy |
a number. Number of lags for response for the preparation of second step regression, default is 5, meaning that the furthest response is y^{(t-5)}. |
The most recent time stamp for covariates is t, the same as the response.
The input matrix X is automatically shifted given the number of lags. Due to the shifting scheme for the time lags, the length of the output response and extended matrix (nrow) are (t - lagx).
a list of components
X |
a matrix. The original input matrix X |
Y |
a vector. The generated linear time lagged response |
ExtendX |
a matrix. Dimension is (t - lagx) by lagx*length(beta), 495 by 50 in our examples |
ExtendY |
a matrix. Dimension is (t - lagy) by lagy |
1 | # see
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