y.present: Generate linear time lagged response with time series...
In yymmhaha/PackPaper1: Package related to my first paper

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	y.present(beta, sigmay, X, lagx, lagy)

`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 `XgenSimple, XgenCorr`s.
`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