Performs rolling OLS regressions for a provided vector of dependent data and matrix of independent regressors.


{ coef, res, w } = rolling(yt, xt, window, add, graph)
  • yt (Tx1 numerical vector) – panel series data.

  • xt (TxK numerical matrix) – estimation regressors.

  • window (scalar) – Optional input, a positive integer specifying a fixed window size of K< window <T. A window size of less than zero results in an expanding window. Default = 0.

  • add (scalar) – Optional input, specifying the initial observation for the forward expanding window. Negative values indicate a backward window expansion, beginning with the last add number of observations. The add input is valid only if a negative window size is provided. Default = 0.

  • graph (scalar) – Optional input, any number greater than zero will graph the rolling values of all coefficient estimates, including the constant. Default = 1.

  • coef (matrix) – rolling coefficient estimates.

  • res (matrix) – one-step ahead rolling residuals.

  • w (matrix) – standardized one-step ahead rolling residuals.


library tsmt;
rndseed 23563425;

//This generates 400 observations of an
//linear time series with a break in the constant
//at observations 120

b1 = { 1.2, -2, 0.75 };
b2 = { 5, -2, 0.75 };

n1 = 120;
n_tot = 400;
xt = ones( n_tot, 1 )~rndn( n_tot, 2 );
et = rndn( n_tot, 1 );

//Create series with break
y1 = xt[1:n1, .]*b1 + et[1:n1, .];
y2 = xt[n1+1:n_tot, .]*b2 + et[n1+1:n_tot, .];
yt_break = y1|y2;

//Set parameters to run a rolling window regression
//Positive window sets fixed window
wind = 15;

//Fixed window regression
{ beta, res, w } = rolling( yt_break, xt, wind );

//Next set parameters to run an forward expanding window regression
//Set-up expanding window size
//Negative window results in expanding window size
wind = -15;

//Add specifies increment to increase window size by
//and is irrelevant for rolling window regression
add = 15;

//Draw plot from second call to 'rolling' in new window
plotOpenWindow( );

//Expanding window estimation
{ beta_fwd, res_fwd, w_fwd } = rolling( yt_break, xt, wind, add );


The GAUSS rolling procedure performs rolling OLS regressions for a provided vector of dependent data and matrix of independent regressors.


Zivot, E., and Wang, J. (2002). Modeling Financial Time Series with S-PLUS. Springer-Verlag, New York.