Rolling regression is a procedure of estimating regression parameters at a sample interval with constant width that is gradually shifted in time. Regression enables the user to build trajectories of coefficients estimations together with their confidence limits and check hypothesis about constancy of regression equation coefficients in time.
Indicate a sample interval with constant width as a roll. Let one roll contain w observations, then a model of kth rolling regression with the step h looks as follows:
yk=Xk βk+ek
Where:
yk = (y(k-1)h+1, …, y(k-1)h+w). Vector of dependent variables of the dimension (w x 1).
Xk = (X(k-1)h+1, …, X(k-1)h+w). Matrix showing independent variables of the dimension (w x m).
βk. Vector of estimates of the dimension (m x 1).
ek. Vector of random errors of the dimension (w x 1).
The total amount of rolls is
Where T is the total number of observations.
The following operations can be executed for the obtained βk:
Estimate means of coefficients for each factor and use them as estimates of common model coefficients.
Estimate variances of coefficient values for each factor to test the hypothesis that regression equation coefficients are constant.
Plot lines that show changes in coefficients and visually estimate the development dynamics.
See also:
Library of Methods and Models | ISmRollingRegression