# mmse

Syntax

mmse(Y, X, window, [minPeriods])

Please see Moving Functions (m-functions) for the parameters and windowing logic.

Details

Return the coefficient estimates of X and mean square errors of an ordinary-least-squares regression of Y on X with intercept with a rolling window. The length of the window is given by the parameter window.

The mean square error (MSE) is calculated with the following formula:

$$MSE=\dfrac{1}{n} {\sum\limits_{i = 1}^{n} (Y_i - \hat{Y_i})^2}$$

The result is a tuple with 2 vectors. The first vector is the coefficient estimates and the second vector is the mean square errors. Each vector is of the same length as X and Y.

Examples

$x=0.011 0.006 -0.008 0.012 -0.016 -0.023 0.018$ y=0.016 0.009 -0.012 0.022 0.003 -0.056 0.002;

$mmse(y, x, 5); [,,,,0.818182,1.692379,1.188532]$ mmse(y, x, 5);
[,,,,0.000055,0.000231,0.000332]

\$ select y, x, mmse(y,x,5,3) as mbetammse from table(x,y);


y

x

mbeta

mmse

0.016

0.011

0.009

0.006

-0.012

-0.008

1.479381

2.806415E-8

0.022

0.012

1.594701

0.000003

0.003

-0.016

0.818182

0.000055

-0.056

-0.023

1.692379

0.000231

0.002

0.018

1.188532

0.000332