Beyond curse of dimensionality

We now consider aggregate model and add change in A and Q and make them

fluctuate according to some random process.

We approximate the continuous random model:

by switching model with infinite many states in order:

.

.

.

where

.

.

.

for many states.

We calculate each policy function for each A and Q as it is set like:

independently for each i and calculate the next index number.

We consider some random process of A and Q as

and

where and are error terms with mean zero.

We implement column-by-column calculation:

from j=1 to n

when we calculate each index vector. We then smooth out the points on the gird by one

of the following:

0:linear interpolation

1:polynomial

2:LOESS

3:LOWESS

4:Kernel regression

5:Smoothing natural spline

6:NURBS

7:Bezier Curve

locally by index numbers around the evaluated points only. We also implement

collocation method independently without forming a procedure.

We set K[ind[indn]] and K[indn] rather than K1=K[ind] and K.

All we have to do is change the functional setting of fc. It is optional to change

from small to large letters.