Do your moving averages weight the data prior to averaging?

The ReDim statements and the iMin and iMax statements can all be taken out of the loop. Perhaps the original programmer initially had them inside the loop before I saw the code, and then I never put them in front of the loop.

From the VBA code I would say that LOESS fitting is really a choice for sparse data series. Time series make only sense if there are gaps in between. I used a similar technique already on time series in Excel like in your example.

If the distances are always the same between two X points, then the algorithm is just too general and consuming. My experience is that you always find a moving average that is as almost as good fitting as the moving regression window.

By the way: Why did you use Redim in a for-loop? There is another redim going over
all available data. One second Redim before the for would take more memory and save
time.

A comparison of moving average to loess would make more sense if the calculated moving average was plotted in the middle of the data for the moving average, but conventionally this is not done. Loess never used this convention.

Where I have noted an apparent lag in loess is in cases where the variation in the raw data is not symmetric, for example, when an increase is followed by a decrease which is much more or less steep. Changing the number of points in the moving regression may reduce the apparent lag. The apparent lag may be pronounced near the ends of the data set, where the regression consists of substantially more points on one side of the X value for the loess calculation.

You have a big glitch in your moving average example. MA always get a lag of n/2 points. The reason is that the MA is the 50% trend value of one linear regression of n x,y points. Both smoothing filters are comparable in the X axis if the MA is calculated from the n/2 days in the future. You would use the MA with OFFSET and AVG functions then and not take the diagram’s moving average.
However, some example charts indicate lags in the LOESS .. am I wrong?

By the way, I always was and am a big fan of your Excel experiences.
Big timesavers for me.

NIST(x):=interp(loess(X,Y,.5),X,Y,x)

where x was set as a range variable x:=0,0.1,..20

This creates a function NIST(x) that you can plot versus the range variable x

Here is the MathCAD explanation for the two built-in functions ‘interp’ & ‘loess’:

loess(vx, vy, span) Returns a vector which interp uses to find a set of second-order polynomials that best fit the neighborhood of x and y data values in vx and vy in the least-squares sense. The size of the neighborhood is controlled by span.

interp(vs, vx, vy, x) Returns the interpolated y-value corresponding to x using the output vector vs from loess.

Your new output is the result of LOESS calculation using a 7 point moving regression, using X and Y input as inputs and X input as the X output.

Please see the difference of the output:

X input Y input X output original output new output
0.55782 18.63654 0 -13.07212037 20.59304051
2.021727 103.4965 1 47.06914445 107.1603064
2.577325 150.3539 2 105.8974689 139.7673806
3.414029 190.5103 3 159.6924955 174.2630716
4.301408 208.7012 4 196.8626739 207.2333938
4.744839 213.7114 5 219.0115635 216.6616039
5.107378 228.4935 6 227.6417493 220.5444981
6.541166 233.5539 7 230.2534309 229.8606994
6.721618 234.5505 8 227.0376643 229.8347242
7.260058 223.8923 9 221.246659 229.4301269
8.133587 227.6834 10 202.9876659 226.6044626
9.122438 223.9198 11 187.8518139 220.3904231
11.92967 168.02 12 170.6711911 172.3479193
12.37977 164.9575 13 162.210816 163.8416617
13.27286 152.6111 14 160.7756941 161.8489846
14.27675 160.7874 15 159.7155843 160.3350921
15.3731 168.5557 16 161.0838629 160.1920102
15.64766 152.4266 17 194.5740586 161.0555463
18.56054 221.707 18 215.4190384 227.3399984
18.58664 222.6904 19 236.7904956 227.8985782
18.75728 243.1883

The line of code works fine in VBA, which assigns the values in a range to a 1-based array. You have to adjust the syntax to use the code in C++.

Thank you for the nice code. It helped me easily added a function to a C++ App. There is a small bug you might not notice. The assignment for xNow should be:

xNow = X(xDomain(iPoint, 1) + 1, 1)

instead of:

xNow = xDomain(iPoint, 1)

Thank you,