Linearly Weighted Moving Average

See: Moving Average - MA.

Not to be confused with an exponential moving average because, well, they have different names, so there’s a good chance (like 100%) that they’re different things.

A linearly weighted average is like a normal moving average, except that a linearly weighted moving average adds weight to more recent entries in a moving average, rather than giving each entry an equal weight in the arithmetic average.

Let’s say we had the following data on our Ugli Fruit harvest taken over a six-day period:

12, 14, 11, 10, 16, 18.

A regular moving average (using groups of three) would add up the first three values (12 + 14 + 11 = 37) and divide that value by three, giving us our first moving average of 12.33.

A linearly weighted moving average would multiply each of the same three entries by a weight with the most recent value getting the highest weight. Weights are usually numbered from one up to the number of entries.

That gives us (12 x 1) + (14 x 2) + (11 x 3) = 12 + 28 + 33 = 73. We then divide by the sum of the weights (1 + 2 + 3 = 6), which gives us 12.17.

Naturally, for both moving averages (the normal one and the linearly weighted one), we’d then move one entry down the line and calculate the next moving average, and repeat that until we reached the end of the data.

So think of a linearly iterated curve as one with a generally straight line; an exponent has curves. Teeter-totters versus the double black diamonds at a top-notch ski resort.