The question is about an equation coming from a scientific paper which i find it hard to reproduce. But the problem is as follows:
A range of window lengths varying from twenty days to sixty days are considered. Let l denote the window length, L denote the price series length and i denote an index in price series. For each window length between i and i + l days, where index i ranges from the beginning of price series to L - l - 1 (inclusive range). The price list observed between days [i, i + l] is scaled to a new price list with 20 elements. The price series length scaling is performed using the following equation. Rescaling is analogous to resizing the price series length to 20 days. Price for day j in actual price series becomes the price on day dj in rescaled price series where dj is given by the following equation. Price for days between dj and dj+1 are interpolated.
Given the following price list, how would this formula be applied in for example Excel? I tried to reproduce the result but i get some really weird numbers, so i wonder if someone can help apply this formula for the given price table list
+-----+--------+
| Day | Price |
+-----+--------+
| 1 | 86.5 |
| 2 | 84.76 |
| 3 | 78.7 |
| 4 | 71.21 |
| 5 | 79.84 |
| 6 | 72.83 |
| 7 | 73.01 |
| 8 | 67.42 |
| 9 | 75.79 |
| 10 | 73.52 |
| 11 | 77.61 |
| 12 | 71.43 |
| 13 | 66.81 |
| 14 | 66.54 |
| 15 | 69.44 |
| 16 | 63.33 |
| 17 | 64.73 |
| 18 | 61.14 |
| 19 | 67.52 |
| 20 | 71.12 |
| 21 | 63.93 |
| 22 | 66.59 |
| 23 | 63.78 |
| 24 | 66.65 |
| 25 | 63.34 |
| 26 | 71.13 |
| 27 | 74.63 |
| 28 | 67.08 |
| 29 | 60.44 |
| 30 | 60.87 |
| 31 | 66.35 |
| 32 | 67.53 |
| 33 | 69.62 |
| 34 | 73.98 |
| 35 | 79.52 |
| 36 | 86.74 |
| 37 | 87.9 |
| 38 | 82.19 |
| 39 | 84.98 |
| 40 | 80.11 |
| 41 | 80.69 |
| 42 | 81.28 |
| 43 | 85.92 |
| 44 | 95.83 |
| 45 | 98.66 |
| 46 | 96.84 |
| 47 | 100.3 |
| 48 | 101.91 |
| 49 | 108.97 |
| 50 | 116.54 |
| 51 | 119.52 |
| 52 | 124.37 |
| 53 | 130.74 |
| 54 | 136.83 |
| 55 | 140.88 |
| 56 | 140.68 |
| 57 | 142.73 |
| 58 | 135.58 |
| 59 | 144.65 |
| 60 | 150.3 |
+-----+--------+
The result should be 40 windows with rescaled prices to 20 elements each. The equation is a linear interpolator that rescales the series over interval L elements to one over 20 elements. So basically taking all the prices after the 20th element in the price series and rescale that new list to a 20 elements list. Here is the same table with the windows it should rescale. I created a simple excel file here with the following table:
+-----------+--------------------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+
| | windows length (l) | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 |
+-----------+--------------------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+
| Index (i) | Price | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| 1 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 | 86.5 |
| 2 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 | 84.76 |
| 3 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 | 78.7 |
| 4 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 | 71.21 |
| 5 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 | 79.84 |
| 6 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 | 72.83 |
| 7 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 | 73.01 |
| 8 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 | 67.42 |
| 9 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 | 75.79 |
| 10 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 | 73.52 |
| 11 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 | 77.61 |
| 12 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 | 71.43 |
| 13 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 | 66.81 |
| 14 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 | 66.54 |
| 15 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 | 69.44 |
| 16 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 | 63.33 |
| 17 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 | 64.73 |
| 18 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 | 61.14 |
| 19 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 | 67.52 |
| 20 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 | 71.12 |
| 21 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 | 63.93 |
| 22 | 66.59 | | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 | 66.59 |
| 23 | 63.78 | | | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 | 63.78 |
| 24 | 66.65 | | | | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 | 66.65 |
| 25 | 63.34 | | | | | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 | 63.34 |
| 26 | 71.13 | | | | | | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 | 71.13 |
| 27 | 74.63 | | | | | | | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 | 74.63 |
| 28 | 67.08 | | | | | | | | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 | 67.08 |
| 29 | 60.44 | | | | | | | | | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 | 60.44 |
| 30 | 60.87 | | | | | | | | | | 60.87 | 60.87 | 60.87 | 60.87 | 60.87 | 60.87 | 60.87 | 60.87 | 60.87 | 60.87 | 60.87 | 60.87 | 60.87 | 60.87 | 60.87 | 60.87 | 60.87 | 60.87 | 60.87 | 60.87 | 60.87 | 60.87 | 60.87 | 60.87 | 60.87 | 60.87 | 60.87 | 60.87 | 60.87 | 60.87 | 60.87 |
| 31 | 66.35 | | | | | | | | | | | 66.35 | 66.35 | 66.35 | 66.35 | 66.35 | 66.35 | 66.35 | 66.35 | 66.35 | 66.35 | 66.35 | 66.35 | 66.35 | 66.35 | 66.35 | 66.35 | 66.35 | 66.35 | 66.35 | 66.35 | 66.35 | 66.35 | 66.35 | 66.35 | 66.35 | 66.35 | 66.35 | 66.35 | 66.35 | 66.35 |
| 32 | 67.53 | | | | | | | | | | | | 67.53 | 67.53 | 67.53 | 67.53 | 67.53 | 67.53 | 67.53 | 67.53 | 67.53 | 67.53 | 67.53 | 67.53 | 67.53 | 67.53 | 67.53 | 67.53 | 67.53 | 67.53 | 67.53 | 67.53 | 67.53 | 67.53 | 67.53 | 67.53 | 67.53 | 67.53 | 67.53 | 67.53 | 67.53 |
| 33 | 69.62 | | | | | | | | | | | | | 69.62 | 69.62 | 69.62 | 69.62 | 69.62 | 69.62 | 69.62 | 69.62 | 69.62 | 69.62 | 69.62 | 69.62 | 69.62 | 69.62 | 69.62 | 69.62 | 69.62 | 69.62 | 69.62 | 69.62 | 69.62 | 69.62 | 69.62 | 69.62 | 69.62 | 69.62 | 69.62 | 69.62 |
| 34 | 73.98 | | | | | | | | | | | | | | 73.98 | 73.98 | 73.98 | 73.98 | 73.98 | 73.98 | 73.98 | 73.98 | 73.98 | 73.98 | 73.98 | 73.98 | 73.98 | 73.98 | 73.98 | 73.98 | 73.98 | 73.98 | 73.98 | 73.98 | 73.98 | 73.98 | 73.98 | 73.98 | 73.98 | 73.98 | 73.98 |
| 35 | 79.52 | | | | | | | | | | | | | | | 79.52 | 79.52 | 79.52 | 79.52 | 79.52 | 79.52 | 79.52 | 79.52 | 79.52 | 79.52 | 79.52 | 79.52 | 79.52 | 79.52 | 79.52 | 79.52 | 79.52 | 79.52 | 79.52 | 79.52 | 79.52 | 79.52 | 79.52 | 79.52 | 79.52 | 79.52 |
| 36 | 86.74 | | | | | | | | | | | | | | | | 86.74 | 86.74 | 86.74 | 86.74 | 86.74 | 86.74 | 86.74 | 86.74 | 86.74 | 86.74 | 86.74 | 86.74 | 86.74 | 86.74 | 86.74 | 86.74 | 86.74 | 86.74 | 86.74 | 86.74 | 86.74 | 86.74 | 86.74 | 86.74 | 86.74 |
| 37 | 87.9 | | | | | | | | | | | | | | | | | 87.9 | 87.9 | 87.9 | 87.9 | 87.9 | 87.9 | 87.9 | 87.9 | 87.9 | 87.9 | 87.9 | 87.9 | 87.9 | 87.9 | 87.9 | 87.9 | 87.9 | 87.9 | 87.9 | 87.9 | 87.9 | 87.9 | 87.9 | 87.9 |
| 38 | 82.19 | | | | | | | | | | | | | | | | | | 82.19 | 82.19 | 82.19 | 82.19 | 82.19 | 82.19 | 82.19 | 82.19 | 82.19 | 82.19 | 82.19 | 82.19 | 82.19 | 82.19 | 82.19 | 82.19 | 82.19 | 82.19 | 82.19 | 82.19 | 82.19 | 82.19 | 82.19 |
| 39 | 84.98 | | | | | | | | | | | | | | | | | | | 84.98 | 84.98 | 84.98 | 84.98 | 84.98 | 84.98 | 84.98 | 84.98 | 84.98 | 84.98 | 84.98 | 84.98 | 84.98 | 84.98 | 84.98 | 84.98 | 84.98 | 84.98 | 84.98 | 84.98 | 84.98 | 84.98 |
| 40 | 80.11 | | | | | | | | | | | | | | | | | | | | 80.11 | 80.11 | 80.11 | 80.11 | 80.11 | 80.11 | 80.11 | 80.11 | 80.11 | 80.11 | 80.11 | 80.11 | 80.11 | 80.11 | 80.11 | 80.11 | 80.11 | 80.11 | 80.11 | 80.11 | 80.11 |
| 41 | 80.69 | | | | | | | | | | | | | | | | | | | | | 80.69 | 80.69 | 80.69 | 80.69 | 80.69 | 80.69 | 80.69 | 80.69 | 80.69 | 80.69 | 80.69 | 80.69 | 80.69 | 80.69 | 80.69 | 80.69 | 80.69 | 80.69 | 80.69 | 80.69 |
| 42 | 81.28 | | | | | | | | | | | | | | | | | | | | | | 81.28 | 81.28 | 81.28 | 81.28 | 81.28 | 81.28 | 81.28 | 81.28 | 81.28 | 81.28 | 81.28 | 81.28 | 81.28 | 81.28 | 81.28 | 81.28 | 81.28 | 81.28 | 81.28 |
| 43 | 85.92 | | | | | | | | | | | | | | | | | | | | | | | 85.92 | 85.92 | 85.92 | 85.92 | 85.92 | 85.92 | 85.92 | 85.92 | 85.92 | 85.92 | 85.92 | 85.92 | 85.92 | 85.92 | 85.92 | 85.92 | 85.92 | 85.92 |
| 44 | 95.83 | | | | | | | | | | | | | | | | | | | | | | | | 95.83 | 95.83 | 95.83 | 95.83 | 95.83 | 95.83 | 95.83 | 95.83 | 95.83 | 95.83 | 95.83 | 95.83 | 95.83 | 95.83 | 95.83 | 95.83 | 95.83 |
| 45 | 98.66 | | | | | | | | | | | | | | | | | | | | | | | | | 98.66 | 98.66 | 98.66 | 98.66 | 98.66 | 98.66 | 98.66 | 98.66 | 98.66 | 98.66 | 98.66 | 98.66 | 98.66 | 98.66 | 98.66 | 98.66 |
| 46 | 96.84 | | | | | | | | | | | | | | | | | | | | | | | | | | 96.84 | 96.84 | 96.84 | 96.84 | 96.84 | 96.84 | 96.84 | 96.84 | 96.84 | 96.84 | 96.84 | 96.84 | 96.84 | 96.84 | 96.84 |
| 47 | 100.3 | | | | | | | | | | | | | | | | | | | | | | | | | | | 100.3 | 100.3 | 100.3 | 100.3 | 100.3 | 100.3 | 100.3 | 100.3 | 100.3 | 100.3 | 100.3 | 100.3 | 100.3 | 100.3 |
| 48 | 101.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 101.91 | 101.91 | 101.91 | 101.91 | 101.91 | 101.91 | 101.91 | 101.91 | 101.91 | 101.91 | 101.91 | 101.91 | 101.91 |
| 49 | 108.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 108.97 | 108.97 | 108.97 | 108.97 | 108.97 | 108.97 | 108.97 | 108.97 | 108.97 | 108.97 | 108.97 | 108.97 |
| 50 | 116.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 116.54 | 116.54 | 116.54 | 116.54 | 116.54 | 116.54 | 116.54 | 116.54 | 116.54 | 116.54 | 116.54 |
| 51 | 119.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 119.52 | 119.52 | 119.52 | 119.52 | 119.52 | 119.52 | 119.52 | 119.52 | 119.52 | 119.52 |
| 52 | 124.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 124.37 | 124.37 | 124.37 | 124.37 | 124.37 | 124.37 | 124.37 | 124.37 | 124.37 |
| 53 | 130.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 130.74 | 130.74 | 130.74 | 130.74 | 130.74 | 130.74 | 130.74 | 130.74 |
| 54 | 136.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 136.83 | 136.83 | 136.83 | 136.83 | 136.83 | 136.83 | 136.83 |
| 55 | 140.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 140.88 | 140.88 | 140.88 | 140.88 | 140.88 | 140.88 |
| 56 | 140.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 140.68 | 140.68 | 140.68 | 140.68 | 140.68 |
| 57 | 142.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 142.73 | 142.73 | 142.73 | 142.73 |
| 58 | 135.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 135.58 | 135.58 | 135.58 |
| 59 | 144.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 144.65 | 144.65 |
| 60 | 150.3 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 150.3 |
+-----------+--------------------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+-------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+--------+
I'm going to change some things to simplify the writeup. Assume $i=0$. Write $\ell$ instead of $l$ because $l$ looks like $1$.
Note on iterpolation: if $1 \ge 20/\ell $, then no interpolation is needed, since the formula $$d(j) = \left\lfloor \frac{j}{\ell} \cdot 20 \right\rfloor = \left\lfloor j \cdot \frac{20}{\ell}\right\rfloor$$ hits every integer as $j$ varies. So we do not need to worry about interpolation in the $\ell \ge 20$ case.
Concrete evidence the posted formula is wrong in the case when $\ell > L$: the actual price for day $j$ is supposed to be used on day $d(j)$. But if you check the formula you will see that $d(0)$ and $d(1)$ both equal 0 when $\ell > 20$). If you have different prices on day 0 and day 1, the method is impossible to follow because you do not know which one to use for the new price on day 0.
Conclusion 1: Do not use this formula when the sliding window $\ell$ is greater than 20.
We have already decided that when $\ell > 20$ there is no interpolation, just sampling, so this method isn't very interesting (to me).
Now consider the case when $\ell = 2$. According to the formula, $d(0) = 0$, $d(1) = 10$, and $d(2)=20$. (Note that the closed interval $[i,i+ \ell]$ is used, so you do consider $j=2$.) Other values are interpolated.
How would you do this in Excel?
I am going to assume that you know how to interplate in Excel, but maybe not how to program.
Suggestion (sorry for no link): Window size in \$B\$2 (this is $\ell$). Use this in your $d(j)$ forumla column $B$.
Finally this is my opinion: whoever wrote this formula did it wrong. They should be defining the rescaled price on day $j$, which I will call $r(j)$, in terms of interpolation from the original price data $p(j)$. Instead they push the prices from $p(j)$ forward into $r(d(j))$. This creates a mess when you need to interpolate between days $d(j)$ and $d(j+1)$ because you have to use the "new" data to do the interpolation, not the original data.