Questionable accuracy #40
Description
When inspecting some suspect behavior in my application it turned out moving average values depend on the calculation length. For example, calculating an EMA20 over 500 numbers gives a different last moving average value than calculating the same average over only its last 200 numbers.
Being a programmer, I wrote some code to investigate this:
use yata::core::{ Method, MovingAverageConstructor };
use yata::helpers::MA;
use std::str::FromStr;
fn main() {
let prices = [
195.78, 196.10, 196.48, 196.96, 194.46, 185.14, 182.48, 185.10, 189.12, 188.98,
191.88, 191.34, 191.74, 197.80, 190.50, 192.62, 190.60, 190.06, 188.98, 190.50,
189.36, 188.48, 188.50, 195.32, 195.80, 199.00, 193.50, 189.40, 184.70, 192.30,
196.30, 206.30, 205.50, 199.46, 194.28, 194.76, 194.88, 192.50, 187.54, 187.08,
189.70, 187.50, 185.90, 185.00, 185.12, 187.78, 188.98, 186.64, 187.00, 185.14,
181.48, 177.22, 175.28, 171.94, 167.22, 165.50, 162.50, 164.70, 165.68, 169.26,
167.46, 184.34, 184.90, 181.64, 181.30, 182.82, 182.50, 182.40, 181.20, 170.60,
174.24, 174.28, 176.66, 176.90, 178.78, 178.76, 177.00, 178.00, 181.84, 187.28,
187.30, 189.72, 189.00, 189.00, 189.90, 187.80, 190.64, 194.74, 191.10, 189.04,
191.62, 188.00, 185.50, 178.70, 179.50, 179.90, 186.82, 185.66, 184.02, 186.02,
183.22, 182.26, 177.04, 175.96, 179.00, 188.14, 184.20, 181.90, 182.10, 187.82,
186.38, 184.12, 181.50, 168.50, 189.16, 176.00, 181.76, 179.50, 176.72, 162.00,
159.04, 151.00, 139.00, 132.82, 142.60, 151.50, 144.00, 154.00, 148.20, 157.66,
158.90, 155.38, 153.18, 154.52, 156.74, 152.52, 152.62, 151.58, 154.50, 159.46,
160.88, 157.64, 158.92, 160.30, 156.08, 153.02, 152.78, 151.48, 148.80, 150.00,
151.68, 148.50, 154.06, 154.72, 149.46, 151.22, 147.80, 148.58, 149.00, 148.64,
151.52, 152.52, 145.88, 145.18, 144.56, 144.10, 143.60, 146.18, 146.82, 144.02,
146.48, 148.00, 146.50, 148.30, 154.50, 155.88, 160.18, 158.44, 156.84, 158.70,
158.12, 156.30, 148.32, 146.84, 146.30, 146.80, 143.48, 142.10, 144.20, 144.10,
143.86, 140.00, 140.18, 140.50, 138.30, 133.00, 126.10, 129.02, 127.98, 122.74,
122.48, 126.88, 130.18, 129.58, 127.82, 127.42, 133.74, 134.70, 142.28, 139.92,
135.50, 132.50, 131.90, 131.06, 133.00, 137.40, 138.44, 137.80, 140.12, 144.48,
143.80, 145.00, 145.30, 142.00, 147.14, 147.50, 148.60, 150.40, 150.92, 147.30,
147.54, 145.00, 138.02, 141.42, 142.80, 142.68, 139.80, 143.30, 148.64, 137.48,
142.32, 145.00, 144.94, 147.00, 149.50, 146.50, 149.28, 151.34, 149.00, 150.98,
147.50, 147.38, 148.38, 145.40, 145.44, 147.80, 139.32, 139.90, 135.00, 138.80,
129.62, 125.90, 129.20, 130.62, 130.48, 131.82, 127.84, 123.44, 123.62, 122.60,
126.90, 126.50, 130.48, 131.50, 129.22, 129.34, 131.00, 131.44, 131.00, 130.56,
127.50, 129.04, 130.88, 132.50, 129.62, 128.52, 133.02, 137.36, 135.60, 134.46,
140.92, 143.90, 144.00, 142.96, 138.12, 140.06, 141.02, 139.00, 140.20, 137.78,
137.28, 135.80, 135.86, 138.60, 141.22, 138.38, 140.00, 140.88, 139.18, 136.10,
137.00, 137.20, 136.24, 137.16, 136.44, 133.76, 121.10, 121.50, 119.82, 120.18,
115.04, 117.06, 115.88, 114.96, 116.04, 117.20, 120.04, 122.56, 126.00, 127.42,
129.62, 127.50, 127.80, 128.32, 127.82, 125.72, 126.00, 125.50, 124.06, 124.42,
125.40, 125.44, 123.76, 125.06, 126.20, 126.00, 127.20, 129.00, 132.00, 131.20,
131.32, 130.50, 129.60, 130.00, 128.76, 129.16, 130.60, 131.98, 130.30, 132.46,
132.50, 130.80, 131.76, 132.56, 128.32, 129.00, 130.10, 128.00, 127.82, 142.20,
139.32, 138.76, 140.24, 133.92, 134.70, 128.70, 129.40, 125.56, 122.00, 120.20,
121.24, 123.36, 123.50, 120.12, 120.48, 122.60, 122.50, 123.50, 125.60, 126.20,
126.50, 125.68, 124.14, 125.50, 125.50, 126.84, 128.66, 127.54, 126.26, 124.28,
122.24, 122.20, 121.96, 120.32, 121.50, 123.00, 124.20, 123.44, 125.12, 125.52,
127.64, 127.56, 127.26, 120.00, 119.98, 119.66, 118.12, 116.18, 118.24, 120.80,
120.20, 120.52, 119.72, 118.82, 120.40, 120.02, 118.20, 119.08, 121.72, 122.38,
123.90, 124.70, 126.02, 130.00, 131.34, 131.10, 130.46, 128.30, 127.50, 126.58,
123.84, 123.04, 122.52, 123.00, 120.98, 122.72, 123.28, 123.94, 124.00, 122.90,
123.08, 121.00, 122.16, 122.52, 123.30, 123.40, 123.64, 122.44, 122.14, 123.02,
123.50, 123.90, 124.62, 126.08, 125.60, 121.50, 120.00, 121.26, 120.66, 118.80,
118.50, 119.44, 117.92, 118.28, 117.84, 117.48, 116.78, 116.90, 115.50, 115.00,
113.98, 114.08, 115.12, 114.02, 114.26, 111.82, 112.82, 113.30, 114.16, 113.70,
110.48, 108.60, 107.56, 108.00, 107.00, 106.72, 107.74, 108.78, 108.66, 108.38,
109.34, 109.50, 109.20, 109.52, 111.30, 112.10, 113.90, 113.04, 109.62, 108.40,
108.96, 109.46, 108.30, 106.22, 107.12, 106.54, 105.90, 106.44, 107.86, 110.00,
108.70, 107.68, 107.92, 108.80, 106.00, 104.46, 102.76, 102.14, 102.12, 99.87,
100.06, 99.52, 99.40, 100.56, 101.00, 103.98, 105.50, 104.32, 103.70, 104.50,
103.96, 104.02, 105.58, 108.48, 109.66, 108.30, 109.60, 108.74, 107.08, 107.00,
106.06, 107.00, 105.50, 104.26, 107.38, 107.20, 106.92, 107.36, 110.42, 113.74,
113.00, 115.02, 116.40, 115.36, 116.50, 116.42, 115.10, 114.22, 114.30, 112.20,
112.26, 112.36, 112.62, 112.06, 112.32, 112.86, 111.42, 111.96, 112.50, 114.20,
113.30, 113.98, 113.30, 112.18, 111.16, 109.94, 108.62, 108.06, 107.50, 108.30,
115.68, 115.64, 114.90, 115.00, 116.38, 116.74, 119.66, 119.16, 120.14, 119.68,
];
for ma_name in [
"sma", "wma", "ema", "dma", "tma", "dema", "tema", "smm", "linreg",
"swma", "hma", "rma", "trima", "wsma", "vidya"
] {
for ma_length in [10, 20, 100] {
println!("{} {}:", ma_name, ma_length);
for calc_length in [10, 20, 100, 400] {
let mut ma_result = Vec::new();
let price_pointer = prices.len() - calc_length - ma_length - 1;
let mut ma = MA::from_str(&format!("{}-{}", ma_name, ma_length))
.unwrap().init(prices[price_pointer]).unwrap();
ma_result.push(prices[price_pointer]);
for price_pointer in price_pointer .. prices.len() {
ma_result.push(ma.next(&prices[price_pointer]));
}
let result_len = ma_result.len();
println!(
"{:3.4} {:3.4} {:3.4} {:3.4} {:3.4}",
ma_result[result_len - 5],
ma_result[result_len - 4],
ma_result[result_len - 3],
ma_result[result_len - 2],
ma_result[result_len - 1]
);
}
}
}
}Lo' and behold, this code confirms my observation. The list this code prints out shows good accuracy for some moving averages ...
sma 10:
112.6820 113.7860 114.8960 116.1600 117.2980
112.6820 113.7860 114.8960 116.1600 117.2980
112.6820 113.7860 114.8960 116.1600 117.2980
112.6820 113.7860 114.8960 116.1600 117.2980
... still reasonable accuracy for others ...
wma 20:
113.0019 113.6802 114.2716 114.9221 115.4924
113.0018 113.6801 114.2715 114.9220 115.4923
113.0015 113.6798 114.2712 114.9217 115.4920
112.9991 113.6774 114.2688 114.9193 115.4896
... and not really usable numbers (deviation > 1%) for some:
ema 100:
110.8011 110.9766 111.1386 111.3169 111.4825
110.9291 111.1020 111.2615 111.4373 111.6006
111.6408 111.7996 111.9454 112.1076 112.2576
111.7380 111.8949 112.0388 112.1992 112.3473
[...]
vidya 20:
112.1891 112.4278 112.6161 112.8354 112.9860
113.1411 113.3494 113.5119 113.7051 113.8366
110.5090 110.8014 111.0352 111.3006 111.4850
110.9301 111.2091 111.4314 111.6853 111.8612
My current working hypothesis is that these mathematical shortcuts taken when calculating moving averages sum up numerical inaccuracies, thousands of tiny errors end up in substantial ones. While calculating the next value from the previous one is certainly faster, accurate results would require to calculate "fresh" values from values in the moving average window, ignoring the previous moving average value.