R中两个时间序列之间的分歧
Divergence between two timeseries in R
我有一个 data.table temp_dt，它的索引是 x 和两个时间序列 y 和 z。大多数时候 y 和 z 一起移动，但有时它们不一致（并且向不同的方向移动）。我想创建一个新列，显示这两个时间序列之间的一致程度（同向运动）或不一致程度（不同方向的运动）。如果有人能告诉我更好的方法，我将不胜感激。
library(data.table)
temp_dt = structure(list(x = c(0, 1, 4, 5, 6, 7, 8, 11, 12, 13, 14, 15,
18, 19, 20, 21, 22, 26, 27, 28, 29, 32, 33, 34, 35, 36, 39, 40,
41, 42, 43, 46, 47, 48, 49, 53, 54, 55, 56, 57, 60, 61, 62, 63,
64, 67, 68, 69, 70, 71, 74, 75, 76, 77, 78, 81, 82, 83, 84, 85,
87, 88, 89, 90, 91, 92, 95, 96, 97, 98, 99, 102, 103, 104, 105,
106, 109, 110, 111, 112, 113, 116, 117, 118, 119, 120, 123, 124,
125, 126, 127, 130, 131, 132, 133, 134, 137, 138, 139, 140, 141,
144, 145, 146, 147, 148, 151, 152, 153, 154, 158, 159, 160, 161,
162, 165, 166, 167, 168, 169, 172, 173, 174, 175, 176, 179, 180,
181, 182, 183, 186, 187, 188, 189, 190, 193, 194, 195, 196, 197,
200, 201, 202, 203, 204, 207, 208, 209, 210, 211, 214, 215, 216,
217, 218, 221, 222, 223, 224, 225, 228, 229, 230, 231, 232, 235,
236, 237, 238, 239, 242, 243, 244, 245, 246, 249, 250, 251, 252,
253, 256, 257, 258, 259, 260, 263, 264, 265, 266, 267, 270, 271,
272, 273, 274, 277, 278, 279, 280, 281, 284, 285, 286, 287, 288,
291, 292, 293, 294, 295, 298, 299, 300, 301, 302, 305, 306, 307,
308, 309, 312, 313, 314, 315, 316, 319, 320, 321, 322, 323, 326,
327, 328, 329, 330, 333, 334, 335, 336, 337, 340, 341, 342, 343,
344, 347, 348, 349, 350, 351), y = c(1.51, 1.86, 6.04, 6.11,
5.55, 10, 9.06, 0.99, 1.48, -0.77, 0.44, -0.37, -0.57, -0.64,
-1.25, -0.72, -2.52, -2.65, -2.76, -2.76, -2.84, -2.13, -2.23,
-2.27, -2.35, -2.48, -2.26, -2.38, -2.59, -2.59, -3.41, -3.34,
-3.3, -2.56, -2.42, -1.3, -2.61, -2.61, -2.55, -1.92, -1.92,
-1.98, -1.15, -2.05, -1.8, 0.07, -0.04, -0.07, -0.07, -0.87,
-0.88, -0.99, -0.99, -0.99, -1.31, -1.5, -1.51, -1.65, -1.68,
-1.95, -1.87, -1.87, -1.77, -4.01, -2.83, -2.84, -2.45, -2.98,
-3.14, -4.77, -3.22, -3.11, -3.13, -3.08, -3.3, -3.51, -3.13,
-4.9, -5.45, -6.26, -8, -4.97, -5.52, -5.69, -7.72, -8.17, -7.75,
-7.22, -7.4, -7.31, -7.35, -7.16, -7.13, -4.96, -5, -5.06, -4.82,
-4.86, -4.07, -4.97, -5.04, -2.96, -3.2, -0.96, -5.57, -3.84,
-3.21, -5.59, -1.68, -3.17, -3.36, -3.36, -3.47, -2.77, -2.79,
-3.69, -2.78, -2.8, -2.7, -1.19, -1.72, -1.88, -1.88, -2.13,
-2.17, -2.17, -3.88, -4.05, -4.23, -4.32, -2.19, -2.35, -2.35,
-1.08, -1.13, -1.37, -1.56, -1.59, -1.58, -0.22, 7.18, 6.42,
-0.43, -0.46, -0.54, -1.1, -1.15, -0.99, -2.29, -1.19, -1.13,
-1.13, -1.18, -2.69, -2.71, -2.75, -2.76, -2.85, -2.63, -3, -2.82,
-4.09, -4.17, -5.99, -6.75, -3.54, -3.76, -4.66, -4.54, -4.58,
-4.32, -4.38, -4.38, -4.44, -4.57, -4.36, -3.44, -3.51, -4.52,
-3.6, -4.5, -3.54, -3.62, -3.78, -4.83, -4.1, -4.1, -4.19, -4.16,
-4.19, -4.02, -4.06, -3.05, -3.14, -3.35, -3.39, -3.44, -3.51,
-3.73, -4.7, -4.61, -7.45, -4.72, -4.74, -4.74, -4.63, -7.52,
-7.61, -7.67, -7.57, -3.8, -4, -6.95, -6.95, -4.06, -6.98, -4.04,
-7.23, -7.26, -4.04, -3.98, -7.28, -7.36, -7.38, -7.61, -7.42,
-7.41, -7.57, -8.19, -8.45, -6.18, -6.26, -6.33, -6.42, -6.52,
-7.58, -6.41, -7.9, -6.76, -8.27, -6.77, -6.82, -6.95, -6.25,
-6.84, -6.8, -6.72, -6.08, -6.01, -6.4), z = c(11.17, 11.73,
12.1, 12.815, 12.455, 14.49, 13.87, 11.905, 11.03, 10.6019, 10.91,
10.95, 10.87, 10.465, 9.655, 9.039, 9.28, 7.79, 7.83, 7.83, 7.69,
8.14, 8.83, 8.96, 8.61, 8.5, 8.95, 8.9, 8.36, 8.09, 7.9, 7.44,
7.87, 8.07, 8.59, 8.02, 7.52, 7.83, 7.9, 7.9, 7.84, 7.91, 8.24,
7.78, 7.78, 9.62, 9.28, 9.5, 9.77, 8.97, 8.52, 8.54, 8.6, 8.68,
8.14, 8.14, 8.39, 8.83, 8.68, 8.47, 8.47, 8.44, 8.28, 6.99, 7.36,
7.37, 7.54, 7.34, 7.34, 6.99, 7.33, 7.46, 7.56, 7.51, 7.19, 7.15,
7.15, 6.7, 5.83, 5.32, 4.78, 5.53, 5.16, 5.1, 4.45, 3.67, 3.97,
4.86, 4.5, 4.54, 4.84, 4.5, 4.99, 5.12, 5.31, 5.32, 5.77, 5.71,
6.13, 5.86, 5.96, 5.62, 5.24, 5.16, 4.73, 5, 5.16, 4.51, 4.8,
5.37, 5.63, 5.88, 5.67, 6.16, 6.21, 5.99, 6.1, 6.11, 6.98, 7.23,
7.11, 7.4, 7.74, 7.41, 7.21, 7.16, 6.64, 6.76, 6.35, 6.25, 7.23,
7.01, 7.25, 8.55, 8.92, 8.93, 8.95, 8.53, 8.58, 9.02, 10.27,
10.11, 9.59, 9.81, 9.7, 9.68, 9.58, 9.58, 8.86, 9.08, 9.08, 9.26,
9.17, 8.21, 8.46, 8.41, 8.12, 8.01, 8.71, 8.23, 8.15, 7.79, 7.45,
6.03, 5.75, 6.15, 6.08, 5.96, 5.97, 5.89, 5.7, 5.53, 5.68, 5.58,
5.79, 5.79, 6.29, 6.19, 5.72, 6.13, 5.83, 6.14, 6.33, 6.27, 5.86,
5.54, 5.72, 5.9, 5.74, 5.63, 5.82, 5.99, 6.34, 6.81, 6.77, 6.57,
6.72, 6.65, 6.26, 5.8, 5.56, 4.84, 5.31, 5.05, 5.27, 5.19, 4.97,
4.46, 4.13, 4.23, 5.15, 5.12, 4.85, 4.73, 5.24, 4.81, 5.07, 4.81,
4.87, 5.3, 5.3, 4.85, 4.86, 4.69, 4.35, 4.47, 4.5, 4.36, 3.51,
3.36, 3.65, 3.49, 3.45, 3.23, 3.03, 2.95, 3.1, 2.58, 3.05, 2.99,
3.23, 3.15, 3.45, 3.59, 3.52, 3.44, 3.66, 4.23, 4.57, 4.13)), row.names = c(NA,
-250L), class = c("data.table", "data.frame"))
这是时间序列 -
library(ggplot2)
ggplot(na.omit(temp_dt ), aes(x)) +
geom_line(aes(y = y), color = "red") +
geom_line(aes(y = z), color = "blue")
我曾尝试使用 RollingCorr 函数来发现时间序列之间相关性的变化，但它会导致时间序列非常嘈杂，并且不会显示是否存在收敛或发散。
temp_dt[, div := RollingWindow::RollingCorr(y, z, window = 3, na_method = "ignore") * 10]
我想创建一个时间序列，它可以更可靠地捕捉 y 和 z 的收敛和发散。
不清楚您所说的 disagree 是什么意思。最简单的就是计算差值
temp_dt$difference = temp_dt$x - temp_dt$y
并查看它与自身平均值的差距。
如果您 运行 z 和 y 的相关和回归，您会发现这两个系列确实密切相关：
cor(temp_dt$y, temp_dt$z)
#> [1] 0.9011364
mod <- lm(z ~ y, data = temp_dt)
summary(mod)
#> Call:
#> lm(formula = z ~ y, data = temp_dt)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -3.7403 -0.5549 0.0870 0.6297 2.1267
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 9.13065 0.09238 98.84 <2e-16 ***
#> y 0.67961 0.02076 32.73 <2e-16 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 0.9407 on 248 degrees of freedom
#> Multiple R-squared: 0.812, Adjusted R-squared: 0.8113
#> F-statistic: 1071 on 1 and 248 DF, p-value: < 2.2e-16
我们可以通过以下操作以图形方式查看：
ggplot(temp_dt, aes(y, z)) + geom_point() + geom_smooth(method = lm)
找到两条线“不一致”的点实际上与找到这个模型的残差是一样的。根据您的目的，最好使用残差平方。通过这种方式，您可以获得单一的“分歧”衡量标准，其中接近 0 的数字表示高度一致，而较高的数字表示不同意。
temp_dt$error <- mod$residuals^2
如果你想从视觉上确认这一点，我们可以画一个图，让线条在“不一致”的地方变成红色
df <- data.frame(x = temp_dt$x,
x_end = c(tail(temp_dt$x, -1), tail(temp_dt$x, 1)),
y = temp_dt$y,
y_end = c(tail(temp_dt$y, -1), tail(temp_dt$y, 1)),
z = temp_dt$z,
z_end = c(tail(temp_dt$z, -1), tail(temp_dt$z, 1)),
error = temp_dt$error)
ggplot(df, aes(x, xend = x_end, colour = error)) +
geom_segment(aes(y = y, yend = y_end)) +
geom_segment(aes(y = z, yend = z_end)) +
scale_color_gradient(low = "black", high = "red")
我有一个 data.table temp_dt，它的索引是 x 和两个时间序列 y 和 z。大多数时候 y 和 z 一起移动，但有时它们不一致（并且向不同的方向移动）。我想创建一个新列，显示这两个时间序列之间的一致程度（同向运动）或不一致程度（不同方向的运动）。如果有人能告诉我更好的方法，我将不胜感激。
library(data.table)
temp_dt = structure(list(x = c(0, 1, 4, 5, 6, 7, 8, 11, 12, 13, 14, 15,
18, 19, 20, 21, 22, 26, 27, 28, 29, 32, 33, 34, 35, 36, 39, 40,
41, 42, 43, 46, 47, 48, 49, 53, 54, 55, 56, 57, 60, 61, 62, 63,
64, 67, 68, 69, 70, 71, 74, 75, 76, 77, 78, 81, 82, 83, 84, 85,
87, 88, 89, 90, 91, 92, 95, 96, 97, 98, 99, 102, 103, 104, 105,
106, 109, 110, 111, 112, 113, 116, 117, 118, 119, 120, 123, 124,
125, 126, 127, 130, 131, 132, 133, 134, 137, 138, 139, 140, 141,
144, 145, 146, 147, 148, 151, 152, 153, 154, 158, 159, 160, 161,
162, 165, 166, 167, 168, 169, 172, 173, 174, 175, 176, 179, 180,
181, 182, 183, 186, 187, 188, 189, 190, 193, 194, 195, 196, 197,
200, 201, 202, 203, 204, 207, 208, 209, 210, 211, 214, 215, 216,
217, 218, 221, 222, 223, 224, 225, 228, 229, 230, 231, 232, 235,
236, 237, 238, 239, 242, 243, 244, 245, 246, 249, 250, 251, 252,
253, 256, 257, 258, 259, 260, 263, 264, 265, 266, 267, 270, 271,
272, 273, 274, 277, 278, 279, 280, 281, 284, 285, 286, 287, 288,
291, 292, 293, 294, 295, 298, 299, 300, 301, 302, 305, 306, 307,
308, 309, 312, 313, 314, 315, 316, 319, 320, 321, 322, 323, 326,
327, 328, 329, 330, 333, 334, 335, 336, 337, 340, 341, 342, 343,
344, 347, 348, 349, 350, 351), y = c(1.51, 1.86, 6.04, 6.11,
5.55, 10, 9.06, 0.99, 1.48, -0.77, 0.44, -0.37, -0.57, -0.64,
-1.25, -0.72, -2.52, -2.65, -2.76, -2.76, -2.84, -2.13, -2.23,
-2.27, -2.35, -2.48, -2.26, -2.38, -2.59, -2.59, -3.41, -3.34,
-3.3, -2.56, -2.42, -1.3, -2.61, -2.61, -2.55, -1.92, -1.92,
-1.98, -1.15, -2.05, -1.8, 0.07, -0.04, -0.07, -0.07, -0.87,
-0.88, -0.99, -0.99, -0.99, -1.31, -1.5, -1.51, -1.65, -1.68,
-1.95, -1.87, -1.87, -1.77, -4.01, -2.83, -2.84, -2.45, -2.98,
-3.14, -4.77, -3.22, -3.11, -3.13, -3.08, -3.3, -3.51, -3.13,
-4.9, -5.45, -6.26, -8, -4.97, -5.52, -5.69, -7.72, -8.17, -7.75,
-7.22, -7.4, -7.31, -7.35, -7.16, -7.13, -4.96, -5, -5.06, -4.82,
-4.86, -4.07, -4.97, -5.04, -2.96, -3.2, -0.96, -5.57, -3.84,
-3.21, -5.59, -1.68, -3.17, -3.36, -3.36, -3.47, -2.77, -2.79,
-3.69, -2.78, -2.8, -2.7, -1.19, -1.72, -1.88, -1.88, -2.13,
-2.17, -2.17, -3.88, -4.05, -4.23, -4.32, -2.19, -2.35, -2.35,
-1.08, -1.13, -1.37, -1.56, -1.59, -1.58, -0.22, 7.18, 6.42,
-0.43, -0.46, -0.54, -1.1, -1.15, -0.99, -2.29, -1.19, -1.13,
-1.13, -1.18, -2.69, -2.71, -2.75, -2.76, -2.85, -2.63, -3, -2.82,
-4.09, -4.17, -5.99, -6.75, -3.54, -3.76, -4.66, -4.54, -4.58,
-4.32, -4.38, -4.38, -4.44, -4.57, -4.36, -3.44, -3.51, -4.52,
-3.6, -4.5, -3.54, -3.62, -3.78, -4.83, -4.1, -4.1, -4.19, -4.16,
-4.19, -4.02, -4.06, -3.05, -3.14, -3.35, -3.39, -3.44, -3.51,
-3.73, -4.7, -4.61, -7.45, -4.72, -4.74, -4.74, -4.63, -7.52,
-7.61, -7.67, -7.57, -3.8, -4, -6.95, -6.95, -4.06, -6.98, -4.04,
-7.23, -7.26, -4.04, -3.98, -7.28, -7.36, -7.38, -7.61, -7.42,
-7.41, -7.57, -8.19, -8.45, -6.18, -6.26, -6.33, -6.42, -6.52,
-7.58, -6.41, -7.9, -6.76, -8.27, -6.77, -6.82, -6.95, -6.25,
-6.84, -6.8, -6.72, -6.08, -6.01, -6.4), z = c(11.17, 11.73,
12.1, 12.815, 12.455, 14.49, 13.87, 11.905, 11.03, 10.6019, 10.91,
10.95, 10.87, 10.465, 9.655, 9.039, 9.28, 7.79, 7.83, 7.83, 7.69,
8.14, 8.83, 8.96, 8.61, 8.5, 8.95, 8.9, 8.36, 8.09, 7.9, 7.44,
7.87, 8.07, 8.59, 8.02, 7.52, 7.83, 7.9, 7.9, 7.84, 7.91, 8.24,
7.78, 7.78, 9.62, 9.28, 9.5, 9.77, 8.97, 8.52, 8.54, 8.6, 8.68,
8.14, 8.14, 8.39, 8.83, 8.68, 8.47, 8.47, 8.44, 8.28, 6.99, 7.36,
7.37, 7.54, 7.34, 7.34, 6.99, 7.33, 7.46, 7.56, 7.51, 7.19, 7.15,
7.15, 6.7, 5.83, 5.32, 4.78, 5.53, 5.16, 5.1, 4.45, 3.67, 3.97,
4.86, 4.5, 4.54, 4.84, 4.5, 4.99, 5.12, 5.31, 5.32, 5.77, 5.71,
6.13, 5.86, 5.96, 5.62, 5.24, 5.16, 4.73, 5, 5.16, 4.51, 4.8,
5.37, 5.63, 5.88, 5.67, 6.16, 6.21, 5.99, 6.1, 6.11, 6.98, 7.23,
7.11, 7.4, 7.74, 7.41, 7.21, 7.16, 6.64, 6.76, 6.35, 6.25, 7.23,
7.01, 7.25, 8.55, 8.92, 8.93, 8.95, 8.53, 8.58, 9.02, 10.27,
10.11, 9.59, 9.81, 9.7, 9.68, 9.58, 9.58, 8.86, 9.08, 9.08, 9.26,
9.17, 8.21, 8.46, 8.41, 8.12, 8.01, 8.71, 8.23, 8.15, 7.79, 7.45,
6.03, 5.75, 6.15, 6.08, 5.96, 5.97, 5.89, 5.7, 5.53, 5.68, 5.58,
5.79, 5.79, 6.29, 6.19, 5.72, 6.13, 5.83, 6.14, 6.33, 6.27, 5.86,
5.54, 5.72, 5.9, 5.74, 5.63, 5.82, 5.99, 6.34, 6.81, 6.77, 6.57,
6.72, 6.65, 6.26, 5.8, 5.56, 4.84, 5.31, 5.05, 5.27, 5.19, 4.97,
4.46, 4.13, 4.23, 5.15, 5.12, 4.85, 4.73, 5.24, 4.81, 5.07, 4.81,
4.87, 5.3, 5.3, 4.85, 4.86, 4.69, 4.35, 4.47, 4.5, 4.36, 3.51,
3.36, 3.65, 3.49, 3.45, 3.23, 3.03, 2.95, 3.1, 2.58, 3.05, 2.99,
3.23, 3.15, 3.45, 3.59, 3.52, 3.44, 3.66, 4.23, 4.57, 4.13)), row.names = c(NA,
-250L), class = c("data.table", "data.frame"))
这是时间序列 -
library(ggplot2)
ggplot(na.omit(temp_dt ), aes(x)) +
geom_line(aes(y = y), color = "red") +
geom_line(aes(y = z), color = "blue")
我曾尝试使用 RollingCorr 函数来发现时间序列之间相关性的变化，但它会导致时间序列非常嘈杂，并且不会显示是否存在收敛或发散。
temp_dt[, div := RollingWindow::RollingCorr(y, z, window = 3, na_method = "ignore") * 10]
我想创建一个时间序列，它可以更可靠地捕捉 y 和 z 的收敛和发散。
不清楚您所说的 disagree 是什么意思。最简单的就是计算差值
temp_dt$difference = temp_dt$x - temp_dt$y
并查看它与自身平均值的差距。
如果您 运行 z 和 y 的相关和回归，您会发现这两个系列确实密切相关：
cor(temp_dt$y, temp_dt$z)
#> [1] 0.9011364
mod <- lm(z ~ y, data = temp_dt)
summary(mod)
#> Call:
#> lm(formula = z ~ y, data = temp_dt)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -3.7403 -0.5549 0.0870 0.6297 2.1267
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 9.13065 0.09238 98.84 <2e-16 ***
#> y 0.67961 0.02076 32.73 <2e-16 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 0.9407 on 248 degrees of freedom
#> Multiple R-squared: 0.812, Adjusted R-squared: 0.8113
#> F-statistic: 1071 on 1 and 248 DF, p-value: < 2.2e-16
我们可以通过以下操作以图形方式查看：
ggplot(temp_dt, aes(y, z)) + geom_point() + geom_smooth(method = lm)
找到两条线“不一致”的点实际上与找到这个模型的残差是一样的。根据您的目的，最好使用残差平方。通过这种方式，您可以获得单一的“分歧”衡量标准，其中接近 0 的数字表示高度一致，而较高的数字表示不同意。
temp_dt$error <- mod$residuals^2
如果你想从视觉上确认这一点，我们可以画一个图，让线条在“不一致”的地方变成红色
df <- data.frame(x = temp_dt$x,
x_end = c(tail(temp_dt$x, -1), tail(temp_dt$x, 1)),
y = temp_dt$y,
y_end = c(tail(temp_dt$y, -1), tail(temp_dt$y, 1)),
z = temp_dt$z,
z_end = c(tail(temp_dt$z, -1), tail(temp_dt$z, 1)),
error = temp_dt$error)
ggplot(df, aes(x, xend = x_end, colour = error)) +
geom_segment(aes(y = y, yend = y_end)) +
geom_segment(aes(y = z, yend = z_end)) +
scale_color_gradient(low = "black", high = "red")