Question

当前，我们正在研究120个单元以上的学生的预测（这将使他们毕业）。以下是我们正在处理的当前数据集。

structure(list(Term = structure(c(5L, 9L, 1L, 6L, 10L, 2L, 7L, 
11L, 3L, 8L, 12L, 4L), .Label = c("F - 2014", "F - 2015", "F - 2016", 
"F - 2017", "S - 2014", "S - 2015", "S - 2016", "S - 2017", "Sp - 2014", 
"Sp - 2015", "Sp - 2016", "Sp - 2017"), class = "factor"), Bachelors = c(182L, 
1103L, 496L, 177L, 1236L, 511L, 161L, 1264L, 544L, 150L, 1479L, 
607L), Masters = c(33L, 144L, 35L, 22L, 175L, 55L, 57L, 114L, 
66L, 52L, 147L, 50L), Seniors = c(577L, 2485L, 2339L, 604L, 2660L, 
2474L, 545L, 2628L, 2594L, 712L, 2807L, 2546L), Over.120 = structure(c(235L, 
1746L, 1188L, 235L, 1837L, 1192L, 200L, 1883L, 1217L, 255L, 2002L, 
1245L), .Tsp = c(2014, 2017.66666666667, 3), class = "ts")), row.names = c(NA, 
-12L), class = "data.frame")

我们希望使用ARIMA预测-考察一年中的3个不同时期：2014年至2017年的春季，夏季，秋季-以此来查看趋势的变化趋势未来6年（2018年至2023年）

data <- read.csv("Graduation3.csv")
str(data)
library(forecast)

data$Over.120 <- ts(data$Over.120, start=c(2014,1), end=c(2017,3), frequency = 3)
summary(data)

dOver120 <- diff(data$Over.120)
dOver120 <- diff(data$Over.120,3)

plot(dOver120)

fit_diff_ar <- arima(dOver120, order=c(3,0,0))
summary(fit_diff_ar)

fit_diff_arf <- forecast(fit_diff_ar,h=18)
print(fit_diff_arf)
plot(fit_diff_arf,include=12)

plot of ARIMA forecast (sidenote: I don't have enough rep to directly post an image)

我们希望预测图的条件异常线遵循与前几年相同的趋势（Zig Zaging），但是随着时间的推移，该线开始围绕均值趋于平坦。目前还停留在这个问题上，并且不确定代码中是否包含某些内容，或者仅仅是趋势应该如何发生。

Answer 1

模型ARIMA（3,0,0）具有3个自回归系数，因此在预测下一个值时，只会查看序列的最后三个值。在这种情况下，假定拟合系数具有缓和预测值的衰减效果。随着模型被外推出来，用于预测下一个值的每个3个值将继续受到抑制。

如果您查看summary(fit_diff_ar)中的系数，则可以手动计算每个预测值，从而可以更好地理解结果。

尝试fit_diff_ar <- auto.arima(dOver120)，看看系数与您估计的模型有何不同。这可能会使预测值继续波动。

Answer 2

data <- structure(list(Term = structure(c(5L, 9L, 1L, 6L, 10L, 2L, 7L, 11L, 3L, 8L, 12L, 4L), 
                        .Label = c("F - 2014", "F - 2015", "F - 2016", "F - 2017", "S - 2014", "S - 2015", "S - 2016", "S - 2017", "Sp - 2014", "Sp - 2015", "Sp - 2016", "Sp - 2017"), class = "factor"), 
                       Bachelors = c(182L, 1103L, 496L, 177L, 1236L, 511L, 161L, 1264L, 544L, 150L, 1479L, 607L), 
                       Masters = c(33L, 144L, 35L, 22L, 175L, 55L, 57L, 114L, 66L, 52L, 147L, 50L), 
                       Seniors = c(577L, 2485L, 2339L, 604L, 2660L, 2474L, 545L, 2628L, 2594L, 712L, 2807L, 2546L), 
                       Over.120 = structure(c(235L, 1746L, 1188L, 235L, 1837L, 1192L, 200L, 1883L, 1217L, 255L, 2002L, 1245L), 
                      .Tsp = c(2014, 2017.66666666667, 3), class = "ts")), 
                  row.names = c(NA, -12L), class = "data.frame")

data$Term <- as.character(data$Term)
data$year <- as.numeric(gsub(".* - (.*)", "\\1",  data$Term))

# Create a numeric variable to represent the term
data$Term2 <- NA
# make spring 1
data$Term2 <- ifelse(grepl("Sp -", data$Term), 1, data$Term2)
# make summer 2
data$Term2 <- ifelse(grepl("S -", data$Term), 2, data$Term2)
# make fall 3
data$Term2 <- ifelse(grepl("F -", data$Term), 3, data$Term2)
# order the data
data <- data[order(data$year, data$Term2),]

library(forecast)
# still using your same original model
fit <- Arima(data$Over.120, order=c(3,0,0))
summary(fit)
# Series: data$Over.120 
# ARIMA(3,0,0) with non-zero mean 
# 
# Coefficients:
#   ar1      ar2     ar3       mean
# -0.0693  -0.0947  0.9151  1113.3012
# s.e.   0.1126   0.1106  0.1117    39.4385
# 
# sigma^2 estimated as 4573:  log likelihood=-70.94
# AIC=151.87   AICc=161.87   BIC=154.3
# 
# Training set error measures:
#   ME     RMSE      MAE       MPE   MAPE       MASE       ACF1
# Training set 20.15158 55.21532 50.34405 -1.440427 8.5131 0.04400354 0.04719142

preds <- forecast(fit, h = 18)
preds
# Point Forecast      Lo 80     Hi 80       Lo 95     Hi 95
# 13      1998.6938 1912.02930 2085.3583 1866.151880 2131.2357
# 14       254.0220  167.14935  340.8946  121.161754  386.8822
# 15      1209.5318 1122.31031 1296.7532 1076.138065 1342.9255
# 16      1998.2207 1879.58698 2116.8543 1816.786098 2179.6552
# 17       256.5197  137.43643  375.6029   74.397577  438.6418
# 18      1176.9475 1057.04047 1296.8545  993.565520 1360.3295
# 19      1999.8107 1858.09461 2141.5268 1783.074649 2216.5467
# 20       261.7816  119.43633  404.1268   44.083310  479.4798
# 21      1146.6151 1002.99843 1290.2318  926.972345 1366.2579
# 22      2002.8707 1842.34640 2163.3949 1757.369987 2248.3713
# 23       269.2577  107.99642  430.5189   22.629865  515.8855
# 24      1118.0506  955.13282 1280.9684  868.889357 1367.2118
# 25      2006.9434 1830.13885 2183.7480 1736.544176 2277.3426
# 26       278.5222  100.93452  456.1100    6.925256  550.1192
# 27      1090.8838  911.32145 1270.4462  816.266885 1365.5007
# 28      2011.6766 1820.27506 2203.0781 1718.953221 2304.3999
# 29       289.2452   97.06116  481.4292   -4.674897  583.1652
# 30      1064.8324  870.41604 1259.2487  767.498250 1362.1665

plot(preds)

当ARIMA预测图趋势逐渐变为水平时，如何评估？

2 个答案: