ISMとCLI(composite leading indicator )の関連について

データの用意

cliとismのxtsデータをマージしてデータセットwを用意する。
それぞれの列名の適切に変更する。

TERM <- "2014-10::2023-10"
merge(cli_g20[TERM],cli_usa[TERM],ism_mfg[TERM],ism_svc[TERM]) -> w
colnames(w)
colnames(w) <- c("g20","usa","ismmfg","ismsvc")

完成したデータセット

w


                 g20       usa ismmfg ismsvc
2014-10-01 100.22750 100.90270   56.6   58.6
2014-11-01 100.22250 100.85760   59.0   57.1
2014-12-01 100.21390 100.78940   58.7   59.3
2015-01-01 100.19840 100.69890   55.5   56.2
2015-02-01 100.18450 100.59270   53.5   56.7
2015-03-01 100.17940 100.48130   52.9   56.9
2015-04-01 100.16710 100.37000   51.5   56.5
2015-05-01 100.12700 100.25220   51.5   57.8
2015-06-01 100.04920 100.12390   52.8   55.7
2015-07-01  99.93338  99.96368   53.5   56.0
       ...                                  
2023-01-01  99.05477  98.84855   48.4   49.6
2023-02-01  99.19228  98.84138   47.4   55.2
2023-03-01  99.33978  98.85299   47.7   55.1
2023-04-01  99.48746  98.90076   46.3   51.2
2023-05-01  99.63204  98.98556   47.1   51.9
2023-06-01  99.77857  99.10077   46.9   50.3
2023-07-01  99.92024  99.21838   46.0   53.9
2023-08-01 100.05250  99.32928   46.4   52.7
2023-09-01 100.17240  99.43206   47.6   54.5
2023-10-01        NA        NA   49.0   53.6

重回帰分析

「summary(lm(w$usa ~ w$ismmfg+w$ismsvc))」を実施。結果は以下のとおり。ISMとCLIでデータ日付と実際のデータの参照先が違うので、配列のインデックスで調整する。

dim(w)
[1] 109   4

summary(lm(w$usa[1:108,] ~ w$ismmfg[2:109,]+w$ismsvc[2:109,]))

Call:
lm(formula = w$usa[1:108, ] ~ w$ismmfg[2:109, ] + w$ismsvc[2:109, 
    ])

Residuals:
    Min      1Q  Median      3Q     Max 
-3.5275 -0.2382  0.0672  0.4412  1.1163 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)       85.75022    1.19021  72.046  < 2e-16 ***
w$ismmfg[2:109, ]  0.09724    0.02387   4.073 9.03e-05 ***
w$ismsvc[2:109, ]  0.15234    0.03186   4.782 5.69e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.7867 on 105 degrees of freedom
Multiple R-squared:  0.6041,	Adjusted R-squared:  0.5965 
F-statistic:  80.1 on 2 and 105 DF,  p-value: < 2.2e-16

決定係数は低め(0.5965)だが、p値は十分以上に低い(p-value: < 2.2e-16)。統計学的に有意である。

参考

dim(w)[1]
# [1] 109
summary(lm(w$usa[1:(dim(w)[1]-1),] ~ w$ismmfg[2:(dim(w)[1]),]+w$ismsvc[2:(dim(w)[1]),]))

Call:
lm(formula = w$usa[1:(dim(w)[1] - 1), ] ~ w$ismmfg[2:(dim(w)[1]), 
    ] + w$ismsvc[2:(dim(w)[1]), ])

Residuals:
    Min      1Q  Median      3Q     Max 
-3.5275 -0.2382  0.0672  0.4412  1.1163 

Coefficients:
                          Estimate Std. Error t value Pr(>|t|)    
(Intercept)               85.75022    1.19021  72.046  < 2e-16 ***
w$ismmfg[2:(dim(w)[1]), ]  0.09724    0.02387   4.073 9.03e-05 ***
w$ismsvc[2:(dim(w)[1]), ]  0.15234    0.03186   4.782 5.69e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.7867 on 105 degrees of freedom
Multiple R-squared:  0.6041,	Adjusted R-squared:  0.5965 
F-statistic:  80.1 on 2 and 105 DF,  p-value: < 2.2e-16