ISMとCLI(composite leading indicator )の関連について - その2 NFCIを加えた場合

データの用意

TERM <- "2014-10::2023-10"
merge(cli_g20[TERM],cli_usa[TERM],ism_mfg[TERM],ism_svc[TERM]) -> w
colnames(w) <- c("g20","usa","ismmfg","ismsvc")
cbind(w,to.monthly(NFCI)[,4][TERM]) -> w
cbind(w,diff(to.monthly(NFCI)[,4])[TERM]) -> w
colnames(w)[5:6] <- c('nfci','nfcidelta')



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

 データ

w
＃
                 g20       usa ismmfg ismsvc     nfci nfcidelta
2014-10-01 100.22750 100.90270   56.6   58.6 -0.65314   0.03232
2014-11-01 100.22250 100.85760   59.0   57.1 -0.66106  -0.00792
2014-12-01 100.21390 100.78940   58.7   59.3 -0.58280   0.07826
2015-01-01 100.19840 100.69890   55.5   56.2 -0.52050   0.06230
2015-02-01 100.18450 100.59270   53.5   56.7 -0.54767  -0.02717
2015-03-01 100.17940 100.48130   52.9   56.9 -0.56570  -0.01803
2015-04-01 100.16710 100.37000   51.5   56.5 -0.57459  -0.00889
2015-05-01 100.12700 100.25220   51.5   57.8 -0.56671   0.00788
2015-06-01 100.04920 100.12390   52.8   55.7 -0.55463   0.01208
2015-07-01  99.93338  99.96368   53.5   56.0 -0.51446   0.04017
       ...                                                     
2023-01-01  99.05477  98.84855   48.4   49.6 -0.34512  -0.10462
2023-02-01  99.19228  98.84138   47.4   55.2 -0.27659   0.06853
2023-03-01  99.33978  98.85299   47.7   55.1 -0.13263   0.14396
2023-04-01  99.48746  98.90076   46.3   51.2 -0.23399  -0.10136
2023-05-01  99.63204  98.98556   47.1   51.9 -0.24626  -0.01227
2023-06-01  99.77857  99.10077   46.9   50.3 -0.26116  -0.01490
2023-07-01  99.92024  99.21838   46.0   53.9 -0.32023  -0.05907
2023-08-01 100.05250  99.32928   46.4   52.7 -0.36257  -0.04234
2023-09-01 100.17240  99.43206   47.6   54.5 -0.38134  -0.01877
2023-10-01        NA        NA   49.0   53.6 -0.38988  -0.00854

重回帰分析

以下の式で回帰分析を行う
OECD composite leading indicator = ism 製造業 + ism サービス + NFCI 月間終値+ NFCI 月間変化値
ism関連のデータだけデータの日付と示すデータの内容が違っているので序数を変更して調整する。

ソースコードと分析結果

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

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

Residuals:
     Min       1Q   Median       3Q      Max 
-2.69579 -0.31000  0.09083  0.44916  1.13291 

Coefficients:
                     Estimate Std. Error t value Pr(>|t|)    
(Intercept)          90.18392    1.32230  68.202  < 2e-16 ***
w$ismmfg[2:109, ]     0.05886    0.02276   2.585  0.01112 *  
w$ismsvc[2:109, ]     0.08661    0.03035   2.854  0.00522 ** 
w$nfci[1:108, ]      -2.97302    0.59297  -5.014 2.23e-06 ***
w$nfcidelta[1:108, ]  3.74023    0.77831   4.806 5.27e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.6928 on 103 degrees of freedom
Multiple R-squared:  0.6988,	Adjusted R-squared:  0.6871 
F-statistic: 59.74 on 4 and 103 DF,  p-value: < 2.2e-16

結論

決定係数=0.6988は若干低めだがp値 < 2.2e-16 は十分以上