Load libraries
library(tidyquant)
library(tidyverse)
library(broom)
library(knitr)
library(kableExtra)
library(tsibble)
library(ggcorrplot)
library(ggfittext)
library(psych)
library(data.table)
library(ivreg)
library(janitor)
library(readxl)
library(fable)
library(mFilter)
library(ggrepel)
library(lmtest)
library(magrittr)
library(sandwich)
library(car)
library(slider)
Create dataframes
real_df <-
read_csv("real_assets.csv") %>%
mutate(date = floor_date(date(mdy_hm(date)), "month"))
real_long_df <-
read_csv("real_assets_long.csv")%>%
mutate(date = floor_date(date(mdy_hm(date)), "month"))
sp_real_df <-
read_csv("sp_real.csv") %>%
mutate(date = mdy(date),
date = floor_date(date, "month")) %>%
group_by(date) %>%
filter(row_number() == n()) %>%
ungroup %>%
mutate(sp_real = 100*((sp_real / lag(sp_real, 1)) - 1))
infl <-
c("MEDCPIM158SFRBCLE", "TRMMEANCPIM158SFRBCLE", "CPIAUCSL", "CPILFESL") %>%
tq_get(get = "economic.data", from = "2014-12-01") %>%
pivot_wider(names_from = symbol, values_from = price) %>%
set_colnames(c("date", "median_cpi", "trimmed_mean_cpi", "cpi", "core_cpi")) %>%
mutate(cpi = 100*((cpi / lag(cpi, 1)) - 1),
core_cpi = 100*((core_cpi / lag(core_cpi, 1)) - 1),
median_cpi = ((((median_cpi / 100) + 1)^(1/12)) - 1)*100,
trimmed_mean_cpi = ((((trimmed_mean_cpi / 100) + 1)^(1/12)) - 1)*100,
headline_shock = cpi - median_cpi) %>%
drop_na
Join dataframes
real_df <-
real_df %>%
left_join(sp_real_df, by = "date") %>%
left_join(infl, by = "date")
real_long_df <-
real_long_df %>%
left_join(sp_real_df, by = "date") %>%
left_join(infl, by = "date")
Correlation matrices
real_df %>%
filter(between(year(date), 2021, 2023)) %>%
select(-date) %>%
cor(use = "complete.obs") %>%
round(2)
## NTRAA SPGI SNRU TIPS BCTR NTGRE SPXTR sp_real median_cpi
## NTRAA 1.00 0.95 0.90 0.72 0.53 0.91 0.89 0.97 -0.30
## SPGI 0.95 1.00 0.83 0.69 0.51 0.86 0.82 0.94 -0.17
## SNRU 0.90 0.83 1.00 0.49 0.71 0.72 0.69 0.85 -0.21
## TIPS 0.72 0.69 0.49 1.00 0.25 0.76 0.76 0.78 -0.35
## BCTR 0.53 0.51 0.71 0.25 1.00 0.36 0.30 0.53 -0.30
## NTGRE 0.91 0.86 0.72 0.76 0.36 1.00 0.90 0.95 -0.35
## SPXTR 0.89 0.82 0.69 0.76 0.30 0.90 1.00 0.89 -0.33
## sp_real 0.97 0.94 0.85 0.78 0.53 0.95 0.89 1.00 -0.34
## median_cpi -0.30 -0.17 -0.21 -0.35 -0.30 -0.35 -0.33 -0.34 1.00
## trimmed_mean_cpi -0.20 -0.11 -0.11 -0.26 -0.11 -0.23 -0.28 -0.23 0.77
## cpi -0.03 -0.01 -0.02 -0.17 0.03 -0.04 -0.09 -0.07 0.24
## core_cpi -0.17 -0.14 -0.16 -0.08 -0.09 -0.14 -0.17 -0.15 0.41
## headline_shock 0.11 0.06 0.08 -0.01 0.17 0.12 0.06 0.09 -0.23
## trimmed_mean_cpi cpi core_cpi headline_shock
## NTRAA -0.20 -0.03 -0.17 0.11
## SPGI -0.11 -0.01 -0.14 0.06
## SNRU -0.11 -0.02 -0.16 0.08
## TIPS -0.26 -0.17 -0.08 -0.01
## BCTR -0.11 0.03 -0.09 0.17
## NTGRE -0.23 -0.04 -0.14 0.12
## SPXTR -0.28 -0.09 -0.17 0.06
## sp_real -0.23 -0.07 -0.15 0.09
## median_cpi 0.77 0.24 0.41 -0.23
## trimmed_mean_cpi 1.00 0.65 0.67 0.28
## cpi 0.65 1.00 0.57 0.89
## core_cpi 0.67 0.57 1.00 0.38
## headline_shock 0.28 0.89 0.38 1.00
real_long_df %>%
select(-date) %>%
cor(use = "complete.obs") %>%
round(2)
## NTRAA SPGI SNRU TIPS BCTR NTGRE SPXTR sp_real median_cpi
## NTRAA 1.00 0.94 0.84 0.61 0.55 0.93 0.86 0.96 -0.14
## SPGI 0.94 1.00 0.80 0.55 0.54 0.88 0.78 0.94 -0.09
## SNRU 0.84 0.80 1.00 0.36 0.69 0.71 0.73 0.84 -0.09
## TIPS 0.61 0.55 0.36 1.00 0.19 0.67 0.54 0.65 -0.27
## BCTR 0.55 0.54 0.69 0.19 1.00 0.42 0.43 0.59 -0.04
## NTGRE 0.93 0.88 0.71 0.67 0.42 1.00 0.83 0.95 -0.20
## SPXTR 0.86 0.78 0.73 0.54 0.43 0.83 1.00 0.84 -0.15
## sp_real 0.96 0.94 0.84 0.65 0.59 0.95 0.84 1.00 -0.17
## median_cpi -0.14 -0.09 -0.09 -0.27 -0.04 -0.20 -0.15 -0.17 1.00
## trimmed_mean_cpi -0.10 -0.07 -0.03 -0.23 0.09 -0.14 -0.13 -0.12 0.88
## cpi 0.01 0.01 0.06 -0.20 0.25 -0.01 -0.03 0.02 0.48
## core_cpi -0.04 -0.04 -0.04 -0.12 0.15 -0.05 -0.09 -0.04 0.65
## headline_shock 0.09 0.07 0.12 -0.08 0.31 0.10 0.05 0.12 0.00
## trimmed_mean_cpi cpi core_cpi headline_shock
## NTRAA -0.10 0.01 -0.04 0.09
## SPGI -0.07 0.01 -0.04 0.07
## SNRU -0.03 0.06 -0.04 0.12
## TIPS -0.23 -0.20 -0.12 -0.08
## BCTR 0.09 0.25 0.15 0.31
## NTGRE -0.14 -0.01 -0.05 0.10
## SPXTR -0.13 -0.03 -0.09 0.05
## sp_real -0.12 0.02 -0.04 0.12
## median_cpi 0.88 0.48 0.65 0.00
## trimmed_mean_cpi 1.00 0.72 0.80 0.33
## cpi 0.72 1.00 0.73 0.87
## core_cpi 0.80 0.73 1.00 0.47
## headline_shock 0.33 0.87 0.47 1.00
Testing correlations
real_df %>%
cor.test(~ NTRAA + cpi, data = .)
##
## Pearson's product-moment correlation
##
## data: NTRAA and cpi
## t = 0.33064, df = 58, p-value = 0.7421
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2128952 0.2940602
## sample estimates:
## cor
## 0.04337425
real_df %>%
cor.test(~ sp_real + cpi, data = .)
##
## Pearson's product-moment correlation
##
## data: sp_real and cpi
## t = 0.21483, df = 58, p-value = 0.8307
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2273550 0.2801166
## sample estimates:
## cor
## 0.02819756
Scatterplot: NTRAA vs. CPI
real_df %>%
ggplot(aes(x = cpi, y = NTRAA)) +
geom_point() +
geom_smooth(method = "lm")
## `geom_smooth()` using formula = 'y ~ x'
real_df %>%
ggplot(aes(x = cpi, y = sp_real)) +
geom_point() +
geom_smooth(method = "lm")
## `geom_smooth()` using formula = 'y ~ x'
Regressions on CPI
real_long_df %>%
lm(NTRAA ~ cpi, data = .) %>%
confint()
## 2.5 % 97.5 %
## (Intercept) -0.9228037 1.321700
## cpi -2.7160342 3.104141
real_long_df %>%
lm(sp_real ~ cpi, data = .) %>%
confint()
## 2.5 % 97.5 %
## (Intercept) -0.4761304 1.272969
## cpi -2.0090178 2.526535
real_long_df %>%
lm(SPGI ~ cpi, data = .) %>%
confint()
## 2.5 % 97.5 %
## (Intercept) -0.8514538 1.547949
## cpi -2.8898350 3.332007
real_long_df %>%
lm(SNRU ~ cpi, data = .) %>%
confint()
## 2.5 % 97.5 %
## (Intercept) -1.337006 1.709129
## cpi -2.651250 5.247619
real_long_df %>%
lm(NTGRE ~ cpi, data = .) %>%
confint()
## 2.5 % 97.5 %
## (Intercept) -1.120958 1.520157
## cpi -3.595476 3.253143
Regressions on median_cpi
real_long_df %>%
lm(NTRAA ~ median_cpi, data = .) %>%
summary()
##
## Call:
## lm(formula = NTRAA ~ median_cpi, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17.9490 -2.3760 0.2459 2.2716 10.4962
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.554 0.970 1.602 0.112
## median_cpi -4.439 3.001 -1.479 0.142
##
## Residual standard error: 4.242 on 107 degrees of freedom
## Multiple R-squared: 0.02003, Adjusted R-squared: 0.01088
## F-statistic: 2.187 on 1 and 107 DF, p-value: 0.1421
real_long_df %>%
lm(sp_real ~ median_cpi, data = .) %>%
summary()
##
## Call:
## lm(formula = sp_real ~ median_cpi, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.6092 -1.5555 -0.0703 1.6713 7.2624
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.6937 0.7525 2.251 0.0264 *
## median_cpi -4.1796 2.3282 -1.795 0.0754 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.291 on 107 degrees of freedom
## Multiple R-squared: 0.02924, Adjusted R-squared: 0.02017
## F-statistic: 3.223 on 1 and 107 DF, p-value: 0.07545
real_long_df %>%
lm(SPGI ~ median_cpi, data = .) %>%
summary()
##
## Call:
## lm(formula = SPGI ~ median_cpi, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -23.6447 -2.5862 0.5844 2.4062 11.5538
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.327 1.043 1.273 0.206
## median_cpi -3.137 3.227 -0.972 0.333
##
## Residual standard error: 4.561 on 107 degrees of freedom
## Multiple R-squared: 0.008753, Adjusted R-squared: -0.0005114
## F-statistic: 0.9448 on 1 and 107 DF, p-value: 0.3332
real_long_df %>%
lm(SNRU ~ median_cpi, data = .) %>%
summary()
##
## Call:
## lm(formula = SNRU ~ median_cpi, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -19.3324 -3.6105 0.0702 3.9674 15.9592
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.622 1.327 1.222 0.225
## median_cpi -3.716 4.107 -0.905 0.368
##
## Residual standard error: 5.805 on 107 degrees of freedom
## Multiple R-squared: 0.007595, Adjusted R-squared: -0.001679
## F-statistic: 0.8189 on 1 and 107 DF, p-value: 0.3675
real_long_df %>%
lm(NTGRE ~ median_cpi, data = .) %>%
summary()
##
## Call:
## lm(formula = NTGRE ~ median_cpi, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22.3505 -3.0062 0.2156 2.2447 12.1389
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.299 1.130 2.034 0.0444 *
## median_cpi -7.307 3.497 -2.090 0.0390 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.942 on 107 degrees of freedom
## Multiple R-squared: 0.03921, Adjusted R-squared: 0.03023
## F-statistic: 4.366 on 1 and 107 DF, p-value: 0.03902