library(forecast)
library(ggplot2)
library(readxl)
Data
# Consumer price index CPI-U, "U.S. Bureau of Labor Statistics"
cpi.wide<-read_xlsx("C:\\Users\\Jaire\\OneDrive\\Desktop\\Exploratory Research\\Data\\cpi.xlsx")
head(cpi.wide)
## # A tibble: 6 × 112
## ID month `1914` `1915` `1916` `1917` `1918` `1919` `1920` `1921` `1922`
## <dbl> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 Jan 2 1 3 12.5 19.7 17.9 17 -1.6 -11.1
## 2 2 Feb 1 1 4 15.4 17.5 14.9 20.4 -5.6 -8.2
## 3 3 Mar 1 0 6.1 14.3 16.7 17.1 20.1 -7.1 -8.7
## 4 4 Apr 0 2 6 18.9 12.7 17.6 21.6 -10.8 -7.7
## 5 5 May 2.1 2 5.9 19.6 13.3 16.6 21.9 -14.1 -5.6
## 6 6 Jun 1 2 6.9 20.4 13.1 15 23.7 -15.8 -5.1
## # ℹ 101 more variables: `1923` <dbl>, `1924` <dbl>, `1925` <dbl>, `1926` <dbl>,
## # `1927` <dbl>, `1928` <dbl>, `1929` <dbl>, `1930` <dbl>, `1931` <dbl>,
## # `1932` <dbl>, `1933` <dbl>, `1934` <dbl>, `1935` <dbl>, `1936` <dbl>,
## # `1937` <dbl>, `1938` <dbl>, `1939` <dbl>, `1940` <dbl>, `1941` <dbl>,
## # `1942` <dbl>, `1943` <dbl>, `1944` <dbl>, `1945` <dbl>, `1946` <dbl>,
## # `1947` <dbl>, `1948` <dbl>, `1949` <dbl>, `1950` <dbl>, `1951` <dbl>,
## # `1952` <dbl>, `1953` <dbl>, `1954` <dbl>, `1955` <dbl>, `1956` <dbl>, …
nrow(cpi.wide)
## [1] 12
ncol(cpi.wide)
## [1] 112
cpi.wide$ID <- factor(cpi.wide$ID)
is.factor(cpi.wide$ID)
## [1] TRUE
library(tidyr)
cpi.long <- gather(cpi.wide, year, cpi, "1914":"2023", factor_key=TRUE)
head(cpi.long)
## # A tibble: 6 × 4
## ID month year cpi
## <fct> <chr> <fct> <dbl>
## 1 1 Jan 1914 2
## 2 2 Feb 1914 1
## 3 3 Mar 1914 1
## 4 4 Apr 1914 0
## 5 5 May 1914 2.1
## 6 6 Jun 1914 1
nrow(cpi.long)
## [1] 1320
ncol(cpi.long)
## [1] 4
Create time-series object
cpi.ts <- ts(cpi.long$cpi, frequency=12, start=c(1914,1))
summary(cpi.ts)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -15.800 1.200 2.700 3.284 4.700 23.700
Autocorrelation
plot(cpi.ts)
acf(cpi.ts, main = "ACF of CPI")
pacf(cpi.ts, main = "PACF of CPI")
library(TTR)
cpi.tscomponents <- decompose(cpi.ts)
cpi.s_adj<-cpi.ts-cpi.tscomponents$seasonal
plot(cpi.tscomponents)
plot(cpi.s_adj)
ARIMA forecasts
cpi.ts_arima <- auto.arima(cpi.ts)
cpi.s_adj_arima <- auto.arima(cpi.s_adj) # seasonally adjusted
summary(cpi.ts_arima)
## Series: cpi.ts
## ARIMA(2,0,2)(2,0,2)[12] with non-zero mean
##
## Coefficients:
## ar1 ar2 ma1 ma2 sar1 sar2 sma1 sma2
## 1.9466 -0.9472 -0.6717 -0.0790 0.826 -0.0101 -1.7518 0.7763
## s.e. 0.0152 0.0151 0.0313 0.0295 0.133 0.0356 0.1312 0.1144
## mean
## 3.2462
## s.e. 0.8798
##
## sigma^2 = 0.3245: log likelihood = -1137.24
## AIC=2294.47 AICc=2294.64 BIC=2346.32
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 0.0006712528 0.5677221 0.3605604 NaN Inf 0.1305503 0.002171613
summary(cpi.s_adj_arima)# seasonally adjusted
## Series: cpi.s_adj
## ARIMA(2,0,2)(2,0,1)[12] with non-zero mean
##
## Coefficients:
## ar1 ar2 ma1 ma2 sar1 sar2 sma1 mean
## 1.9399 -0.9405 -0.6783 -0.0607 -0.0411 -0.0295 -0.881 3.2337
## s.e. 0.0159 0.0159 0.0320 0.0295 0.0324 0.0319 0.016 0.7119
##
## sigma^2 = 0.3241: log likelihood = -1136.71
## AIC=2291.43 AICc=2291.56 BIC=2338.09
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 0.001547545 0.567609 0.3612519 69.42792 174.8825 0.1308007
## ACF1
## Training set 0.001265064
plot(cpi.ts_arima)
plot(cpi.s_adj_arima)# seasonally adjusted
cpi.ts_arima_fcst <- forecast(cpi.ts_arima, 12)
cpi.s_adj_arima_fcst <- forecast(cpi.s_adj_arima, 12) # seasonally adjusted
# Forecast, 12 months after DEC 2023
plot(cpi.ts_arima_fcst)
cpi.ts_arima_fcst
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 2024 3.019010 2.2889522 3.749069 1.90248269 4.135538
## Feb 2024 3.076544 1.8936149 4.259472 1.26741032 4.885677
## Mar 2024 3.233247 1.6430745 4.823420 0.80128801 5.665206
## Apr 2024 3.062032 1.0776575 5.046407 0.02719308 6.096871
## May 2024 3.263662 0.8890922 5.638231 -0.36792888 6.895252
## Jun 2024 3.282139 0.5182757 6.046003 -0.94482535 7.509104
## Jul 2024 3.299347 0.1461031 6.452591 -1.52312345 8.121818
## Aug 2024 2.969042 -0.5737732 6.511857 -2.44922620 8.387310
## Sep 2024 2.934101 -0.9981902 6.866392 -3.07981921 8.948021
## Oct 2024 3.208882 -1.1123341 7.530098 -3.39984774 9.817612
## Nov 2024 3.226618 -1.4824549 7.935692 -3.97528778 10.428525
## Dec 2024 3.132181 -1.9631547 8.227517 -4.66046251 10.924825
plot(cpi.s_adj_arima_fcst)
cpi.s_adj_arima_fcst
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 2024 3.171871 2.4422368 3.901506 2.0559916 4.287751
## Feb 2024 3.366625 2.1920336 4.541217 1.5702423 5.163008
## Mar 2024 3.557494 1.9786159 5.136372 1.1428082 5.972180
## Apr 2024 3.584470 1.6127720 5.556169 0.5690179 6.599923
## May 2024 3.749349 1.3883930 6.110305 0.1385783 7.360120
## Jun 2024 3.834020 1.0848391 6.583201 -0.3704895 8.038530
## Jul 2024 3.759835 0.6228194 6.896850 -1.0378162 8.557486
## Aug 2024 3.339349 -0.1849924 6.863691 -2.0506662 8.729364
## Sep 2024 3.305049 -0.6056799 7.215777 -2.6758944 9.285991
## Oct 2024 3.585503 -0.7101230 7.881129 -2.9840900 10.155096
## Nov 2024 3.592264 -1.0861937 8.270722 -3.5628195 10.747347
## Dec 2024 3.517797 -1.5408675 8.576462 -4.2187628 11.254357
plot(cpi.ts_arima_fcst, xlim = c(2020,2025))
cpi.ts_arima_fcst
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 2024 3.019010 2.2889522 3.749069 1.90248269 4.135538
## Feb 2024 3.076544 1.8936149 4.259472 1.26741032 4.885677
## Mar 2024 3.233247 1.6430745 4.823420 0.80128801 5.665206
## Apr 2024 3.062032 1.0776575 5.046407 0.02719308 6.096871
## May 2024 3.263662 0.8890922 5.638231 -0.36792888 6.895252
## Jun 2024 3.282139 0.5182757 6.046003 -0.94482535 7.509104
## Jul 2024 3.299347 0.1461031 6.452591 -1.52312345 8.121818
## Aug 2024 2.969042 -0.5737732 6.511857 -2.44922620 8.387310
## Sep 2024 2.934101 -0.9981902 6.866392 -3.07981921 8.948021
## Oct 2024 3.208882 -1.1123341 7.530098 -3.39984774 9.817612
## Nov 2024 3.226618 -1.4824549 7.935692 -3.97528778 10.428525
## Dec 2024 3.132181 -1.9631547 8.227517 -4.66046251 10.924825
plot(cpi.s_adj_arima_fcst, xlim = c(2020,2025))
cpi.s_adj_arima_fcst
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 2024 3.171871 2.4422368 3.901506 2.0559916 4.287751
## Feb 2024 3.366625 2.1920336 4.541217 1.5702423 5.163008
## Mar 2024 3.557494 1.9786159 5.136372 1.1428082 5.972180
## Apr 2024 3.584470 1.6127720 5.556169 0.5690179 6.599923
## May 2024 3.749349 1.3883930 6.110305 0.1385783 7.360120
## Jun 2024 3.834020 1.0848391 6.583201 -0.3704895 8.038530
## Jul 2024 3.759835 0.6228194 6.896850 -1.0378162 8.557486
## Aug 2024 3.339349 -0.1849924 6.863691 -2.0506662 8.729364
## Sep 2024 3.305049 -0.6056799 7.215777 -2.6758944 9.285991
## Oct 2024 3.585503 -0.7101230 7.881129 -2.9840900 10.155096
## Nov 2024 3.592264 -1.0861937 8.270722 -3.5628195 10.747347
## Dec 2024 3.517797 -1.5408675 8.576462 -4.2187628 11.254357