#For this assignment, I decided to take a look at CPI over the last 30 years based on monthly CPI values where 100 is represented by the years 1980-1984.
CPIAUCSL$observation_date = as.Date(CPIAUCSL$observation_date, "%Y-%m-%d")
## Warning in as.POSIXlt.POSIXct(x, tz = tz): unknown timezone '%Y-%m-%d'
ts_cpi_changes = ts(data = CPIAUCSL$CPIAUCSL, start = 1991, end = 2021, frequency = 12)
autoplot(ts_cpi_changes)
cpi_hw = hw(ts_cpi_changes,
seasonal = "multiplicative")
hw_damp_cpi <- hw(ts_cpi_changes,
seasonal = "multiplicative",
damped = TRUE)
autoplot(cpi_hw)
autoplot(hw_damp_cpi)
ts_cpi_train = window(ts_cpi_changes,
end = c(2006))
ts_cpi_test = window(ts_cpi_changes,
start = 1991)
# Holt-Winters' damped method.
damp_hw_cpi = hw(ts_cpi_train,
h = 180,
seasonal = "multiplicative",
damped = TRUE)
dam_hw_cpi_plot = autoplot(damp_hw_cpi)
dam_hw_cpi_plot
damp_check_cpi = accuracy(damp_hw_cpi, ts_cpi_test)
# try Holt-Winters' method.
hw_cpi = hw(ts_cpi_train,
h = 180,
seasonal = "multiplicative")
hw_cpi_plot = autoplot(hw_cpi)
hw_cpi_plot
hw_check_cpi = accuracy(hw_cpi, ts_cpi_test)
damp_check_cpi
## ME RMSE MAE MPE MAPE MASE
## Training set 0.05726379 0.3925191 0.2662088 0.03294098 0.1526409 0.0608786
## Test set 23.98546177 28.1580287 23.9858390 9.80065621 9.8008430 5.4852595
## ACF1 Theil's U
## Training set 0.2070482 NA
## Test set 0.9721291 31.80726
hw_check_cpi
## ME RMSE MAE MPE MAPE MASE
## Training set -0.01365886 0.5317786 0.3737332 -0.008831955 0.2157153 0.08546808
## Test set 8.52105684 9.7908169 8.5552362 3.509109100 3.5259759 1.95647486
## ACF1 Theil's U
## Training set 0.5741122 NA
## Test set 0.9338561 11.14658
stl_cpi_train = ts_cpi_train %>%
stlm(
s.window = 12,
robust = TRUE,
method = "ets",
lambda = BoxCox.lambda(ts_cpi_train)
) %>%
forecast(
h = 180,
lambda = BoxCox.lambda(ts_cpi_train)
)
## Warning in InvBoxCox(fcast$mean, lambda, biasadj, fcast): biasadj information
## not found, defaulting to FALSE.
stl_cpi_plot = autoplot(stl_cpi_train)
stl_cpi_plot
accuracy(stl_cpi_train, ts_cpi_test)
## ME RMSE MAE MPE MAPE
## Training set 5.659981e-04 0.3830648 0.2510037 0.002650424 0.1433799
## Test set -2.711643e+01 35.7643265 27.7342462 -10.896917589 11.1853786
## MASE ACF1 Theil's U
## Training set 0.05740139 0.2232740 NA
## Test set 6.34247308 0.9875923 40.01661
arima_cpi = forecast(auto.arima(ts_cpi_train), h=180)
arima_cpi_plot = autoplot(arima_cpi)
arima_cpi_plot
accuracy(arima_cpi)
## ME RMSE MAE MPE MAPE MASE
## Training set 0.001161479 0.3392318 0.2210139 -0.001256395 0.1270708 0.05054311
## ACF1
## Training set 0.005858209
checkresiduals(damp_hw_cpi)
##
## Ljung-Box test
##
## data: Residuals from Damped Holt-Winters' multiplicative method
## Q* = 115.37, df = 7, p-value < 2.2e-16
##
## Model df: 17. Total lags used: 24
accuracy(damp_hw_cpi)
## ME RMSE MAE MPE MAPE MASE
## Training set 0.05726379 0.3925191 0.2662088 0.03294098 0.1526409 0.0608786
## ACF1
## Training set 0.2070482
checkresiduals(hw_cpi)
##
## Ljung-Box test
##
## data: Residuals from Holt-Winters' multiplicative method
## Q* = 151.91, df = 8, p-value < 2.2e-16
##
## Model df: 16. Total lags used: 24
accuracy(hw_cpi)
## ME RMSE MAE MPE MAPE MASE
## Training set -0.01365886 0.5317786 0.3737332 -0.008831955 0.2157153 0.08546808
## ACF1
## Training set 0.5741122
checkresiduals(stl_cpi_train)
## Warning in checkresiduals(stl_cpi_train): The fitted degrees of freedom is based
## on the model used for the seasonally adjusted data.
##
## Ljung-Box test
##
## data: Residuals from STL + ETS(M,A,N)
## Q* = 102.39, df = 20, p-value = 4.703e-13
##
## Model df: 4. Total lags used: 24
accuracy(stl_cpi_train)
## ME RMSE MAE MPE MAPE MASE
## Training set 0.0005659981 0.3830648 0.2510037 0.002650424 0.1433799 0.05740139
## ACF1
## Training set 0.223274
checkresiduals(arima_cpi)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(1,1,4)(0,0,1)[12] with drift
## Q* = 30.588, df = 17, p-value = 0.02241
##
## Model df: 7. Total lags used: 24
accuracy(arima_cpi)
## ME RMSE MAE MPE MAPE MASE
## Training set 0.001161479 0.3392318 0.2210139 -0.001256395 0.1270708 0.05054311
## ACF1
## Training set 0.005858209
#After looking at the residuals and the ME, RSME, and ACF of each of the created models, I narrowed it down to 2 contenders: The ARIMA model and the STL model
arima_layer = autoplot(ts_cpi_changes) +
autolayer(arima_cpi)
arima_layer
stl_layer = autoplot(ts_cpi_changes) +
autolayer(stl_cpi_train)
stl_layer
#After looking at the comparisons of each model against previous data, the ARIMA model clearly follows the historical CPI much more closely than the STL model, this is the one to use for producing CPI forecasts going forward.