library(fpp3)
library(fredr)
library(dplyr)
library(tseries)
library(fabletools)
library(ggplot2)
library(readr)
library(tidyverse)
library(tsibble)
library(feasts)
library(scales)
library(patchwork)
library(ggtime)
library(tseries)
fredr_has_key()[1] TRUE#Housing Inventory: Active Listing Count in the United States (ACTLISCOUUS)
Housing_Inventory <- fredr(series_id = "ACTLISCOUUS") |>
transmute(month = yearmonth(date),value) |>
as_tsibble(index = month)
autoplot(Housing_Inventory, value) +
labs(title = "Housing Inventory: Active Listing Count in the U.S.",x = "Month",y = "Active Listings") #Not Stationary, Downward Trend and Then Upward Trend
adf.test(Housing_Inventory$value) #The Augmented Dickey-Fuller test returned a p-value of 0.9698, which is greater than 0.05. Therefore, we fail to reject the null hypothesis of a unit root, indicating that the time series is non-stationary. This is consistent with the observed trend and seasonality in the data.
Augmented Dickey-Fuller Test
data: Housing_Inventory$value
Dickey-Fuller = -0.68087, Lag order = 4, p-value = 0.9698
alternative hypothesis: stationary# First difference
housing_diff1 <- Housing_Inventory |>
mutate(diff_1 = difference(value))
autoplot(housing_diff1, diff_1) +
labs(title = "First-Differenced Housing Inventory",x = "Month",y = "First Difference")
adf.test(na.omit(housing_diff1$diff_1)) #P value 0.01 -> Series is Stationary
Augmented Dickey-Fuller Test
data: na.omit(housing_diff1$diff_1)
Dickey-Fuller = -6.8908, Lag order = 4, p-value = 0.01
alternative hypothesis: stationaryhousing_diff1 |>
gg_tsdisplay(diff_1, plot_type = "partial")
# ACF and PACF Interpretation:
# The ACF plot of the first-differenced series shows a strong spike at lag 1,
# followed by a gradual decay, which is indicative of a moving average process.
# The PACF plot also shows an initial spike at lag 1 but does not exhibit a clear
# cutoff, instead tapering off across subsequent lags. This pattern suggests that
# autoregressive terms are less dominant, while a moving average component is more appropriate.
#
# Based on these observations, I selected an ARIMA(0,1,1) model, where:
# p = 0 reflects the lack of a clear autoregressive cutoff in the PACF,
# d = 1 accounts for the first differencing required to achieve stationarity,
# and q = 1 captures the strong lag 1 correlation observed in the ACF.
#
# While a seasonal spike is visible at lag 12 in the ACF, the model is intentionally
# kept simple for this analysis, focusing on the dominant short-term dynamics.manual_fit <- Housing_Inventory |>
model(ARIMA(value ~ pdq(0,1,1)))
auto_fit <- Housing_Inventory |>
model(ARIMA(value))manual_fc <- forecast(manual_fit, h = 12)
auto_fc <- forecast(auto_fit, h = 12)autoplot(Housing_Inventory, value) +
autolayer(manual_fc, level = 95, series = "Manual ARIMA") +
autolayer(auto_fc, level = 95, series = "Auto ARIMA") +
labs(title = "Housing Inventory Forecast",x = "Month",y = "Active Listings")
report(auto_fit)Series: value
Model: ARIMA(0,1,3)(2,1,0)[12]
Coefficients:
ma1 ma2 ma3 sar1 sar2
0.9035 0.6612 0.3519 -0.4369 -0.2545
s.e. 0.1025 0.0986 0.0926 0.0976 0.0909
sigma^2 estimated as 359379322: log likelihood=-1171.49
AIC=2354.97 AICc=2355.84 BIC=2370.84glance(manual_fit)# A tibble: 1 × 8
.model sigma2 log_lik AIC AICc BIC ar_roots ma_roots
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <list> <list>
1 ARIMA(value ~ pdq(0, 1, 1)) 4.33e8 -1186. 2381. 2382. 2394. <cpl> <cpl> glance(auto_fit)# A tibble: 1 × 8
.model sigma2 log_lik AIC AICc BIC ar_roots ma_roots
<chr> <dbl> <dbl> <dbl> <dbl> <dbl> <list> <list>
1 ARIMA(value) 359379322. -1171. 2355. 2356. 2371. <cpl [24]> <cpl [3]>#Retail Sales: Retail Trade (MRTSSM44000USN)
Retail_Sales <- fredr(series_id = "MRTSSM44000USN") |>
transmute(month = yearmonth(date),value) |>
as_tsibble(index = month)
autoplot(Retail_Sales, value) +
labs(title = "Retail Sales: Retail Trade Millions of DOllars, U.S.",x = "Month",y = "Millions of Dollars") #Not Stationary, Upward Trend With Extreme Seasonality
adf.test(Retail_Sales$value) #The Augmented Dickey-Fuller test returned a p-value of 0.9789, which is greater than 0.05. Therefore, we fail to reject the null hypothesis of a unit root, indicating that the time series is non-stationary. This is consistent with the observed trend and seasonality in the data.
Augmented Dickey-Fuller Test
data: Retail_Sales$value
Dickey-Fuller = -0.56141, Lag order = 7, p-value = 0.9789
alternative hypothesis: stationaryseasonal_fit <- Retail_Sales |>
model(auto_arima = ARIMA(value))
report(seasonal_fit)Series: value
Model: ARIMA(1,1,2)(0,1,1)[12]
Coefficients:
ar1 ma1 ma2 sma1
-0.5720 0.2437 -0.4553 -0.7042
s.e. 0.0909 0.0840 0.0440 0.0352
sigma^2 estimated as 92665162: log likelihood=-4196.47
AIC=8402.93 AICc=8403.09 BIC=8422.84