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_ch6_lesson2_retail_fullserve_restaurants.qmd
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---
title: "Untitled"
---
```{r}
#| include: false
source("common_functions.R")
```
```{r}
#| echo: false
#| warning: false
# Read in retail sales data for "Full-Service Restaurants"
retail_ts <- rio::import("https://byuistats.github.io/timeseries/data/retail_by_business_type.parquet") |>
filter(naics == 722511) |>
mutate(
month = yearmonth(as_date(month)),
month_number = month(month)
) |>
mutate(t = 1:n()) |>
mutate(std_t = (t - mean(t)) / sd(t)) |>
mutate(
cos1 = cos(2 * pi * 1 * t / 12),
cos2 = cos(2 * pi * 2 * t / 12),
cos3 = cos(2 * pi * 3 * t / 12),
cos4 = cos(2 * pi * 4 * t / 12),
cos5 = cos(2 * pi * 5 * t / 12),
cos6 = cos(2 * pi * 6 * t / 12),
sin1 = sin(2 * pi * 1 * t / 12),
sin2 = sin(2 * pi * 2 * t / 12),
sin3 = sin(2 * pi * 3 * t / 12),
sin4 = sin(2 * pi * 4 * t / 12),
sin5 = sin(2 * pi * 5 * t / 12)
) |>
mutate(
in_great_recession = ifelse(ym(month) >= my("December 2007") & month <= my("June 2009"), 1, 0),
after_great_recession = ifelse(ym(month) > my("June 2009"), 1, 0)
) |>
as_tsibble(index = month)
retail_ts |>
autoplot(.vars = sales_millions) +
stat_smooth(method = "lm",
formula = y ~ x,
geom = "smooth",
se = FALSE,
color = "#E69F00",
linetype = "dotted") +
labs(
x = "Month",
y = "Sales (Millions of U.S. Dollars)",
title = paste0(retail_ts$business[1], " (", retail_ts$naics[1], ")")
) +
theme_minimal() +
theme(plot.title = element_text(hjust = 0.5))
retail_ts |>
autoplot(.vars = log(sales_millions)) +
stat_smooth(method = "lm",
formula = y ~ x,
geom = "smooth",
se = FALSE,
color = "#E69F00",
linetype = "dotted") +
labs(
x = "Month",
y = "Sales (Millions of U.S. Dollars)",
title = paste0(retail_ts$business[1], " (", retail_ts$naics[1], ")")
) +
theme_minimal() +
theme(plot.title = element_text(hjust = 0.5))
```
<!-- @fig-retailSideBySidePlot shows the "Full service Restaurants" retail sales data. -->
```{r}
#| include: false
#| label: fig-retailSideBySidePlot
#| fig-cap: "Time plot of the time series (left) and the natural logarithm of the time series (right)"
#| code-fold: true
#| code-summary: "Show the code"
#| warning: false
#| fig-height: 3.5
retail_plot_raw <- retail_ts |>
autoplot(.vars = sales_millions) +
labs(
x = "Month",
y = "sales_millions",
title = "Other General Merchandise Sales"
) +
theme_minimal() +
theme(
plot.title = element_text(hjust = 0.5)
)
retail_plot_log <- retail_ts |>
autoplot(.vars = log(sales_millions)) +
labs(
x = "Month",
y = "log(sales_millions)",
title = "Logarithm of Other Gen. Merch. Sales"
) +
theme_minimal() +
theme(
plot.title = element_text(hjust = 0.5)
)
retail_plot_raw | retail_plot_log
```
```{r}
#| label: modelFitting
#| code-fold: true
#| code-summary: "Show the code"
retail_final_lm <- retail_ts |>
model(retail_full = TSLM(log(sales_millions) ~
(in_great_recession * std_t) + (after_great_recession * std_t)
+ (in_great_recession * I(std_t^2) ) + (after_great_recession * I(std_t^2) )
+ (in_great_recession * I(std_t^3) ) + (after_great_recession * I(std_t^3) )
+ sin1 + cos1 + sin2 + cos2 + sin3 + cos3
+ sin4 + cos4 + sin5 + cos5 + cos6 # Note sin6 is omitted
)
)
retail_final_lm |>
tidy() |>
mutate(sig = p.value < 0.05)
retail_resid_df <- retail_final_lm |>
residuals() |>
as_tibble() |>
dplyr::select(.resid) |>
rename(x = .resid)
retail_resid_df |>
mutate(density = dnorm(x, mean(retail_resid_df$x), sd(retail_resid_df$x))) |>
ggplot(aes(x = x)) +
geom_histogram(aes(y = after_stat(density)),
color = "white", fill = "#56B4E9", binwidth = 0.02) +
geom_line(aes(x = x, y = density)) +
theme_bw() +
labs(
x = "Values",
y = "Frequency",
title = "Histogram of Residuals"
) +
theme(
plot.title = element_text(hjust = 0.5)
)
skewness(retail_resid_df$x)
retail_final_lm |>
residuals() |>
ACF() |>
autoplot(var = .resid)
retail_final_lm |>
residuals() |>
PACF() |>
autoplot(var = .resid)
```
```{r}
#| warning: false
retail_no_seasonal_lm <- retail_ts |>
model(retail_full_quad = TSLM(log(sales_millions) ~
(in_great_recession * std_t) + (after_great_recession * std_t)
+ (in_great_recession * I(std_t^2) ) + (after_great_recession * I(std_t^2) )
)
)
retail_ts |>
autoplot(.vars = sales_millions) +
# ggplot(mapping = aes(x = month, y = sales_millions)) +
# geom_line() +
geom_line(data = augment(retail_no_seasonal_lm),
aes(x = month, y = .fitted),
color = "#E69F00",
linewidth = 1
) +
geom_line(data = augment(retail_final_lm),
aes(x = month, y = .fitted),
color = "blue",
alpha = 0.7,
# linewidth = 1
) +
labs(
x = "Month",
y = "Sales (Millions of U.S. Dollars)",
title = paste0(retail_ts$business[1], " (", retail_ts$naics[1], ")")
) +
theme_minimal() +
theme(plot.title = element_text(hjust = 0.5))
```
```{r}
model_resid <- retail_final_lm |>
residuals() |>
select(-.model) |>
model(
auto = ARIMA(.resid ~ 1 + pdq(0:5,0,0:5) + PDQ(0, 0, 0)),
a000 = ARIMA(.resid ~ 1 + pdq(0,0,0) + PDQ(0, 0, 0)),
a001 = ARIMA(.resid ~ 1 + pdq(0,0,1) + PDQ(0, 0, 0)),
a002 = ARIMA(.resid ~ 1 + pdq(0,0,2) + PDQ(0, 0, 0)),
a003 = ARIMA(.resid ~ 1 + pdq(0,0,3) + PDQ(0, 0, 0)),
a004 = ARIMA(.resid ~ 1 + pdq(0,0,4) + PDQ(0, 0, 0)),
a005 = ARIMA(.resid ~ 1 + pdq(0,0,5) + PDQ(0, 0, 0)),
a100 = ARIMA(.resid ~ 1 + pdq(1,0,0) + PDQ(0, 0, 0)),
a101 = ARIMA(.resid ~ 1 + pdq(1,0,1) + PDQ(0, 0, 0)),
a102 = ARIMA(.resid ~ 1 + pdq(1,0,2) + PDQ(0, 0, 0)),
a103 = ARIMA(.resid ~ 1 + pdq(1,0,3) + PDQ(0, 0, 0)),
a104 = ARIMA(.resid ~ 1 + pdq(1,0,4) + PDQ(0, 0, 0)),
a105 = ARIMA(.resid ~ 1 + pdq(1,0,5) + PDQ(0, 0, 0)),
a200 = ARIMA(.resid ~ 1 + pdq(2,0,0) + PDQ(0, 0, 0)),
a201 = ARIMA(.resid ~ 1 + pdq(2,0,1) + PDQ(0, 0, 0)),
a202 = ARIMA(.resid ~ 1 + pdq(2,0,2) + PDQ(0, 0, 0)),
a203 = ARIMA(.resid ~ 1 + pdq(2,0,3) + PDQ(0, 0, 0)),
a204 = ARIMA(.resid ~ 1 + pdq(2,0,4) + PDQ(0, 0, 0)),
a205 = ARIMA(.resid ~ 1 + pdq(2,0,5) + PDQ(0, 0, 0)),
a300 = ARIMA(.resid ~ 1 + pdq(3,0,0) + PDQ(0, 0, 0)),
a301 = ARIMA(.resid ~ 1 + pdq(3,0,1) + PDQ(0, 0, 0)),
a302 = ARIMA(.resid ~ 1 + pdq(3,0,2) + PDQ(0, 0, 0)),
a303 = ARIMA(.resid ~ 1 + pdq(3,0,3) + PDQ(0, 0, 0)),
a304 = ARIMA(.resid ~ 1 + pdq(3,0,4) + PDQ(0, 0, 0)),
a305 = ARIMA(.resid ~ 1 + pdq(3,0,5) + PDQ(0, 0, 0)),
a400 = ARIMA(.resid ~ 1 + pdq(4,0,0) + PDQ(0, 0, 0)),
a401 = ARIMA(.resid ~ 1 + pdq(4,0,1) + PDQ(0, 0, 0)),
a402 = ARIMA(.resid ~ 1 + pdq(4,0,2) + PDQ(0, 0, 0)),
a403 = ARIMA(.resid ~ 1 + pdq(4,0,3) + PDQ(0, 0, 0)),
a404 = ARIMA(.resid ~ 1 + pdq(4,0,4) + PDQ(0, 0, 0)),
a405 = ARIMA(.resid ~ 1 + pdq(4,0,5) + PDQ(0, 0, 0)),
a500 = ARIMA(.resid ~ 1 + pdq(5,0,0) + PDQ(0, 0, 0)),
a501 = ARIMA(.resid ~ 1 + pdq(5,0,1) + PDQ(0, 0, 0)),
a502 = ARIMA(.resid ~ 1 + pdq(5,0,2) + PDQ(0, 0, 0)),
a503 = ARIMA(.resid ~ 1 + pdq(5,0,3) + PDQ(0, 0, 0)),
a504 = ARIMA(.resid ~ 1 + pdq(5,0,4) + PDQ(0, 0, 0)),
a505 = ARIMA(.resid ~ 1 + pdq(5,0,5) + PDQ(0, 0, 0))
)
model_resid |> select(auto)
model_resid |>
glance() |>
filter(AIC == min(AIC) | AICc == min(AICc) | BIC == min(BIC) | .model == "auto")
```
```{r}
model_resid |>
select(a504) |>
residuals() |>
ACF() |>
autoplot(var = .resid)
model_resid |>
select(a504) |>
residuals() |>
PACF() |>
autoplot(var = .resid)
```