This Gist contains an R script that calculates and visualizes the date of Easter over a range of years (2000-2025). It uses the timeDate package to determine Easter dates, dplyr for data manipulation, ggplot2 for creating trend lines, frequency bar charts, and box plots, lubridate for date manipulation, and forecast for analyzing the autocorrela…

Easter_functions_and_graph_analysis.R

# Functions to calculate easter day
library(timeDate)

calculate_easter <- function(year) {
  easter_date <- as.Date(Easter(year))
  return(easter_date)
}

desired_year <- 2025
easter_date_year <- calculate_easter(desired_year)
print(paste("Easter in", desired_year, "will be on:", format(easter_date_year, "%d of %B of %Y")))

previous_years <- seq(2000, 2024)
previous_easter_dates <- lapply(previous_years, calculate_easter)
print("Easter dates in the last years:")
for (i in 1:length(previous_years)) {
  print(paste(previous_years[i], ":", format(previous_easter_dates[[i]], "%d of %B of %Y")))
}

future_years <- seq(2026, 2030)
future_easter_dates <- lapply(future_years, calculate_easter)
print("Easter dates in the next few years:")
for (i in 1:length(future_years)) {
  print(paste(future_years[i], ":", format(future_easter_dates[[i]], "%d of %B of %Y")))
}

# Plotting the easter day trend graph
library(ggplot2)
library(dplyr)
library(lubridate)

fig<-function(x,y){
  options(repr.plot.width = x, repr.plot.height = y)
}

years <- 2000:2025
easter_dates <- as.Date(Easter(years))
easter_df <- data.frame(
  Year = years,
  EasterDate = easter_dates
)

easter_df$DayOfYear <- yday(easter_df$EasterDate)
y_breaks <- seq(80, 120, by = 5)
labels_march <- paste0(1:31, " Mar")
labels_april <- paste0(1:30, " Apr")
all_labels <- c(
  labels_march[which(
    1:31 %in% day(seq(
      as.Date("2000-03-01"),
      as.Date("2000-03-31"),
      by = "day"
    ))
  )],
  labels_april[which(
    1:30 %in% day(seq(
      as.Date("2000-04-01"),
      as.Date("2000-04-30"),
      by = "day"
    ))
  )]
)

relevant_breaks_index <- which(
  y_breaks >= 80 & y_breaks <= 120
)

relevant_breaks <- y_breaks[relevant_breaks_index]
date_sequence <- seq(
  as.Date("2000-03-20"),
  as.Date("2000-04-30"),
  by = "day"
)

relevant_labels <- format(
  date_sequence[which(
    yday(date_sequence) %in% relevant_breaks
  )], "%d of %b"
)

fig(12,8)
easter_df %>%
  ggplot(aes(
    x = Year,
    y = DayOfYear
  )) +
  geom_line(
    linewidth = 1
  ) +
  scale_y_continuous(
    breaks = relevant_breaks,
    labels = relevant_labels
  ) +
  labs(
    title = "Easter date trend and variation over the years",
    x = "Years",
    y = "Easter days"
  ) +
  theme_minimal() +
  theme(
    axis.text.x = element_text(angle = 45, hjust = 1),
    axis.text.y = element_text(size = 8)
  ) +
geom_smooth(se = FALSE, color = "red")

# Plotting easter day monthly frequency
easter_mar_apr <- easter_df %>%
  mutate(Month = month(EasterDate)) %>%
  filter(Month %in% c(3, 4)) %>%
  mutate(MonthName = case_when(
    Month == 3 ~ "March",
    Month == 4 ~ "Aoril"
  ))

monthly_frequency <- easter_mar_apr %>%
  group_by(MonthName) %>%
  summarize(Frequency = n())

fig(12,8)
ggplot(monthly_frequency, aes(x = MonthName, y = Frequency)) +
  geom_bar(stat = "identity", color = "black") +
  labs(title = "Easter frequency in March and April",
       x = "Month",
       y = "Frequency") +
  theme_minimal()

# Plotting the easter distribution
fig(12,8)
ggplot(easter_df, aes(y = DayOfYear)) +
  geom_boxplot(color = "black") +
  scale_y_continuous(breaks = y_breaks, labels = relevant_labels) +
  labs(title = "Distribution of Easter date over the year",
       y = "Easter days") +
  theme_minimal() +
  theme(axis.text.x = element_blank())

# Analysis of autocorrelation
library(forecast)

easter_ts <- ts(easter_df$DayOfYear, start = min(years), end = max(years), frequency = 1)
values <- list(
  acf = acf(easter_ts, plot = FALSE),
  pacf = pacf(easter_ts, plot = FALSE)
)

acf_df <- data.frame(
  lag = values$acf$lag,
  acf = values$acf$acf
)

pacf_df <- data.frame(
  lag = values$pacf$lag,
  pacf = values$pacf$acf
)

n <- length(easter_ts)
conf_level <- 1.96 / sqrt(n)

# ACF
fig(12,8)
acf_df %>% 
  ggplot(aes(
    x = lag,
    y = acf
  )) +
  geom_bar(stat = "identity") +
  geom_hline(
    yintercept = 0,
    color = "black"
  ) +
  geom_hline(
    yintercept = conf_level,
    color = "red",
    linetype = "dashed"
  ) +
  geom_hline(
    yintercept = -conf_level,
    color = "red",
    linetype = "dashed"
  ) +
  labs(
    title = "Autocorrelation of the Easter Date",
    x = "Lag (Years)",
    y = "Autocorrelation"
  ) +
  theme_minimal()

# PACF
fig(12,8)
pacf_df %>% 
  ggplot(aes(
    x = lag,
    y = pacf
  )) +
  geom_bar(stat = "identity") +
  geom_hline(
    yintercept = 0,
    color = "black"
  ) +
  geom_hline(
    yintercept = conf_level,
    color = "red",
    linetype = "dashed"
  ) +
  geom_hline(
    yintercept = -conf_level,
    color = "red",
    linetype = "dashed"
  ) +
  labs(
    title = "Parcial Autocorrelation of the Easter Date",
    x = "Lag (Years)",
    y = "Autocorrelation"
  ) +
  theme_minimal()