Time Series Analysis: Exploratory Data Analysis

1. Loading Required Libraries

library(tidyverse)
library(lubridate)
library(tsibble)
library(feasts)
library(forecast)
library(plotly)

2. Data Loading and Initial Inspection

# Reading the data
crimes_data <- read.csv("Crimes_2001_to_present.csv")

# Initial look at the data
head(crimes_data)

##         ID Case.Number                   Date                   Block IUCR
## 1 13689808    JH539692 12/11/2024 11:40:00 PM      022XX N LEAVITT ST 031A
## 2 13689797    JH539688 12/11/2024 11:38:00 PM      087XX S BURLEY AVE 0326
## 3 13690325    JH539659 12/11/2024 10:50:00 PM 014XX S SPRINGFIELD AVE 0325
## 4 13689749    JH539636 12/11/2024 10:36:00 PM     006XX N ASHLAND AVE 031A
## 5 13689743    JH539668 12/11/2024 09:41:00 PM      049XX S CICERO AVE 031A
## 6 13689599    JH539522 12/11/2024 07:49:00 PM     064XX S RICHMOND ST 0320
##   Primary.Type                    Description Location.Description Arrest
## 1      ROBBERY                ARMED - HANDGUN             SIDEWALK  false
## 2      ROBBERY AGGRAVATED VEHICULAR HIJACKING            APARTMENT  false
## 3      ROBBERY            VEHICULAR HIJACKING               STREET  false
## 4      ROBBERY                ARMED - HANDGUN          GAS STATION  false
## 5      ROBBERY                ARMED - HANDGUN          GAS STATION  false
## 6      ROBBERY         STRONG ARM - NO WEAPON             SIDEWALK  false
##   Domestic Beat District Ward Community.Area FBI.Code X.Coordinate Y.Coordinate
## 1    false 1432       14   32             22        3      1161323      1914920
## 2    false  424        4   10             46        3      1199184      1847735
## 3    false 1011       10   24             29        3      1150611      1892853
## 4    false 1215       12    1             24        3      1165609      1904556
## 5    false  814        8   22             56        3      1145191      1871544
## 6    false  823        8   15             66        3      1157824      1861716
##   Year             Updated.On Latitude Longitude                      Location
## 1 2024 12/19/2024 03:41:35 PM 41.92222 -87.68267 (41.922223823, -87.682674421)
## 2 2024 12/19/2024 03:41:35 PM 41.73699 -87.54583 (41.736993626, -87.545827764)
## 3 2024 12/19/2024 03:41:35 PM 41.86189 -87.72261 (41.861885976, -87.722610798)
## 4 2024 12/19/2024 03:41:35 PM 41.89369 -87.66722 (41.893693999, -87.667222147)
## 5 2024 12/19/2024 03:41:35 PM 41.80352 -87.74304 (41.803515121, -87.743044463)
## 6 2024 12/19/2024 03:41:35 PM 41.77630 -87.69698 (41.776298295, -87.696979416)

str(crimes_data)

## 'data.frame':    309431 obs. of  22 variables:
##  $ ID                  : int  13689808 13689797 13690325 13689749 13689743 13689599 13690171 13689477 13689503 13689479 ...
##  $ Case.Number         : chr  "JH539692" "JH539688" "JH539659" "JH539636" ...
##  $ Date                : chr  "12/11/2024 11:40:00 PM" "12/11/2024 11:38:00 PM" "12/11/2024 10:50:00 PM" "12/11/2024 10:36:00 PM" ...
##  $ Block               : chr  "022XX N LEAVITT ST" "087XX S BURLEY AVE" "014XX S SPRINGFIELD AVE" "006XX N ASHLAND AVE" ...
##  $ IUCR                : chr  "031A" "0326" "0325" "031A" ...
##  $ Primary.Type        : chr  "ROBBERY" "ROBBERY" "ROBBERY" "ROBBERY" ...
##  $ Description         : chr  "ARMED - HANDGUN" "AGGRAVATED VEHICULAR HIJACKING" "VEHICULAR HIJACKING" "ARMED - HANDGUN" ...
##  $ Location.Description: chr  "SIDEWALK" "APARTMENT" "STREET" "GAS STATION" ...
##  $ Arrest              : chr  "false" "false" "false" "false" ...
##  $ Domestic            : chr  "false" "false" "false" "false" ...
##  $ Beat                : int  1432 424 1011 1215 814 823 1011 422 914 825 ...
##  $ District            : int  14 4 10 12 8 8 10 4 9 8 ...
##  $ Ward                : int  32 10 24 1 22 15 24 7 11 16 ...
##  $ Community.Area      : int  22 46 29 24 56 66 29 46 34 66 ...
##  $ FBI.Code            : int  3 3 3 3 3 3 3 3 3 3 ...
##  $ X.Coordinate        : int  1161323 1199184 1150611 1165609 1145191 1157824 1147575 1195224 1172636 1160426 ...
##  $ Y.Coordinate        : int  1914920 1847735 1892853 1904556 1871544 1861716 1894183 1852934 1888149 1863809 ...
##  $ Year                : int  2024 2024 2024 2024 2024 2024 2024 2024 2024 2024 ...
##  $ Updated.On          : chr  "12/19/2024 03:41:35 PM" "12/19/2024 03:41:35 PM" "12/19/2024 03:41:35 PM" "12/19/2024 03:41:35 PM" ...
##  $ Latitude            : num  41.9 41.7 41.9 41.9 41.8 ...
##  $ Longitude           : num  -87.7 -87.5 -87.7 -87.7 -87.7 ...
##  $ Location            : chr  "(41.922223823, -87.682674421)" "(41.736993626, -87.545827764)" "(41.861885976, -87.722610798)" "(41.893693999, -87.667222147)" ...

3. Data Preprocessing

# Converting date format and selecting relevant columns
crimes_clean <- crimes_data %>%
  mutate(
    Date = as.Date(Date, format = "%m/%d/%Y"),
    Year = year(Date),
    Month = month(Date),
    Day = day(Date),
    Weekday = wday(Date, label = TRUE)
  ) %>%
  select(Date, Primary.Type, Year, Month, Day, Weekday)

# Check for missing values
sapply(crimes_clean, function(x) sum(is.na(x)))

##         Date Primary.Type         Year        Month          Day      Weekday 
##            0            0            0            0            0            0

4. Basic Time Series Analysis

4.1 Crime Frequency by Type

# Top 10 most frequent crime types
crime_freq <- crimes_clean %>%
  count(Primary.Type, sort = TRUE) %>%
  head(10)

# Plot
ggplot(crime_freq, aes(x = reorder(Primary.Type, n), y = n)) +
  geom_bar(stat = "identity", fill = "steelblue") +
  coord_flip() +
  labs(
    title = "Top 10 Most Frequent Crime Types",
    x = "Crime Type",
    y = "Frequency"
  ) +
  theme_minimal()

4.2 Time Series Creation for Most Common Crime

# Select most common crime type
most_common_crime <- crime_freq$Primary.Type[1]

# Create daily time series
daily_crimes <- crimes_clean %>%
  filter(Primary.Type == most_common_crime) %>%
  count(Date, name = "count") %>%
  complete(Date = seq.Date(
    from = min(Date),
    to = max(Date),
    by = "day"
  ),
  fill = list(count = 0))

# Convert to tsibble
ts_crimes <- daily_crimes %>%
  as_tsibble(index = Date)

5. Temporal Patterns Analysis

5.1 Daily Trend

# Plot daily trend
ts_crimes %>%
  ggplot(aes(x = Date, y = count)) +
  geom_line(color = "steelblue") +
  labs(
    title = paste("Daily", most_common_crime, "Incidents"),
    y = "Number of Incidents",
    x = "Date"
  ) +
  theme_minimal()

5.2 Monthly Pattern

# Monthly aggregation
monthly_crimes <- crimes_clean %>%
  filter(Primary.Type == most_common_crime) %>%
  count(Year, Month) %>%
  mutate(Date = make_date(Year, Month, 1))

# Plot monthly pattern
ggplot(monthly_crimes, aes(x = Date, y = n)) +
  geom_line(color = "steelblue") +
  geom_smooth(method = "loess", se = FALSE, color = "red") +
  labs(
    title = paste("Monthly", most_common_crime, "Incidents with Trend"),
    y = "Number of Incidents",
    x = "Date"
  ) +
  theme_minimal()

5.3 Seasonal Patterns

# Weekly pattern
weekly_pattern <- crimes_clean %>%
  filter(Primary.Type == most_common_crime) %>%
  count(Weekday) %>%
  mutate(Weekday = fct_reorder(Weekday, n))

ggplot(weekly_pattern, aes(x = Weekday, y = n)) +
  geom_bar(stat = "identity", fill = "steelblue") +
  labs(
    title = paste("Weekly Pattern of", most_common_crime),
    y = "Total Incidents",
    x = "Day of Week"
  ) +
  theme_minimal()

# Monthly pattern across years
monthly_pattern <- crimes_clean %>%
  filter(Primary.Type == most_common_crime) %>%
  count(Month, Year) %>%
  group_by(Month) %>%
  summarise(avg_crimes = mean(n))

ggplot(monthly_pattern, aes(x = Month, y = avg_crimes)) +
  geom_line(group = 1, color = "steelblue") +
  geom_point(color = "steelblue") +
  scale_x_continuous(breaks = 1:12) +
  labs(
    title = paste("Average Monthly Pattern of", most_common_crime),
    y = "Average Incidents",
    x = "Month"
  ) +
  theme_minimal()

6. Decomposition Analysis

# Convert to ts object
crimes_ts <- ts(ts_crimes$count, 
                frequency = 7)  # Weekly seasonality

# Decomposition
decomp <- decompose(crimes_ts)

# Plot decomposition
plot(decomp)

7. Statistical Summary

# Basic statistics
summary_stats <- ts_crimes %>%
  summarise(
    mean_daily = mean(count),
    median_daily = median(count),
    sd_daily = sd(count),
    min_daily = min(count),
    max_daily = max(count)
  )

print(summary_stats)

## # A tsibble: 8,746 x 6 [1D]
##    Date       mean_daily median_daily sd_daily min_daily max_daily
##    <date>          <dbl>        <int>    <dbl>     <int>     <int>
##  1 2001-01-01         41           41       NA        41        41
##  2 2001-01-02         35           35       NA        35        35
##  3 2001-01-03         51           51       NA        51        51
##  4 2001-01-04         55           55       NA        55        55
##  5 2001-01-05         55           55       NA        55        55
##  6 2001-01-06         54           54       NA        54        54
##  7 2001-01-07         36           36       NA        36        36
##  8 2001-01-08         44           44       NA        44        44
##  9 2001-01-09         38           38       NA        38        38
## 10 2001-01-10         41           41       NA        41        41
## # ℹ 8,736 more rows

# ACF plot
acf(ts_crimes$count, main = "Autocorrelation Function")

8. Initial Findings

Based on the exploratory data analysis:

Data Structure:
- Time period covered
- Frequency of observations
- Quality of data (missing values, outliers)
Temporal Patterns:
- Overall trend direction
- Seasonal patterns (weekly, monthly, yearly)
- Notable anomalies or changes in patterns
Key Statistics:
- Average daily incidents
- Variation in incidents
- Peak periods

These findings will inform our model selection and feature engineering in the next phase.

Time Series Analysis: Exploratory Data Analysis

Kevin Adam Prasetya

2024-12-20

1. Loading Required Libraries

2. Data Loading and Initial Inspection

3. Data Preprocessing

4. Basic Time Series Analysis

4.1 Crime Frequency by Type

4.2 Time Series Creation for Most Common Crime

5. Temporal Patterns Analysis

5.1 Daily Trend

5.2 Monthly Pattern

5.3 Seasonal Patterns

6. Decomposition Analysis

7. Statistical Summary

8. Initial Findings