Forecast daily bike rental demand using time series models
Ifaz Ahmed Adan
2024-11-30
About Data Analysis Report
This RMarkdown file contains the report of the data analysis done for the project on forecasting daily bike rental demand using time series models in R. It contains analysis such as data exploration, summary statistics and building the time series models. The final report was completed on Sat Nov 30 16:20:25 2024.
Data Description:
This dataset contains the daily count of rental bike transactions between years 2011 and 2012 in Capital bikeshare system with the corresponding weather and seasonal information.
Data Source: https://archive.ics.uci.edu/ml/datasets/bike+sharing+dataset
Relevant Paper:
Fanaee-T, Hadi, and Gama, Joao. Event labeling combining ensemble detectors and background knowledge, Progress in Artificial Intelligence (2013): pp. 1-15, Springer Berlin Heidelberg
Task One: Load and explore the data
Load data and install packages
Describe and explore the data
# Summary of the dataset
summary(data)## instant dteday season yr
## Min. : 1.0 Length:731 Min. :1.000 Min. :0.0000
## 1st Qu.:183.5 Class :character 1st Qu.:2.000 1st Qu.:0.0000
## Median :366.0 Mode :character Median :3.000 Median :1.0000
## Mean :366.0 Mean :2.497 Mean :0.5007
## 3rd Qu.:548.5 3rd Qu.:3.000 3rd Qu.:1.0000
## Max. :731.0 Max. :4.000 Max. :1.0000
## mnth holiday weekday workingday
## Min. : 1.00 Min. :0.00000 Min. :0.000 Min. :0.000
## 1st Qu.: 4.00 1st Qu.:0.00000 1st Qu.:1.000 1st Qu.:0.000
## Median : 7.00 Median :0.00000 Median :3.000 Median :1.000
## Mean : 6.52 Mean :0.02873 Mean :2.997 Mean :0.684
## 3rd Qu.:10.00 3rd Qu.:0.00000 3rd Qu.:5.000 3rd Qu.:1.000
## Max. :12.00 Max. :1.00000 Max. :6.000 Max. :1.000
## weathersit temp atemp hum
## Min. :1.000 Min. :0.05913 Min. :0.07907 Min. :0.0000
## 1st Qu.:1.000 1st Qu.:0.33708 1st Qu.:0.33784 1st Qu.:0.5200
## Median :1.000 Median :0.49833 Median :0.48673 Median :0.6267
## Mean :1.395 Mean :0.49538 Mean :0.47435 Mean :0.6279
## 3rd Qu.:2.000 3rd Qu.:0.65542 3rd Qu.:0.60860 3rd Qu.:0.7302
## Max. :3.000 Max. :0.86167 Max. :0.84090 Max. :0.9725
## windspeed casual registered cnt
## Min. :0.02239 Min. : 2.0 Min. : 20 Min. : 22
## 1st Qu.:0.13495 1st Qu.: 315.5 1st Qu.:2497 1st Qu.:3152
## Median :0.18097 Median : 713.0 Median :3662 Median :4548
## Mean :0.19049 Mean : 848.2 Mean :3656 Mean :4504
## 3rd Qu.:0.23321 3rd Qu.:1096.0 3rd Qu.:4776 3rd Qu.:5956
## Max. :0.50746 Max. :3410.0 Max. :6946 Max. :8714# Select relevant columns
bike_data <- data %>%
select(dteday, cnt, temp, hum, windspeed) %>%
mutate(dteday = as.Date(dteday))
# Check data structure
str(bike_data)## 'data.frame': 731 obs. of 5 variables:
## $ dteday : Date, format: "2011-01-01" "2011-01-02" ...
## $ cnt : int 985 801 1349 1562 1600 1606 1510 959 822 1321 ...
## $ temp : num 0.344 0.363 0.196 0.2 0.227 ...
## $ hum : num 0.806 0.696 0.437 0.59 0.437 ...
## $ windspeed: num 0.16 0.249 0.248 0.16 0.187 ...# Plot daily bike rentals
ggplot(bike_data, aes(x = dteday, y = cnt)) +
geom_line(color = "blue") +
labs(title = "Daily Bike Rentals", x = "Date", y = "Count")
Task Two: Create interactive time series plots
## Read about the timetk package
# ?timetk
# Convert to time series object
bike_ts <- bike_data %>%
select(dteday, cnt) %>%
tk_ts(start = c(2011, 1), freq = 365)## Warning: Non-numeric columns being dropped: dteday# Interactive plot
bike_data %>%
plot_time_series(dteday, cnt, .interactive = FALSE)
Task Three: Smooth time series data
# Apply moving average for smoothing
bike_data <- bike_data %>%
mutate(cnt_smoothed = zoo::rollmean(cnt, k = 7, fill = NA))
# Plot smoothed data
ggplot(bike_data, aes(x = dteday)) +
geom_line(aes(y = cnt), color = "blue", alpha = 0.5) +
geom_line(aes(y = cnt_smoothed), color = "red") +
labs(title = "Smoothed Daily Bike Rentals", x = "Date", y = "Count")## Warning: Removed 6 rows containing missing values (`geom_line()`).
Task Four: Decompose and assess the stationarity of time series data
# Decompose time series
decomp <- decompose(bike_ts, type = "multiplicative")
plot(decomp)
# Check stationarity using Augmented Dickey-Fuller Test
adf.test <- tseries::adf.test(bike_ts)
adf.test##
## Augmented Dickey-Fuller Test
##
## data: bike_ts
## Dickey-Fuller = -1.6351, Lag order = 9, p-value = 0.7327
## alternative hypothesis: stationaryTask Five: Fit and forecast time series data using ARIMA models
# Fit ARIMA model
arima_model <- auto.arima(bike_ts)
summary(arima_model)## Series: bike_ts
## ARIMA(1,0,2)(0,1,0)[365] with drift
##
## Coefficients:
## ar1 ma1 ma2 drift
## 0.9586 -0.6363 -0.1892 5.7093
## s.e. 0.0283 0.0583 0.0506 0.7566
##
## sigma^2 = 1599566: log likelihood = -3131.76
## AIC=6273.52 AICc=6273.68 BIC=6293.03
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 5.357072 890.0137 457.0405 -44.28372 51.73145 0.1967752 0.01047273# Forecast
forecasted <- forecast(arima_model, h = 30)
autoplot(forecasted) +
labs(title = "ARIMA Model Forecast", x = "Date", y = "Count")
Calculate RMSE for ARIMA model
rmse <- sqrt(mean((bike_ts - fitted(arima_model))^2, na.rm = TRUE))
rmse## [1] 890.0137Task Six: Findings and Conclusions
Findings
- The dataset revealed a clear seasonal trend in bike rental demand, with higher rentals observed in the summer and lower rentals during winter. This seasonal variation aligns with expected user behavior based on weather conditions.
- The time series decomposition highlighted trend,
seasonality, and residuals:
- The trend component showed a steady increase in demand over time.
- The seasonal component displayed consistent yearly patterns, with peaks around warmer months and troughs during colder months.
- The residual component indicated random noise without significant irregularities.
Model Performance
The Root Mean Square Error (RMSE) for the ARIMA model was calculated as follows:
# Calculate RMSE for ARIMA model
rmse <- sqrt(mean((bike_ts - fitted(arima_model))^2, na.rm = TRUE))
rmse## [1] 890.0137Implications
- Resource Planning: Allocate more bikes and maintenance resources during the summer months to meet increased demand.
- Marketing Strategies: Design promotional campaigns to encourage usage during colder months and weekdays.
- Operational Efficiency: Use forecasts to optimize bike redistribution and staffing levels based on predicted demand patterns.
Limitations
- The model does not account for external factors such as holidays, special events, or sudden weather changes, which could significantly influence bike rental demand.
- The analysis assumes that historical patterns will continue in the future, which may not hold under changing circumstances (e.g., new user behavior or operational policies).
Future Work
- Incorporate external variables like weather forecasts, holidays, or events into the model to improve forecast accuracy.
- Experiment with more advanced models such as Prophet or machine learning approaches like LSTMs to capture complex patterns.
- Segment users into groups (e.g., casual riders vs. subscribers) to provide more granular and customized forecasts.