Time Series Analysis of Bicycle Renting Dataset

library('ggplot2')
library('forecast')
library('tseries')

daily_data = read.csv('day.csv', header=TRUE, stringsAsFactors=FALSE)
daily_data$Date = as.Date(daily_data$dteday)

ggplot(daily_data, aes(Date, cnt)) + geom_line() + scale_x_date('month')  + ylab("Daily Bike Checkouts") +
  xlab("")

count_ts = ts(daily_data[, c('cnt')])
daily_data$clean_cnt = tsclean(count_ts)
ggplot() +
  geom_line(data = daily_data, aes(x = Date, y = clean_cnt)) + ylab('Cleaned Bicycle Count')

daily_data$cnt_ma = ma(daily_data$clean_cnt, order=7) # using the clean count with no outliers
daily_data$cnt_ma30 = ma(daily_data$clean_cnt, order=30)


ggplot() +
  geom_line(data = daily_data, aes(x = Date, y = clean_cnt, colour = "Counts")) +
  geom_line(data = daily_data, aes(x = Date, y = cnt_ma,   colour = "Weekly Moving Average"))  +
  geom_line(data = daily_data, aes(x = Date, y = cnt_ma30, colour = "Monthly Moving Average"))  +
  ylab('Bicycle Count')

count_ma = ts(na.omit(daily_data$cnt_ma), frequency=30)
decomp = stl(count_ma, s.window="periodic")
deseasonal_cnt <- seasadj(decomp)
plot(decomp)

count_d1 = diff(deseasonal_cnt, differences = 1)
plot(count_d1)

adf.test(count_d1, alternative = "stationary")

## 
##  Augmented Dickey-Fuller Test
## 
## data:  count_d1
## Dickey-Fuller = -9.9255, Lag order = 8, p-value = 0.01
## alternative hypothesis: stationary

Acf(count_d1, main='ACF for Differenced Series')

Pacf(count_d1, main='PACF for Differenced Series')

fit<-auto.arima(deseasonal_cnt, seasonal=FALSE)
tsdisplay(residuals(fit), lag.max=45, main='(1,1,1) Model Residuals')

seasonalfit<-arima(deseasonal_cnt, order=c(2,1,7), seasonal=list(order=c(1L,0L,0L), period=24L))
tsdisplay(residuals(seasonalfit), lag.max=45)