# Step 1: Load R Packages
### options(repos='http://cran.rstudio.com/')
#install.packages("astsa")
#install.packages('ggplot2')
#install.packages('forecast')
#install.packages('tseries')
#install.packages("data.table")
library(astsa)
library(forecast)
library(tseries)
library(zoo)
library(tseries)
library(data.table)
library(dplyr)
library(tidyr)
library(naniar)
library(stringr)
library(ggplot2)
library(DT)
library(lubridate)
library(ggpubr)
mytype = 'RMU'
setwd("/scratch/user/cma16/Task4_Deliverable2/OHprocess4/AllCrash/FacilityBased/")
load("./multi-lane_undivided_OH_reduce_withCrash.rData")
setwd(paste0("/scratch/user/cma16/Task4_Deliverable2/OHprocess4/AllCrash/FacilityBased/",mytype))
df_RMU <- OH_mun_nomed
df_RMU$spd_av = 3600*df_RMU$DISTANCE/df_RMU$Travel_TIME_ALL_VEHICLES
df_RMU$spd_pv = 3600*df_RMU$DISTANCE/df_RMU$Travel_TIME_PASSENGER_VEHICLES
df_RMU$spd_ft = 3600*df_RMU$DISTANCE/df_RMU$Travel_TIME_FREIGHT_TRUCKS
### Month, Day
df_RMU$date <- as.character(df_RMU$DATE)
df_RMU$date <- str_pad(df_RMU$DATE, 8, pad = "0")
df_RMU$Month <- substr(df_RMU$date, start = 1, stop = 2)
df_RMU$Day <- substr(df_RMU$date, start = 3, stop = 4)
df_RMU$Year <- substr(df_RMU$date, start = 5, stop = 8)
df_RMU$MonthDay <- paste0(df_RMU$Month,"_", df_RMU$Day)
head(df_RMU)
## TimeStamp TMC DATE EPOCH1h Travel_TIME_ALL_VEHICLES
## 1: 108N06000_0101_0 108N06000 1012015 0 NA
## 2: 108N06000_0101_1 108N06000 1012015 1 299
## 3: 108N06000_0101_10 108N06000 1012015 10 321
## 4: 108N06000_0101_11 108N06000 1012015 11 253
## 5: 108N06000_0101_12 108N06000 1012015 12 321
## 6: 108N06000_0101_13 108N06000 1012015 13 294
## Travel_TIME_PASSENGER_VEHICLES Travel_TIME_FREIGHT_TRUCKS ADMIN_LEVE
## 1: NA NA USA
## 2: NA 299 USA
## 3: NA 321 USA
## 4: NA 253 USA
## 5: NA 321 USA
## 6: NA 294 USA
## ADMIN_LE_1 ADMIN_LE_2 DISTANCE ROAD_NUMBE ROAD_NAME LATITUDE LONGITUDE
## 1: Ohio Williams 2.26922 OH-15 41.44172 -84.55062
## 2: Ohio Williams 2.26922 OH-15 41.44172 -84.55062
## 3: Ohio Williams 2.26922 OH-15 41.44172 -84.55062
## 4: Ohio Williams 2.26922 OH-15 41.44172 -84.55062
## 5: Ohio Williams 2.26922 OH-15 41.44172 -84.55062
## 6: Ohio Williams 2.26922 OH-15 41.44172 -84.55062
## ROAD_DIREC ORN_FID COUNTY divided SURF_TYP NHS_CDE HPMS ACCESS AADT_YR
## 1: Southbound 32246.93 WIL U G N N 14
## 2: Southbound 32246.93 WIL U G N N 14
## 3: Southbound 32246.93 WIL U G N N 14
## 4: Southbound 32246.93 WIL U G N N 14
## 5: Southbound 32246.93 WIL U G N N 14
## 6: Southbound 32246.93 WIL U G N N 14
## FED_FACI PK_LANES MED_TYPE FED_MEDW BEGMP ENDMP SEG_LNG cnty_rte
## 1: 2 4 1 NA 1.05 2 0.3891861 WIL0127R
## 2: 2 4 1 NA 1.05 2 0.3891861 WIL0127R
## 3: 2 4 1 NA 1.05 2 0.3891861 WIL0127R
## 4: 2 4 1 NA 1.05 2 0.3891861 WIL0127R
## 5: 2 4 1 NA 1.05 2 0.3891861 WIL0127R
## 6: 2 4 1 NA 1.05 2 0.3891861 WIL0127R
## rte_nbr aadt aadt_bc aadt_pt surf_wid no_lanes func_cls rodwycls
## 1: 0127R 8274.383 520.5784 7753.805 49.15682 4 2 10
## 2: 0127R 8274.383 520.5784 7753.805 49.15682 4 2 10
## 3: 0127R 8274.383 520.5784 7753.805 49.15682 4 2 10
## 4: 0127R 8274.383 520.5784 7753.805 49.15682 4 2 10
## 5: 0127R 8274.383 520.5784 7753.805 49.15682 4 2 10
## 6: 0127R 8274.383 520.5784 7753.805 49.15682 4 2 10
## Total K A B C O DAYMTH Crash spd_av spd_pv spd_ft date Month
## 1: 1 0 0 0 0 1 0101 0 NA NA NA 01012015 01
## 2: 1 0 0 0 0 1 0101 0 27.32171 NA 27.32171 01012015 01
## 3: 1 0 0 0 0 1 0101 0 25.44920 NA 25.44920 01012015 01
## 4: 1 0 0 0 0 1 0101 0 32.28930 NA 32.28930 01012015 01
## 5: 1 0 0 0 0 1 0101 0 25.44920 NA 25.44920 01012015 01
## 6: 1 0 0 0 0 1 0101 0 27.78637 NA 27.78637 01012015 01
## Day Year MonthDay
## 1: 01 2015 01_01
## 2: 01 2015 01_01
## 3: 01 2015 01_01
## 4: 01 2015 01_01
## 5: 01 2015 01_01
## 6: 01 2015 01_01
day1<- df_RMU[,-c(1)] %>% group_by(MonthDay) %>% summarize(Speed_All_Mean=mean(spd_av, na.rm=TRUE))
day1
## # A tibble: 365 x 2
## MonthDay Speed_All_Mean
## <chr> <dbl>
## 1 01_01 42.5
## 2 01_02 40.1
## 3 01_03 38.9
## 4 01_04 40.6
## 5 01_05 38.3
## 6 01_06 36.2
## 7 01_07 36.7
## 8 01_08 38.0
## 9 01_09 35.1
## 10 01_10 40.4
## # ... with 355 more rows
# Step 2: Examine Data
speed_clean <- tsclean(ts(day1$Speed_All_Mean))
plot.ts(speed_clean)
# ggplot() + geom_line(data = Q1, aes(x = TimeStamp, y = speed_clean)) + ylab('Cleaned Speed Records')
day1$cnt_ma = ma(speed_clean, order=7) # using the clean count with no outliers
day1$cnt_ma30 = ma(speed_clean, order=30)
# Step 3: Decompose Your Data
count_ma = ts(na.omit(speed_clean), frequency=30)
decomp = stl(count_ma, s.window="periodic")
deseasonal_cnt <- seasadj(decomp)
plot(decomp)
# Step 4: Stationarity
# statinary test
adf.test(count_ma, alternative = "stationary")
##
## Augmented Dickey-Fuller Test
##
## data: count_ma
## Dickey-Fuller = -3.6131, Lag order = 7, p-value = 0.03196
## alternative hypothesis: stationary
adf.test(deseasonal_cnt, alternative = "stationary")
##
## Augmented Dickey-Fuller Test
##
## data: deseasonal_cnt
## Dickey-Fuller = -3.5278, Lag order = 7, p-value = 0.04015
## alternative hypothesis: stationary
d1 = diff(deseasonal_cnt)
adf.test(d1, alternative = "stationary")
## Warning in adf.test(d1, alternative = "stationary"): p-value smaller than
## printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: d1
## Dickey-Fuller = -10.846, Lag order = 7, p-value = 0.01
## alternative hypothesis: stationary
# Step 5: Autocorrelations and Choosing Model Order
# check ACF and PACF
acf2(count_ma)
## ACF PACF
## [1,] 0.34 0.34
## [2,] 0.04 -0.09
## [3,] 0.02 0.04
## [4,] -0.05 -0.07
## [5,] -0.03 0.01
## [6,] 0.23 0.27
## [7,] 0.58 0.51
## [8,] 0.25 -0.09
## [9,] -0.02 -0.13
## [10,] -0.04 -0.05
## [11,] -0.06 0.06
## [12,] 0.00 0.09
## [13,] 0.26 0.15
## [14,] 0.51 0.16
## [15,] 0.27 0.02
## [16,] 0.00 -0.06
## [17,] -0.03 0.01
## [18,] -0.06 0.02
## [19,] -0.01 0.03
## [20,] 0.29 0.14
## [21,] 0.46 0.07
## [22,] 0.24 -0.02
## [23,] 0.01 -0.01
## [24,] -0.04 0.00
## [25,] -0.06 0.03
## [26,] 0.04 0.09
## [27,] 0.24 -0.05
## [28,] 0.46 0.15
## [29,] 0.23 -0.05
## [30,] -0.05 -0.12
## [31,] -0.09 -0.05
## [32,] -0.11 -0.04
## [33,] -0.04 -0.04
## [34,] 0.17 -0.04
## [35,] 0.41 0.06
## [36,] 0.25 0.07
## [37,] -0.03 -0.03
## [38,] -0.09 -0.06
## [39,] -0.05 0.07
## [40,] 0.01 0.03
## [41,] 0.17 -0.03
## [42,] 0.41 0.07
## [43,] 0.26 0.02
## [44,] -0.07 -0.08
## [45,] -0.10 0.03
## [46,] -0.08 -0.06
## [47,] -0.04 -0.01
## [48,] 0.16 0.01
## [49,] 0.39 0.07
## [50,] 0.20 -0.08
## [51,] -0.03 0.06
## [52,] -0.08 0.00
## [53,] -0.07 0.05
## [54,] -0.03 -0.02
## [55,] 0.17 0.02
## [56,] 0.39 0.04
## [57,] 0.19 -0.01
## [58,] -0.08 -0.06
## [59,] -0.11 -0.03
## [60,] -0.10 -0.02
## [61,] -0.06 0.02
## [62,] 0.15 -0.02
## [63,] 0.39 0.04
## [64,] 0.19 -0.02
## [65,] -0.07 -0.01
## [66,] -0.12 -0.06
## [67,] -0.10 0.02
## [68,] -0.09 -0.09
## [69,] 0.14 0.05
## [70,] 0.35 0.05
## [71,] 0.17 -0.05
## [72,] -0.07 0.01
## [73,] -0.14 -0.03
## [74,] -0.11 0.02
## [75,] -0.08 -0.01
## [76,] 0.13 0.00
## [77,] 0.37 0.08
## [78,] 0.15 -0.07
## [79,] -0.03 0.05
## [80,] -0.12 -0.01
## [81,] -0.12 0.00
## [82,] -0.09 -0.05
## [83,] 0.09 -0.02
## [84,] 0.32 0.01
## [85,] 0.11 -0.05
## [86,] -0.09 0.00
## [87,] -0.13 0.00
## [88,] -0.13 0.01
## [89,] -0.12 -0.09
## [90,] 0.06 -0.06
## [91,] 0.29 -0.01
## [92,] 0.09 -0.06
## [93,] -0.15 -0.09
## [94,] -0.16 -0.04
## [95,] -0.15 0.02
## [96,] -0.11 0.03
## [97,] 0.07 -0.01
## [98,] 0.27 -0.03
## [99,] 0.08 -0.06
## [100,] -0.13 0.01
## [101,] -0.16 0.02
## [102,] -0.14 0.01
## [103,] -0.13 -0.07
## [104,] 0.04 -0.04
## [105,] 0.26 0.04
## [106,] 0.07 -0.02
## [107,] -0.13 0.05
## [108,] -0.16 -0.02
## [109,] -0.18 0.00
## [110,] -0.16 -0.06
## [111,] 0.01 0.04
## [112,] 0.22 -0.03
## [113,] 0.05 0.04
## [114,] -0.12 0.01
## [115,] -0.18 -0.04
## [116,] -0.17 -0.01
## [117,] -0.15 0.01
## [118,] 0.00 0.00
## [119,] 0.20 0.01
## [120,] 0.08 0.04
## ACF PACF
## [1,] 0.35 0.35
## [2,] 0.05 -0.08
## [3,] 0.02 0.04
## [4,] -0.04 -0.06
## [5,] -0.02 0.02
## [6,] 0.24 0.27
## [7,] 0.59 0.52
## [8,] 0.26 -0.10
## [9,] -0.01 -0.14
## [10,] -0.05 -0.06
## [11,] -0.06 0.06
## [12,] 0.00 0.09
## [13,] 0.26 0.15
## [14,] 0.54 0.18
## [15,] 0.28 0.00
## [16,] 0.00 -0.07
## [17,] -0.04 0.01
## [18,] -0.06 0.02
## [19,] -0.01 0.02
## [20,] 0.30 0.16
## [21,] 0.49 0.07
## [22,] 0.26 -0.01
## [23,] 0.00 -0.04
## [24,] -0.04 0.02
## [25,] -0.05 0.04
## [26,] 0.04 0.10
## [27,] 0.25 -0.06
## [28,] 0.48 0.13
## [29,] 0.24 -0.06
## [30,] -0.08 -0.16
## [31,] -0.09 -0.03
## [32,] -0.11 -0.04
## [33,] -0.04 -0.03
## [34,] 0.18 -0.04
## [35,] 0.44 0.08
## [36,] 0.25 0.06
## [37,] -0.04 0.00
## [38,] -0.09 -0.07
## [39,] -0.06 0.06
## [40,] 0.01 0.01
## [41,] 0.18 -0.03
## [42,] 0.43 0.05
## [43,] 0.27 0.04
## [44,] -0.06 -0.05
## [45,] -0.10 0.02
## [46,] -0.09 -0.07
## [47,] -0.05 -0.03
## [48,] 0.16 0.02
## [49,] 0.40 0.07
## [50,] 0.20 -0.06
## [51,] -0.02 0.07
## [52,] -0.08 0.00
## [53,] -0.07 0.04
## [54,] -0.03 -0.01
## [55,] 0.18 0.04
## [56,] 0.40 0.06
## [57,] 0.20 -0.03
## [58,] -0.08 -0.06
## [59,] -0.11 -0.03
## [60,] -0.13 -0.07
## [61,] -0.06 0.03
## [62,] 0.15 -0.01
## [63,] 0.40 0.04
## [64,] 0.20 -0.03
## [65,] -0.06 -0.01
## [66,] -0.13 -0.07
## [67,] -0.12 0.04
## [68,] -0.09 -0.10
## [69,] 0.15 0.05
## [70,] 0.36 0.04
## [71,] 0.18 -0.05
## [72,] -0.07 0.01
## [73,] -0.14 -0.01
## [74,] -0.11 0.05
## [75,] -0.09 -0.03
## [76,] 0.14 -0.01
## [77,] 0.38 0.05
## [78,] 0.16 -0.06
## [79,] -0.03 0.05
## [80,] -0.12 0.01
## [81,] -0.12 0.00
## [82,] -0.10 -0.05
## [83,] 0.09 -0.03
## [84,] 0.33 0.03
## [85,] 0.13 -0.02
## [86,] -0.08 0.02
## [87,] -0.12 0.00
## [88,] -0.13 0.01
## [89,] -0.13 -0.11
## [90,] 0.04 -0.11
## [91,] 0.29 0.00
## [92,] 0.10 -0.06
## [93,] -0.16 -0.08
## [94,] -0.16 -0.04
## [95,] -0.15 0.02
## [96,] -0.12 0.02
## [97,] 0.06 0.02
## [98,] 0.28 -0.04
## [99,] 0.08 -0.07
## [100,] -0.13 0.01
## [101,] -0.16 0.01
## [102,] -0.15 0.01
## [103,] -0.14 -0.04
## [104,] 0.04 -0.02
## [105,] 0.26 0.02
## [106,] 0.07 -0.03
## [107,] -0.13 0.04
## [108,] -0.16 -0.01
## [109,] -0.18 -0.01
## [110,] -0.17 -0.05
## [111,] 0.01 0.04
## [112,] 0.22 -0.05
## [113,] 0.04 0.02
## [114,] -0.12 0.05
## [115,] -0.16 0.00
## [116,] -0.18 0.01
## [117,] -0.16 0.01
## [118,] 0.01 0.01
## [119,] 0.20 -0.01
## [120,] 0.06 -0.02
Seasonility Not in Consideration
# Step 6: Fitting an ARIMA model
auto.arima(deseasonal_cnt, seasonal=FALSE)
## Series: deseasonal_cnt
## ARIMA(2,1,1)
##
## Coefficients:
## ar1 ar2 ma1
## 0.2855 -0.1739 -0.9480
## s.e. 0.0534 0.0532 0.0167
##
## sigma^2 estimated as 1.018: log likelihood=-519.3
## AIC=1046.6 AICc=1046.72 BIC=1062.19
# Step 7: Evaluate and Iterate
# (try different model)
fit<-auto.arima(deseasonal_cnt, seasonal=FALSE)
tsdisplay(residuals(fit), lag.max=45, main='Model Residuals [Seasonality not considered]')
# step 8 forcast
fcast <- forecast(fit, h=30)
plot(fcast)
Seasonility in Consideration
# Step 6: Fitting an ARIMA model
auto.arima(deseasonal_cnt, seasonal=TRUE)
## Series: deseasonal_cnt
## ARIMA(2,1,3)(2,0,2)[30]
##
## Coefficients:
## ar1 ar2 ma1 ma2 ma3 sar1 sar2 sma1
## -0.580 -0.9230 -0.1916 0.2381 -0.8226 -0.0428 -0.1978 -0.3302
## s.e. 0.039 0.0358 0.0439 0.0434 0.0424 0.1580 0.2335 0.1657
## sma2
## -0.2569
## s.e. 0.2415
##
## sigma^2 estimated as 0.7644: log likelihood=-474.59
## AIC=969.18 AICc=969.8 BIC=1008.15
# Step 7: Evaluate and Iterate
# (try different model)
fit<-auto.arima(deseasonal_cnt, seasonal=TRUE)
tsdisplay(residuals(fit), lag.max=45, main='Model Residuals [Seasonality considered]')
# step 8 forcast
fcast <- forecast(fit, h=30)
plot(fcast)
