# 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 = 'R2'
setwd("/scratch/user/cma16/Task4_Deliverable2/OHprocess4/AllCrash/FacilityBased/")
load("./two-lane_undivided_OH_reduce_withCrash.rData")
setwd(paste0("/scratch/user/cma16/Task4_Deliverable2/OHprocess4/AllCrash/FacilityBased/",mytype))
df_R2 <- OH_2un_nomed
df_R2$spd_av = 3600*df_R2$DISTANCE/df_R2$Travel_TIME_ALL_VEHICLES
df_R2$spd_pv = 3600*df_R2$DISTANCE/df_R2$Travel_TIME_PASSENGER_VEHICLES
df_R2$spd_ft = 3600*df_R2$DISTANCE/df_R2$Travel_TIME_FREIGHT_TRUCKS
### Month, Day
df_R2$date <- as.character(df_R2$DATE)
df_R2$date <- str_pad(df_R2$DATE, 8, pad = "0")
df_R2$Month <- substr(df_R2$date, start = 1, stop = 2)
df_R2$Day <- substr(df_R2$date, start = 3, stop = 4)
df_R2$Year <- substr(df_R2$date, start = 5, stop = 8)
df_R2$MonthDay <- paste0(df_R2$Month,"_", df_R2$Day)
head(df_R2)
## TimeStamp TMC DATE EPOCH1h Travel_TIME_ALL_VEHICLES
## 1: 108N05389_0101_0 108N05389 1012015 0 NA
## 2: 108N05389_0101_1 108N05389 1012015 1 NA
## 3: 108N05389_0101_10 108N05389 1012015 10 201.5
## 4: 108N05389_0101_11 108N05389 1012015 11 NA
## 5: 108N05389_0101_12 108N05389 1012015 12 186.0
## 6: 108N05389_0101_13 108N05389 1012015 13 181.0
## Travel_TIME_PASSENGER_VEHICLES Travel_TIME_FREIGHT_TRUCKS ADMIN_LEVE
## 1: NA NA USA
## 2: NA NA USA
## 3: NA 201.5 USA
## 4: NA NA USA
## 5: NA 186.0 USA
## 6: NA 181.0 USA
## ADMIN_LE_1 ADMIN_LE_2 DISTANCE ROAD_NUMBE ROAD_NAME LATITUDE LONGITUDE
## 1: Ohio Fulton 2.78045 US-20 41.6733 -84.35867
## 2: Ohio Fulton 2.78045 US-20 41.6733 -84.35867
## 3: Ohio Fulton 2.78045 US-20 41.6733 -84.35867
## 4: Ohio Fulton 2.78045 US-20 41.6733 -84.35867
## 5: Ohio Fulton 2.78045 US-20 41.6733 -84.35867
## 6: Ohio Fulton 2.78045 US-20 41.6733 -84.35867
## ROAD_DIREC ORN_FID COUNTY divided SURF_TYP NHS_CDE HPMS ACCESS AADT_YR
## 1: Eastbound 21204.78 FUL U G N N 14
## 2: Eastbound 21204.78 FUL U G N N 14
## 3: Eastbound 21204.78 FUL U G N N 14
## 4: Eastbound 21204.78 FUL U G N N 14
## 5: Eastbound 21204.78 FUL U G N N 14
## 6: Eastbound 21204.78 FUL U G N N 14
## FED_FACI PK_LANES MED_TYPE FED_MEDW BEGMP ENDMP SEG_LNG cnty_rte
## 1: 2 NA 1 NA 0 22.32 0.4074587 FUL0020R
## 2: 2 NA 1 NA 0 22.32 0.4074587 FUL0020R
## 3: 2 NA 1 NA 0 22.32 0.4074587 FUL0020R
## 4: 2 NA 1 NA 0 22.32 0.4074587 FUL0020R
## 5: 2 NA 1 NA 0 22.32 0.4074587 FUL0020R
## 6: 2 NA 1 NA 0 22.32 0.4074587 FUL0020R
## rte_nbr aadt aadt_bc aadt_pt surf_wid no_lanes func_cls rodwycls
## 1: 0020R 2506.222 623.6426 1882.579 24 2 2 8
## 2: 0020R 2506.222 623.6426 1882.579 24 2 2 8
## 3: 0020R 2506.222 623.6426 1882.579 24 2 2 8
## 4: 0020R 2506.222 623.6426 1882.579 24 2 2 8
## 5: 0020R 2506.222 623.6426 1882.579 24 2 2 8
## 6: 0020R 2506.222 623.6426 1882.579 24 2 2 8
## Total K A B C O DAYMTH Crash spd_av spd_pv spd_ft date Month
## 1: 2 0 0 1 0 1 0101 0 NA NA NA 01012015 01
## 2: 2 0 0 1 0 1 0101 0 NA NA NA 01012015 01
## 3: 2 0 0 1 0 1 0101 0 49.67553 NA 49.67553 01012015 01
## 4: 2 0 0 1 0 1 0101 0 NA NA NA 01012015 01
## 5: 2 0 0 1 0 1 0101 0 53.81516 NA 53.81516 01012015 01
## 6: 2 0 0 1 0 1 0101 0 55.30177 NA 55.30177 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_R2[,-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 47.7
## 2 01_02 46.1
## 3 01_03 44.2
## 4 01_04 45.6
## 5 01_05 45.2
## 6 01_06 41.9
## 7 01_07 42.9
## 8 01_08 43.5
## 9 01_09 41.5
## 10 01_10 45.7
## # ... 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 = -3.6804, Lag order = 7, p-value = 0.02548
## alternative hypothesis: stationary
adf.test(deseasonal_cnt, alternative = "stationary")
##
## Augmented Dickey-Fuller Test
##
## data: deseasonal_cnt
## Dickey-Fuller = -3.645, Lag order = 7, p-value = 0.02889
## 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 = -10.672, 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,] 0.42 0.42
## [2,] 0.14 -0.05
## [3,] 0.10 0.07
## [4,] 0.17 0.13
## [5,] 0.16 0.04
## [6,] 0.27 0.23
## [7,] 0.45 0.32
## [8,] 0.27 -0.05
## [9,] 0.07 -0.05
## [10,] 0.02 -0.05
## [11,] -0.01 -0.17
## [12,] 0.05 0.02
## [13,] 0.30 0.25
## [14,] 0.49 0.29
## [15,] 0.23 -0.06
## [16,] 0.03 -0.03
## [17,] 0.08 0.08
## [18,] 0.10 -0.02
## [19,] 0.06 -0.09
## [20,] 0.23 0.06
## [21,] 0.47 0.20
## [22,] 0.32 0.07
## [23,] 0.07 -0.03
## [24,] 0.00 -0.05
## [25,] -0.01 -0.10
## [26,] 0.06 -0.02
## [27,] 0.23 0.01
## [28,] 0.37 0.05
## [29,] 0.18 -0.02
## [30,] -0.03 -0.08
## [31,] -0.08 -0.13
## [32,] -0.09 -0.08
## [33,] -0.06 -0.03
## [34,] 0.13 -0.01
## [35,] 0.37 0.14
## [36,] 0.19 0.02
## [37,] -0.01 0.06
## [38,] -0.05 0.02
## [39,] 0.01 0.03
## [40,] 0.02 -0.05
## [41,] 0.14 -0.08
## [42,] 0.31 0.02
## [43,] 0.16 -0.06
## [44,] -0.06 -0.09
## [45,] -0.14 -0.04
## [46,] -0.10 0.03
## [47,] -0.09 -0.04
## [48,] 0.06 0.00
## [49,] 0.27 0.10
## [50,] 0.13 0.02
## [51,] -0.12 -0.08
## [52,] -0.15 0.00
## [53,] -0.11 -0.03
## [54,] -0.09 -0.02
## [55,] 0.04 -0.01
## [56,] 0.23 0.01
## [57,] 0.10 -0.04
## [58,] -0.12 -0.01
## [59,] -0.17 0.00
## [60,] -0.14 -0.04
## [61,] -0.09 0.01
## [62,] 0.04 0.00
## [63,] 0.22 0.01
## [64,] 0.09 -0.02
## [65,] -0.13 0.02
## [66,] -0.15 0.04
## [67,] -0.12 0.02
## [68,] -0.12 -0.02
## [69,] 0.00 0.03
## [70,] 0.17 -0.01
## [71,] 0.05 -0.03
## [72,] -0.12 0.08
## [73,] -0.16 0.03
## [74,] -0.12 0.03
## [75,] -0.11 -0.03
## [76,] 0.02 -0.04
## [77,] 0.20 0.00
## [78,] 0.09 -0.01
## [79,] -0.12 -0.04
## [80,] -0.15 0.04
## [81,] -0.17 -0.06
## [82,] -0.13 0.02
## [83,] 0.00 0.03
## [84,] 0.15 -0.02
## [85,] 0.05 -0.02
## [86,] -0.14 -0.01
## [87,] -0.18 -0.02
## [88,] -0.16 -0.04
## [89,] -0.14 -0.04
## [90,] -0.01 -0.02
## [91,] 0.14 -0.01
## [92,] 0.06 0.03
## [93,] -0.13 0.01
## [94,] -0.16 0.04
## [95,] -0.14 0.01
## [96,] -0.11 -0.02
## [97,] 0.00 0.03
## [98,] 0.13 -0.02
## [99,] 0.05 -0.02
## [100,] -0.11 0.01
## [101,] -0.15 0.00
## [102,] -0.13 0.01
## [103,] -0.09 0.07
## [104,] 0.01 -0.01
## [105,] 0.14 0.01
## [106,] 0.05 -0.04
## [107,] -0.12 -0.01
## [108,] -0.16 0.00
## [109,] -0.15 -0.05
## [110,] -0.12 -0.01
## [111,] -0.01 0.02
## [112,] 0.12 -0.03
## [113,] 0.05 -0.03
## [114,] -0.09 0.05
## [115,] -0.14 -0.02
## [116,] -0.14 -0.03
## [117,] -0.11 -0.01
## [118,] 0.00 0.01
## [119,] 0.14 0.03
## [120,] 0.06 -0.01
## ACF PACF
## [1,] 0.44 0.44
## [2,] 0.15 -0.06
## [3,] 0.11 0.08
## [4,] 0.18 0.13
## [5,] 0.16 0.04
## [6,] 0.28 0.24
## [7,] 0.46 0.32
## [8,] 0.28 -0.05
## [9,] 0.07 -0.07
## [10,] 0.02 -0.05
## [11,] 0.00 -0.16
## [12,] 0.05 0.01
## [13,] 0.31 0.27
## [14,] 0.50 0.29
## [15,] 0.26 -0.04
## [16,] 0.03 -0.05
## [17,] 0.09 0.09
## [18,] 0.10 -0.04
## [19,] 0.06 -0.08
## [20,] 0.24 0.06
## [21,] 0.48 0.21
## [22,] 0.33 0.05
## [23,] 0.06 -0.04
## [24,] 0.00 -0.03
## [25,] -0.01 -0.11
## [26,] 0.06 -0.01
## [27,] 0.23 0.01
## [28,] 0.38 0.05
## [29,] 0.19 -0.03
## [30,] -0.04 -0.10
## [31,] -0.08 -0.11
## [32,] -0.09 -0.09
## [33,] -0.06 -0.01
## [34,] 0.14 0.01
## [35,] 0.38 0.14
## [36,] 0.19 -0.01
## [37,] -0.01 0.08
## [38,] -0.04 0.02
## [39,] 0.00 0.01
## [40,] 0.02 -0.04
## [41,] 0.15 -0.09
## [42,] 0.32 -0.01
## [43,] 0.16 -0.07
## [44,] -0.06 -0.05
## [45,] -0.13 -0.03
## [46,] -0.11 0.03
## [47,] -0.09 -0.02
## [48,] 0.06 -0.02
## [49,] 0.27 0.10
## [50,] 0.13 0.02
## [51,] -0.11 -0.06
## [52,] -0.15 -0.02
## [53,] -0.12 -0.03
## [54,] -0.09 -0.01
## [55,] 0.04 -0.04
## [56,] 0.24 0.03
## [57,] 0.10 -0.04
## [58,] -0.12 -0.01
## [59,] -0.17 0.00
## [60,] -0.16 -0.06
## [61,] -0.10 0.01
## [62,] 0.03 -0.01
## [63,] 0.23 0.03
## [64,] 0.09 -0.03
## [65,] -0.13 0.02
## [66,] -0.16 0.04
## [67,] -0.12 0.04
## [68,] -0.12 -0.02
## [69,] 0.00 0.01
## [70,] 0.17 0.00
## [71,] 0.05 -0.05
## [72,] -0.12 0.07
## [73,] -0.16 0.03
## [74,] -0.12 0.04
## [75,] -0.11 -0.02
## [76,] 0.02 -0.04
## [77,] 0.20 0.00
## [78,] 0.08 -0.03
## [79,] -0.13 -0.02
## [80,] -0.16 0.04
## [81,] -0.16 -0.04
## [82,] -0.13 0.01
## [83,] -0.01 0.03
## [84,] 0.16 -0.02
## [85,] 0.05 -0.04
## [86,] -0.14 0.01
## [87,] -0.18 -0.04
## [88,] -0.17 -0.04
## [89,] -0.14 -0.04
## [90,] -0.03 -0.04
## [91,] 0.14 0.00
## [92,] 0.06 0.03
## [93,] -0.13 0.03
## [94,] -0.16 0.04
## [95,] -0.15 0.02
## [96,] -0.12 -0.02
## [97,] 0.00 0.04
## [98,] 0.14 -0.02
## [99,] 0.05 -0.04
## [100,] -0.11 0.01
## [101,] -0.15 -0.02
## [102,] -0.13 0.01
## [103,] -0.09 0.08
## [104,] 0.00 0.01
## [105,] 0.15 0.02
## [106,] 0.04 -0.06
## [107,] -0.12 -0.01
## [108,] -0.17 -0.02
## [109,] -0.16 -0.05
## [110,] -0.12 0.00
## [111,] 0.00 0.04
## [112,] 0.12 -0.04
## [113,] 0.04 -0.01
## [114,] -0.09 0.07
## [115,] -0.14 -0.05
## [116,] -0.14 -0.01
## [117,] -0.11 -0.02
## [118,] 0.00 0.00
## [119,] 0.15 0.04
## [120,] 0.04 -0.04
Seasonility Not in Consideration
# Step 6: Fitting an ARIMA model
auto.arima(deseasonal_cnt, seasonal=FALSE)
## Series: deseasonal_cnt
## ARIMA(2,1,5)
##
## Coefficients:
## ar1 ar2 ma1 ma2 ma3 ma4 ma5
## -0.9368 -0.4127 0.3544 -0.5112 -0.7357 -0.0547 0.1788
## s.e. 0.2875 0.1670 0.2872 0.2314 0.1274 0.0924 0.0886
##
## sigma^2 estimated as 0.2206: log likelihood=-238.87
## AIC=493.73 AICc=494.14 BIC=524.91
# 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)(2,0,1)[30]
##
## Coefficients:
## ar1 ar2 ma1 ma2 ma3 sar1 sar2
## -0.5010 -0.9052 -0.2214 0.2989 -0.7969 -0.1350 -0.3966
## s.e. 0.0423 0.0366 0.0431 0.0477 0.0487 0.1476 0.0694
## sma1
## -0.0958
## s.e. 0.1635
##
## sigma^2 estimated as 0.1864: log likelihood=-213.94
## AIC=445.87 AICc=446.38 BIC=480.95
# 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)
