auto loss cost trends q4 2017 - society of actuaries...montana property damage severity 3000 3500...

November 2017 | Auto Loss Cost Trends Report | #

Auto Loss Cost Trends: Q4 2017 August 2018

Q4 2017 Trend Analysis

ContentsARIMA Models 1

Bodily Injury . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Property Damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Comprehensive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Collision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Personal Injury Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Code 33

ARIMA Models

Using FAST TRACK PLUS data, we analyzed how auto insurance claims change over time. In this report,we identify which state-level claims are unexpectedly extreme. Using an ARIMA model, we forecast the 4thquarter 2017 value for each state, metric (frequency, severity and loss cost), and coverage (bodily injury,property damage, comprehensive, collision, and personal injury protection). ARIMA models allow us toaccount for both the quarter-to-quarter trends and any trends across years (for example if all the 3Q valuesare higher than any other quarters in the year). The state maps show the accuracy of the 4th quarterprediction. Blue states indicate that the true 4Q metric was significantly less than expected, and red statesindicate that the true 4Q metric was significantly greater than expected.

Below each state map, full time series plots are displayed for the states that had a 4th quarter metric falloutside of the 10%-90% prediction interval. The green dot represents the true 4th quarter value. The bluedot represents the point forecast with a surrounding grey area representing the 10%-90% prediction interval.

Some states and metrics experienced an extreme or abnormal observation due to weather or other events;these outliers decreased the accuracy of the ARIMA model. The time series with outliers were smoothed asto improve the 4th quarter prediction accuracy. These smoothed outliers are marked with an orange squareon the time series plots.

August 2018 | Auto Loss Cost Trends : Q4 2017 | © CAS, PCI, and SOA | 1

Bodily Injury

>99%

95%−99%

90%−95%

10%−90%

1%−5%

<1%

Bodily Injury Frequency

Florida Bodily InjuryFrequency

0.0090

0.0095

0.0100

0.0105

0.0110

'12 '13 '14 '15 '16 '17

Idaho Bodily InjuryFrequency

0.0060

0.0065

0.0070

0.0075

'12 '13 '14 '15 '16 '17


Missouri Bodily InjuryFrequency

0.00680.00700.00720.00740.00760.00780.0080

'12 '13 '14 '15 '16 '17

North Dakota Bodily InjuryFrequency

0.00100.00120.00140.00160.0018

'12 '13 '14 '15 '16 '17

New Jersey Bodily InjuryFrequency

0.0030

0.0035

0.0040

0.0045

0.0050

'12 '13 '14 '15 '16 '17

Ohio Bodily InjuryFrequency

0.0070

0.0075

0.0080

0.0085

'12 '13 '14 '15 '16 '17

Time Series Legend

Point Forecast True Value Prediction Interval Removed Outlier


>99%

95%−99%

90%−95%

10%−90%

5%−10%

1%−5%

<1%

Bodily Injury Severity

California Bodily InjurySeverity

11000120001300014000150001600017000

'12 '13 '14 '15 '16 '17

Colorado Bodily InjurySeverity

15000

20000

25000

30000

'12 '13 '14 '15 '16 '17


Connecticut Bodily InjurySeverity

22000

24000

26000

28000

'12 '13 '14 '15 '16 '17

Delaware Bodily InjurySeverity

14000150001600017000180001900020000

'12 '13 '14 '15 '16 '17

Idaho Bodily InjurySeverity

12000

14000

16000

18000

'12 '13 '14 '15 '16 '17

Michigan Bodily InjurySeverity

4200044000460004800050000

'12 '13 '14 '15 '16 '17

Missouri Bodily InjurySeverity

120001400016000180002000022000

'12 '13 '14 '15 '16 '17

Nebraska Bodily InjurySeverity

14000

16000

18000

20000

'12 '13 '14 '15 '16 '17


Oklahoma Bodily InjurySeverity

1000011000120001300014000

'12 '13 '14 '15 '16 '17

South CarolinaBodily Injury

Severity

1100012000130001400015000

'12 '13 '14 '15 '16 '17

Utah Bodily InjurySeverity

120001400016000180002000022000

'12 '13 '14 '15 '16 '17

Wyoming Bodily InjurySeverity

15000200002500030000

'12 '13 '14 '15 '16 '17

Time Series Legend



>99%

95%−99%

10%−90%

1%−5%

Bodily Injury Loss Cost

California Bodily Injury Loss Cost

100110120130140150160

'12 '13 '14 '15 '16 '17

Connecticut Bodily Injury Loss Cost

200

220

240

260

'12 '13 '14 '15 '16 '17


Tennessee Bodily Injury Loss Cost

100

110

120

130

'12 '13 '14 '15 '16 '17

Utah Bodily Injury Loss Cost

90100110120130140150

'12 '13 '14 '15 '16 '17

Time Series Legend



Property Damage

95%−99%

10%−90%

5%−10%

<1%

Property Damage Frequency

Florida Property DamageFrequency

0.034

0.036

0.038

0.040

'12 '13 '14 '15 '16 '17

Hawaii Property DamageFrequency

0.0350.0360.0370.0380.039

'12 '13 '14 '15 '16 '17


Iowa Property DamageFrequency

0.024

0.026

0.028

0.030

'12 '13 '14 '15 '16 '17

Louisiana Property DamageFrequency

0.036

0.038

0.040

0.042

0.044

'12 '13 '14 '15 '16 '17

Washington Property DamageFrequency

0.0320.0330.0340.0350.0360.0370.0380.039

'12 '13 '14 '15 '16 '17

Time Series Legend



>99%

95%−99%

90%−95%

10%−90%

5%−10%

1%−5%

Property Damage Severity

Iowa Property DamageSeverity

260028003000320034003600

'12 '13 '14 '15 '16 '17

Kentucky Property DamageSeverity

28003000320034003600380040004200

'12 '13 '14 '15 '16 '17


Montana Property DamageSeverity

3000

3500

4000

4500

'12 '13 '14 '15 '16 '17

North CarolinaProperty Damage

Severity

2600280030003200340036003800

'12 '13 '14 '15 '16 '17

North DakotaProperty Damage

Severity

260028003000320034003600

'12 '13 '14 '15 '16 '17

Oregon Property DamageSeverity

2600280030003200340036003800

'12 '13 '14 '15 '16 '17

South CarolinaProperty Damage

Severity

2600280030003200340036003800

'12 '13 '14 '15 '16 '17

Vermont Property DamageSeverity

240026002800300032003400

'12 '13 '14 '15 '16 '17

Time Series Legend



>99%

95%−99%

90%−95%

10%−90%

5%−10%

<1%

Property Damage Loss Cost

Florida Property Damage Loss Cost

100110120130140150

'12 '13 '14 '15 '16 '17

Iowa Property Damage Loss Cost

70

80

90

100

'12 '13 '14 '15 '16 '17


Illinois Property Damage Loss Cost

90100110120130140

'12 '13 '14 '15 '16 '17

Indiana Property Damage Loss Cost

8090

100110

120

'12 '13 '14 '15 '16 '17

Michigan Property Damage Loss Cost

8

9

10

11

'12 '13 '14 '15 '16 '17

Ohio Property Damage Loss Cost

8090

100110120

'12 '13 '14 '15 '16 '17

Rhode IslandProperty Damage

Loss Cost

140

160

180

200

220

'12 '13 '14 '15 '16 '17

South CarolinaProperty Damage

Loss Cost

90100110120130

'12 '13 '14 '15 '16 '17


Texas Property Damage Loss Cost

130140150160170180

'12 '13 '14 '15 '16 '17

Vermont Property Damage Loss Cost

65707580859095

'12 '13 '14 '15 '16 '17

Time Series Legend



Comprehensive

Several states’ comprehensive metrics seemed to be correlated with severe weather events. In Iowa, there wasmuch less storm damage than usual, possibly leading to a small observed frequency metric. In Connecticut,storm damage was much higher than expected, thus the severity and loss cost metrics were high as well. NewHampshire had flash floods that caused significant damage and the severity and loss cost metrics were bothextremely high. Oregon had a much lower damage amount than usual, thus our severity metric was alsosmaller than usual.

10%−90%

1%−5%

Comprehensive Frequency


Iowa ComprehensiveFrequency

0.000.020.040.060.080.100.12

'12 '13 '14 '15 '16 '17

Time Series Legend



>99%

90%−95%

10%−90%

5%−10%

1%−5%

Comprehensive Severity

California ComprehensiveSeverity

100012001400160018002000

'12 '13 '14 '15 '16 '17

Connecticut ComprehensiveSeverity

8001000120014001600

'12 '13 '14 '15 '16 '17


Florida ComprehensiveSeverity

600800

10001200140016001800

'12 '13 '14 '15 '16 '17

Maine ComprehensiveSeverity

600800

10001200140016001800

'12 '13 '14 '15 '16 '17

New Hampshire ComprehensiveSeverity

600

800

1000

1200

1400

'12 '13 '14 '15 '16 '17

New Jersey ComprehensiveSeverity

0

2000

4000

6000

8000

'12 '13 '14 '15 '16 '17

Nevada ComprehensiveSeverity

700800900

100011001200

'12 '13 '14 '15 '16 '17

Oregon ComprehensiveSeverity

600

800

1000

1200

1400

'12 '13 '14 '15 '16 '17


Pennsylvania ComprehensiveSeverity

1000

1500

2000

2500

'12 '13 '14 '15 '16 '17

Wisconsin ComprehensiveSeverity

1500

2000

2500

'12 '13 '14 '15 '16 '17

Wyoming ComprehensiveSeverity

100015002000250030003500

'12 '13 '14 '15 '16 '17

Time Series Legend



>99%

95%−99%

90%−95%

10%−90%

<1%

Comprehensive Loss Cost

California Comprehensive Loss Cost

5055606570758085

'12 '13 '14 '15 '16 '17

Connecticut Comprehensive Loss Cost

40

60

80

100

'12 '13 '14 '15 '16 '17


Maine Comprehensive Loss Cost

2030405060708090

'12 '13 '14 '15 '16 '17

New Hampshire Comprehensive Loss Cost

304050607080

'12 '13 '14 '15 '16 '17

Rhode Island Comprehensive Loss Cost

40

60

80

100

'12 '13 '14 '15 '16 '17

Tennessee Comprehensive Loss Cost

0

50

100

150

'12 '13 '14 '15 '16 '17

Texas Comprehensive Loss Cost

0200400600800

1000

'12 '13 '14 '15 '16 '17

Time Series Legend



Collision

Several states’ collision metrics often have an inverse relationship with severe weather damage amounts. Ourguess is that due to severe weather, less vehicles are on the road and less collision claims are made. In Florida,there was very little weather damage this quarter, and our frequency, severity, and loss coss metrics wereextremely high in this quarter. Georgia often experiences a variety of severe weather events in the fourthquarter of each year, but in 2017 those metrics were very low; this could have possibly lead to the high losscost and severity metrics.

>99%

10%−90%

5%−10%

1%−5%

Collision Frequency

District of ColumbiaCollision

Frequency

0.09

0.10

0.11

0.12

0.13

'12 '13 '14 '15 '16 '17

Florida CollisionFrequency

0.0500.0520.0540.0560.0580.060

'12 '13 '14 '15 '16 '17


Oklahoma CollisionFrequency

0.0460.0480.0500.0520.0540.056

'12 '13 '14 '15 '16 '17

Oregon CollisionFrequency

0.040

0.045

0.050

0.055

'12 '13 '14 '15 '16 '17

Time Series Legend



>99%

95%−99%

90%−95%

10%−90%

5%−10%

1%−5%

Collision Severity

Alabama CollisionSeverity

3000320034003600380040004200

'12 '13 '14 '15 '16 '17

Florida CollisionSeverity

280030003200340036003800

'12 '13 '14 '15 '16 '17


Georgia CollisionSeverity

300032003400360038004000

'12 '13 '14 '15 '16 '17

Hawaii CollisionSeverity

260028003000320034003600

'12 '13 '14 '15 '16 '17

Mississippi CollisionSeverity

3200

3400

3600

3800

'12 '13 '14 '15 '16 '17

New Mexico CollisionSeverity

300032003400360038004000

'12 '13 '14 '15 '16 '17

Rhode Island CollisionSeverity

3500

4000

4500

'12 '13 '14 '15 '16 '17

Tennessee CollisionSeverity

300032003400360038004000

'12 '13 '14 '15 '16 '17


Texas CollisionSeverity

320034003600380040004200

'12 '13 '14 '15 '16 '17

Time Series Legend



>99%

95%−99%

10%−90%

Collision Loss Cost

Alabama Collision Loss Cost

170180190200210220

'12 '13 '14 '15 '16 '17

Florida Collision Loss Cost

140160180200220240

'12 '13 '14 '15 '16 '17


Georgia Collision Loss Cost

160180200220240

'12 '13 '14 '15 '16 '17

Hawaii Collision Loss Cost

160

180

200

220

'12 '13 '14 '15 '16 '17

South Carolina Collision Loss Cost

140

160

180

200

'12 '13 '14 '15 '16 '17

Texas Collision Loss Cost

200220240260280

'12 '13 '14 '15 '16 '17

Washington Collision Loss Cost

120140160180200220

'12 '13 '14 '15 '16 '17

Time Series Legend



Personal Injury Protection

The PIP data are different than the other insurance coverages. The amount of PIP data we have varies foreach state; specifically, when the data begin and end is not consistent. The plot below gives us informationabout the start and end dates for each state we have data on.

WY

WV

WI

WA

VT

VA

UT

TX

TN

SD

SC

RI

PA

OR

OK

OH

NY

NJ

ND

NC

MN

MI

MD

MA

KY

KS

HI

FL

DE

AK

2012 2014 2016 2018

Sta

te

When the PIP Data Begin and End


ARIMA model on PIP data

The same ARIMA model was used to forecast the 2017 4Q values on the PIP data. However, only 18 stateshad PIP data through quarter 4 of 2017; these were the states included in the model.

Of the 54 metrics forecasted, only 6 4Q metrics fell outside of the 10%-90% prediction interval. These plotsare shown below.

KentuckyPersonal Injury Protection

Loss Cost

60

65

70

75

'14 '15 '16 '17

North DakotaPersonal Injury Protection

Severity

02000400060008000

10000

'12 '13 '14 '15 '16 '17

New JerseyPersonal Injury Protection

Frequency

0.0105

0.0110

0.0115

0.0120

'14 '15 '16 '17

New JerseyPersonal Injury Protection

Loss Cost

170175180185190195

'14 '15 '16 '17


New YorkPersonal Injury Protection

Severity

80009000

10000110001200013000

'14 '15 '16 '17

New YorkPersonal Injury Protection

Loss Cost

120130140150160170

'14 '15 '16 '17

Time Series Legend



Code

All the code used to create this document:# libraries needed for the analysislibrary(readxl)library(data.table)library(dplyr)library(ggplot2)library(maps)library(tseries)library(tsoutliers)library(forecast)library(zoo)library(gridExtra)library(devtools)# install_github('sinhrks/ggfortify')library(ggfortify)

# Reading in the raw Q3 and Q4 data:setwd("~/Google Drive/AutoLossCosts")ts4 <- read_excel("AutoLossCostv20_2017Q4.xlsm",

sheet = "TSData") %>% data.table()ts3 <- read_excel("AutoLossCostv20_2017Q3_TJ-EH.xlsm",

sheet = "TSData") %>% data.table()

# Joining the 2 data fileskey1 <- paste0(ts3$State, ts3$Coverage, ts3$Metric)key2 <- paste0(ts4$State, ts4$Coverage, ts4$Metric)ts_data <- ts3 %>% select(State:`2012 Q4`) %>% cbind(ts4 %>%

select(`2013 Q1`:`2017 Q4`))

# outlier analysis and removal Smoothing just# these series with outliersoutlier.metrics <- c("PA, Comp, SeverityMI, Comp, SeverityAR, Comp, SeverityID, Coll, FrequencyLA, Comp, SeverityMT, BI, SeverityNC, Comp, SeveritySD, BI, SeverityTX, Comp, SeverityVA, Comp, SeverityCT, Comp, SeverityCO, Comp, SeverityNY, Comp, SeverityNJ, Comp, Severity")remove <- x <- strsplit(outlier.metrics, "\n") %>%

unlist()remove <- gsub(pattern = " ", replacement = "",

gsub(pattern = "\\,", replacement = "", remove))boolVec <- paste0(ts_data$State, ts_data$Coverage,


ts_data$Metric) %in% remove# making sure I detected each rowsum(boolVec) == length(x)# the outliers b4 they're smoothedoutliers <- ts_data[boolVec, ]

# cleaning these time series by replacing# outlierscleanTS <- function(x, critical = NULL) {

outliers[x, ] %>% select(`2012 Q1`:`2017 Q4`) %>%t() %>% ts(start = c(2012, 1), end = c(2017,4), frequency = 4) %>% tso(type = "AO",cval = critical)

}

smoothedValues <- rbind(c(cleanTS(1)$yadj), c(cleanTS(2)$yadj),c(cleanTS(3, 5)$yadj), c(cleanTS(4)$yadj), c(cleanTS(5,

4.1)$yadj), c(cleanTS(6, 5)$yadj), c(cleanTS(7)$yadj),c(cleanTS(8)$yadj), c(cleanTS(9)$yadj), c(cleanTS(10)$yadj),c(cleanTS(11)$yadj), c(cleanTS(12)$yadj), c(cleanTS(13,

5)$yadj), c(cleanTS(14, 5)$yadj))smoothedValuesDF <- cbind(outliers[, 1:3], smoothedValues)names(smoothedValuesDF) <- names(outliers)

# data frame w/ outliers smoothedtsAdj <- ts_data[!boolVec, ]tsAdj <- tsAdj %>% rbind(smoothedValuesDF) %>% arrange(Coverage,

State, Metric)

# loop through each 612 values and predict the# 4Q data valuedf.1 <- data.frame(Point.Forecast = c(1), Lo.90 = c(1),

Hi.90 = c(1), Lo.95 = c(1), Hi.95 = c(1), Lo.99 = c(1),Hi.99 = c(1))

for (i in 1:nrow(tsAdj)) {ar.fit <- tsAdj[i, ] %>% select(`2012 Q1`:`2017 Q3`) %>%

t() %>% ts(start = c(2012, 1), end = c(2017,3), frequency = 4) %>% auto.arima()

pred <- forecast(ar.fit, h = 1, level = c(90,95, 99)) %>% data.frame()

df.1[i, ] <- pred}

pred.df <- tsAdj %>% select(State, Coverage, Metric,`2017 Q4`) %>% cbind(df.1) %>% data.table()

pred.df$true <- pred.df$`2017 Q4`pred.df[, `:=`(pi, ifelse(true < Lo.99, "<1%", ifelse(true <

Lo.95, "1%-5%", ifelse(true < Lo.90, "5%-10%",ifelse(true < Hi.90, "10%-90%", ifelse(true <

Hi.95, "90%-95%", ifelse(true < Hi.99, "95%-99%",">99%")))))))]

pred.df <- pred.df %>% select(State:Metric, true,


Point.Forecast, pi)

# Saved the results, and re-read in the datapred.df1 <- read_excel("AutoLossCostv20_2017Q4-TJ.xlsm",

sheet = "Q4Forecast") %>% data.table()state.mappings <- read_excel("AutoLossCostv20_2017Q3_TJ-EH.xlsm",

sheet = "Sheet1")[, 6:8] %>% data.table()ts_adj <- read_excel("AutoLossCostv20_2017Q4-TJ.xlsm",

sheet = "TS_adjusted") %>% data.table()map.data <- pred.df1 %>% left_join(state.mappings,

by = c(State = "Abbreviation")) %>% right_join(map_data("state"),by = c(LCState = "region")) %>% data.table()

# data cleaningpi.levels <- c("<1%", "1%-5%", "5%-10%", "10%-90%",

"90%-95%", "95%-99%", ">99%")map.data[, `:=`(my.col, ifelse(pi == pi.levels[1],

1, ifelse(pi == pi.levels[2], 2, ifelse(pi ==pi.levels[3], 3, ifelse(pi == pi.levels[4],4, ifelse(pi == pi.levels[5], 5, ifelse(pi ==

pi.levels[6], 6, 7)))))))]map.data$pi <- factor(map.data$pi, levels = pi.levels)coverage.df <- data.frame(abrev = c("BI", "Coll",

"Comp", "PD", "PIP"), full = c("Bodily Injury","Collision", "Comprehensive", "Property Damage","Personal Injury Protection"))

# making functions to make maps and ARIMA plotsmake.map <- function(coverage = "PD", metric = "Severity") {

map.dat <- filter(map.data, Coverage == coverage,Metric == metric)

labs <- sort(unique(map.dat$pi))brks <- sort(unique(map.dat$my.col))

if (metric == "LossCost") {plt.title <- paste0(coverage.df$full[coverage.df$abrev ==

coverage], " Loss Cost")} else {

plt.title <- paste0(coverage.df$full[coverage.df$abrev ==coverage], " ", metric)

}

ggplot(data = map.dat) + geom_polygon(aes(x = long,y = lat, fill = my.col, group = group),color = "white") + coord_fixed(1.3) + labs(x = NULL,y = NULL, title = plt.title) + theme_bw() +theme(panel.grid.major = element_blank(),

panel.grid.minor = element_blank(),panel.border = element_blank(), axis.ticks = element_blank(),axis.text = element_blank()) + theme(legend.title = element_blank()) +

guides(fill = guide_legend(reverse = TRUE)) +scale_fill_gradient2(midpoint = 4, low = "blue",


mid = "grey", high = "red", breaks = brks,labels = labs)

}

arima.plot <- function(state = "AL", coverage = "Comp",metric = "Severity", pi = 90) {dat <- ts_adj %>% filter(State == state, Coverage ==

coverage, Metric == metric)orig <- ts_data %>% filter(State == state, Coverage ==

coverage, Metric == metric) %>% select(`2012 Q1`:`2017 Q4`)true.val <- dat$`2017 Q4`ar.fit <- dat %>% select(`2012 Q1`:`2017 Q3`) %>%

t() %>% ts(start = c(2012, 1), end = c(2017,3), frequency = 4) %>% auto.arima()

params <- arimaorder(ar.fit)pred <- forecast(ar.fit, h = 1, level = pi)upr <- max(select(dat, `2012 Q1`:`2017 Q4`),

pred$upper, orig)lwr <- min(select(dat, `2012 Q1`:`2017 Q4`),

pred$lower, orig)range <- upr - lwrcov.full <- coverage.df$full[coverage.df$abrev ==

coverage]state.full <- state.mappings$State[state.mappings$Abbreviation ==

state]

main.l <- nchar(paste0(state.full, " ", cov.full))

if (metric == "LossCost") {if (main.l >= 28) {

main.title <- paste0(state.full, "\n",cov.full, "\n", " Loss Cost")

} else {main.title <- paste0(state.full, " ",

cov.full, "\n", " Loss Cost")}

} else {if (main.l >= 28) {

main.title <- paste0(state.full, "\n",cov.full, "\n", metric)

} else {main.title <- paste0(state.full, " ",

cov.full, "\n", metric)}

}

plot(pred, ylim = c(lwr - 0.1 * range, upr +0.1 * range), las = 1, main = main.title,xaxt = "n")

lines(c(2017.5, 2017.75), c(dat$`2017 Q3`, dat$`2017 Q4`),col = "black")

points(2017.75, true.val, col = "darkgreen",pch = 19)


axis(1, at = c(2012:2017), labels = c("'12","'13", "'14", "'15", "'16", "'17"))

Hmisc::minor.tick(nx = 4)

out <- tryCatch(removedBoolean %>% filter(State ==state, Coverage == coverage, Metric == metric) ==FALSE, error = function(x) x)

if (!(any(class(out) == "error"))) {ind <- removedBoolean %>% filter(State ==

state, Coverage == coverage, Metric ==metric) == FALSE

y. <- filter(outliers, State == state, Coverage ==coverage, Metric == metric)[ind] %>%as.numeric()

x. <- names(ts_adj)[ind] %>% as.yearqtr() %>%as.numeric()

points(x., y., col = "orange2", pch = 15)}

}arima.plots <- function(cov, met, loops = "all",

pi = 90) {x <- pred.df1 %>% filter(pi != "10%-90%", Coverage ==

cov, Metric == met) %>% select(State, Coverage,Metric)

if (loops == "all") {for (i in 1:nrow(x)) {

arima.plot(x[i, 1], x[i, 2], x[i, 3],pi)

}} else {

for (i in 1:loops) {arima.plot(x[i, 1], x[i, 2], x[i, 3],

pi)}

}}

# Printing all the maps and plots

## BImake.map("BI", "Frequency")par(mfrow = c(1, 2))arima.plots("BI", "Frequency")l.names <- c("Point Forecast", "True Value", "Prediction Interval",

"Removed Outlier")l.cols <- c("blue", "darkgreen", "grey", "orange2")legend.plt <- function() {

par(mfrow = c(1, 1))par(mar = c(0, 0, 0, 0))plot.new()legend(x = "top", inset = 0, title = "Time Series Legend",

legend = l.names, fill = l.cols, cex = 0.9,


horiz = TRUE, bty = "n")}

legend.plt()

make.map("BI", "Severity")par(mfrow = c(1, 2))arima.plots("BI", "Severity")legend.plt()

make.map("BI", "LossCost")par(mfrow = c(1, 2))arima.plots("BI", "LossCost")legend.plt()

## Property Damagemake.map("PD", "Frequency")par(mfrow = c(1, 2))arima.plots("PD", "Frequency")legend.plt()

make.map("PD", "Severity")par(mfrow = c(1, 2))arima.plots("PD", "Severity")legend.plt()

make.map("PD", "LossCost")par(mfrow = c(1, 2))arima.plots("PD", "LossCost")legend.plt()

## Comprehensivemake.map("Comp", "Frequency")par(mfrow = c(1, 2))arima.plots("Comp", "Frequency")legend.plt()

make.map("Comp", "Severity")par(mfrow = c(1, 2))arima.plots("Comp", "Severity")legend.plt()

make.map("Comp", "LossCost")par(mfrow = c(1, 2))arima.plots("Comp", "LossCost")legend.plt()

## Collisionmake.map("Coll", "Frequency")par(mfrow = c(1, 2))


arima.plots("Coll", "Frequency")legend.plt()

make.map("Coll", "Severity")par(mfrow = c(1, 2))arima.plots("Coll", "Severity")legend.plt()

make.map("Coll", "LossCost")par(mfrow = c(1, 2))arima.plots("Coll", "LossCost")legend.plt()

# the PIP analysispip <- read_excel("AutoLossCostv20_2017Q4-TJ.xlsm",

sheet = "PIPdata") %>% select(StateName, Year,Quarter, Frequency__1, Severity__1, LossCost__1) %>%data.table()

names(pip) <- c("State", "year", "quarter", "Frequency","Severity", "LossCost")

pip$time <- paste0(pip$year, " Q", pip$quarter)pip <- pip[!is.na(State), ] %>% select(-year, -quarter)pip <- melt.data.table(pip, id.vars = c("State",

"time"), variable.name = "Metric", value.name = "value")pip <- dcast.data.table(pip, State + Metric ~ time,

fun.aggregate = sum)# removing CW and DCpip <- pip[!(pip$State %in% c("CW", "DC")), ]

missing.df <- data.frame(State = "0", Start = 0,End = 0, Data.Missing = 0)

statez <- unique(pip$State)

missing.fun <- function(state) {temp <- pip %>% filter(State == state, Metric ==

"Frequency") %>% data.table()temp <- melt.data.table(temp, id.vars = c("State",

"Metric"), variable.name = "time")temp$time <- as.yearqtr(temp$time, format = "%Y Q%q")times <- temp[temp$value != 0, ]$timefirst <- times[1]last <- times[length(times)]numMis.inbetween <- sum(temp$value[inds <- temp$time >

first & temp$time < last] == 0)data.frame(State = state, Start = first, End = last,

Data.Missing = numMis.inbetween)}

for (i in 1:length(statez)) {missing.df <- rbind(missing.df, missing.fun(statez[i]))

}state.df <- missing.df[-1, ]


state.df$Data.Missing <- NULLstate.df$End <- as.yearqtr(state.df$End, format = "%Y Q%q")state.df$Start <- as.yearqtr(state.df$Start, format = "%Y Q%q")row.names(state.df) <- NULL

# Put on ggplotstate.df3 <- state.df %>% data.table()state.df3$Start <- state.df3$Start %>% as.numeric()state.df3$End <- state.df3$End %>% as.numeric()state.df3 <- melt.data.table(state.df3, id.vars = "State",

variable.name = "When", value.name = "Times")state.df3 <- state.df3 %>% arrange(desc(State))ggplot(state.df3, aes(x = State, y = Times, group = State)) +

geom_point(color = "steelblue") + geom_line(color = "steelblue") +coord_flip() + labs(title = "When the PIP Data Begin and End",y = NULL) + theme(legend.position = "none") +theme_bw() + theme(panel.border = element_blank()) +scale_x_discrete(limits = rev(levels(state.df3$State)[-1]))

missing.df <- data.frame(State = "0", Start = 0,End = 0, Data.Missing = 0)

missing.fun <- function(state) {temp <- pip %>% filter(State == state, Metric ==

"Frequency") %>% data.table()temp <- melt.data.table(temp, id.vars = c("State",

"Metric"), variable.name = "time")temp$time <- as.yearqtr(temp$time, format = "%Y Q%q")times <- temp[temp$value != 0, ]$timefirst <- times[1]last <- times[length(times)]numMis.inbetween <- sum(temp$value[inds <- temp$time >

first & temp$time < last] == 0)data.frame(State = state, Start = first, End = last,

Data.Missing = numMis.inbetween)}

for (i in 1:length(statez)) {missing.df <- rbind(missing.df, missing.fun(statez[i]))

}state.df <- missing.df[-1, ]state.df$Data.Missing <- NULLstate.df$End <- as.yearqtr(state.df$End, format = "%Y Q%q")state.df$Start <- as.yearqtr(state.df$Start, format = "%Y Q%q")row.names(state.df) <- NULL

tsdat <- pip[pip$`2017 Q4` != 0, ]pip.pred.plot <- function(st, met, PI = 90) {

start.date <- state.df %>% filter(State == st) %>%select(Start)

loop.dat <- tsdat %>% filter(State == st, Metric ==met) %>% select(-State, -Metric) %>% t()

inds <- row.names(loop.dat) %>% as.yearqtr() >=start.date


loop.dat <- loop.dat[inds, ]true <- loop.dat[length(loop.dat)]loop.dat <- loop.dat[-length(loop.dat)]loop.ts <- ts(loop.dat, start = c(as.numeric(substr(start.date,

0, 4)), as.numeric(substr(start.date, 4,5))), end = c(2017, 3), frequency = 4)

fit <- auto.arima(loop.ts)fc <- forecast(fit, h = 1, level = PI)min. <- min(loop.dat, true, fc$lower)max. <- max(loop.dat, true, fc$upper)params <- arimaorder(fit)cov.full <- coverage.df$full[coverage.df$abrev ==

"PIP"]state.full <- state.mappings$State[state.mappings$Abbreviation ==

st]

if (met == "LossCost") {main.title <- paste0(state.full, "\n", cov.full,

"\n", "Loss Cost")} else {

main.title <- paste0(state.full, "\n", cov.full,"\n", met)

}

plot(fc, ylim = c(min. - 0.1 * (max. - min.),max. + 0.1 * (max. - min.)), main = main.title,las = 1, axt = "n")

lines(c(2017.5, 2017.75), c(loop.ts[length(loop.ts)],true), col = "black")

points(2017.75, true, col = "darkgreen", pch = 19)axis(1, at = c(2012:2017), labels = c("'12",

"'13", "'14", "'15", "'16", "'17"))Hmisc::minor.tick(nx = 4)

}

par(mfrow = c(1, 2))pip.pred.plot("KY", "LossCost", 90)pip.pred.plot("ND", "Severity", 90)pip.pred.plot("NJ", "Frequency", 90)pip.pred.plot("NJ", "LossCost", 90)pip.pred.plot("NY", "Severity", 90)pip.pred.plot("NY", "LossCost", 90)legend.plt()


auto loss cost trends q4 2017 - society of actuaries...montana property damage severity 3000 3500...

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