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appendix.Rmd
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---
title: "Stat 248 Project Appendix"
author: "Sara Stoudt"
date: "May 3, 2017"
output: html_document
---
GitHub Repository: https://github.com/sastoudt/stat248project_BayDeltaTS
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```
## Finding good subsets of the data that have the most complete records.
```{r}
setwd("~/Desktop/sfei")
sfei<-read.csv("sfeiPlusDates.csv",stringsAsFactors=F)
names(sfei)
require(ggplot2)
sub=subset(sfei,Station%in%c("D10","D12","D4","D22","D26")) ## middle/most connected region of interest
```
```{r}
## EDA to find out which station/variable combos have most complete records
ggplot(sub, aes(x=date_dec, y=din, colour=as.factor(Station)))+geom_line()+xlim(2000,2015) ## care about recent past
```
## See how much missingness.
```{r}
##percent
percentMissingChl=percentMissingDo=percentMissingPheo=percentMissingTemp=percentMissingSal=c()
perStation=unique(sfei$Station)
for(i in 1:length(perStation)){
data=subset(sfei,date_dec>2000 &Station==perStation[i])
percentMissingChl<-c(percentMissingChl,length(which(is.na(data$chl)))/nrow(data))
percentMissingDo<-c(percentMissingDo,length(which(is.na(data$do)))/nrow(data))
percentMissingPheo<-c(percentMissingPheo,length(which(is.na(data$pheo)))/nrow(data))
percentMissingTemp<-c(percentMissingTemp,length(which(is.na(data$temp)))/nrow(data))
percentMissingSal<-c(percentMissingSal,length(which(is.na(data$sal)))/nrow(data))
## chl
## do
## pheo
## temp
## sal
}
percentMissingChl[which(perStation%in%c("D10","D12","D4","D22","D26"))]
percentMissingDo[which(perStation%in%c("D10","D12","D4","D22","D26"))]
percentMissingPheo[which(perStation%in%c("D10","D12","D4","D22","D26"))]
percentMissingTemp[which(perStation%in%c("D10","D12","D4","D22","D26"))]
percentMissingSal[which(perStation%in%c("D10","D12","D4","D22","D26"))]
```
```{r}
## counts
percentMissingChl=percentMissingDo=percentMissingPheo=percentMissingTemp=percentMissingSal=c()
perStation=c("D10","D12","D4","D22","D26")
for(i in 1:length(perStation)){
data=subset(sfei,date_dec>2000 &Station==perStation[i])
percentMissingChl<-c(percentMissingChl,length(which(is.na(data$chl))))
percentMissingDo<-c(percentMissingDo,length(which(is.na(data$do))))
percentMissingPheo<-c(percentMissingPheo,length(which(is.na(data$pheo))))
percentMissingTemp<-c(percentMissingTemp,length(which(is.na(data$temp))))
percentMissingSal<-c(percentMissingSal,length(which(is.na(data$sal))))
## chl
## do
## pheo
## temp
## sal
}
percentMissingDo
percentMissingTemp
percentMissingSal
```
```{r}
## any back to back missing values?
## avg value before and after missing values
stationUse=c("D10","D12","D4","D22","D26")
for(i in 1:length(stationUse)){
data=subset(sfei,date_dec>2000 &Station==stationUse[i])
print(sum(diff(which(is.na(data$do)))==1))
print(sum(diff(which(is.na(data$temp)))==1))
print(sum(diff(which(is.na(data$sal)))==1))
}
```
```{r}
## missingness same for all variables within a station?
## often but not always
stationUse=c("D10","D12","D4","D22","D26")
for(i in 1:length(stationUse)){
data=subset(sfei,date_dec>2000 &Station==stationUse[i])
print(intersect(which(is.na(data$do)),which(is.na(data$temp))))
print(intersect(which(is.na(data$temp)),which(is.na(data$sal))))
}
```
## Simple Imputation
```{r}
stationUse=c("D10","D12","D4","D22","D26")
dataBeforeImputation=subset(sfei,date_dec>=2000 & Station%in%stationUse)
nrow(dataBeforeImputation) ## 864
length(which(is.na(dataBeforeImputation$chl))) ## 0
length(which(is.na(dataBeforeImputation$pheo))) ## 0
length(which(is.na(dataBeforeImputation$do))) ## 29
length(which(is.na(dataBeforeImputation$sal))) ## 21
length(which(is.na(dataBeforeImputation$temp))) ## 19
```
## Get complete year-month combinations
```{r}
sfei=dataBeforeImputation
sfei$yr=as.numeric(as.character(format(as.Date(sfei$Date), "%Y")))
sfei$mon=as.numeric(as.character(format(as.Date(sfei$Date),"%m")))
sfei=sfei[,c("Date","Station","Longitude","Latitude","chl","do","pheo","sal","temp","date_dec","doy","yr","mon")]
yrSeq=seq(2000,2015,by=1)
monSeq=seq(1,12,by=1)
dataTimeFull=as.data.frame(expand.grid(yrSeq,monSeq))
names(dataTimeFull)=c("yr","mon")
D10<-subset(sfei,Station=="D10")
D10f=merge(dataTimeFull,D10,by.x=c("yr","mon"),by.y=c("yr","mon"),all.x=T)
D12<-subset(sfei,Station=="D12")
D12f=merge(dataTimeFull,D12,by.x=c("yr","mon"),by.y=c("yr","mon"),all.x=T)
D22<-subset(sfei,Station=="D22")
D22f=merge(dataTimeFull,D22,by.x=c("yr","mon"),by.y=c("yr","mon"),all.x=T)
D26<-subset(sfei,Station=="D26")
D26f=merge(dataTimeFull,D26,by.x=c("yr","mon"),by.y=c("yr","mon"),all.x=T)
D4<-subset(sfei,Station=="D4")
D4f=merge(dataTimeFull,D4,by.x=c("yr","mon"),by.y=c("yr","mon"),all.x=T)
```
```{r}
## now need to fill in NAs
D10f[which(is.na(D10f$Date)),"Date"]=paste(D10f[which(is.na(D10f$Date)),"yr"],D10f[which(is.na(D10f$Date)),"mon"],
"01",sep="-" )
D10f$Date=as.Date(D10f$Date)
D10f[which(is.na(D10f$Station)),"Station"]="D10"
D10f[which(is.na(D10f$Longitude)),"Longitude"]=D10f$Longitude[1]
D10f[which(is.na(D10f$Latitude)),"Latitude"]=D10f$Latitude[1]
require(lubridate)
require(WRTDStidal)
D10f[which(is.na(D10f$date_dec)),"date_dec"]=as.numeric(dec_time(D10f[which(is.na(D10f$date_dec)),"Date"])$dec_time)
D10f[which(is.na(D10f$doy)),"doy"]=as.numeric(strftime(D10f[which(is.na(D10f$doy)),"Date"], format = "%j"))
D12f[which(is.na(D12f$Date)),"Date"]=paste(D12f[which(is.na(D12f$Date)),"yr"],D12f[which(is.na(D12f$Date)),"mon"],
"01",sep="-" )
D12f$Date=as.Date(D12f$Date)
D12f[which(is.na(D12f$Station)),"Station"]="D12"
D12f[which(is.na(D12f$Longitude)),"Longitude"]=D12f$Longitude[1]
D12f[which(is.na(D12f$Latitude)),"Latitude"]=D12f$Latitude[1]
D12f[which(is.na(D12f$date_dec)),"date_dec"]=as.numeric(dec_time(D12f[which(is.na(D12f$date_dec)),"Date"])$dec_time)
D12f[which(is.na(D12f$doy)),"doy"]=as.numeric(strftime(D12f[which(is.na(D12f$doy)),"Date"], format = "%j"))
D22f[which(is.na(D22f$Date)),"Date"]=paste(D22f[which(is.na(D22f$Date)),"yr"],D22f[which(is.na(D22f$Date)),"mon"],
"01",sep="-" )
D22f$Date=as.Date(D22f$Date)
D22f[which(is.na(D22f$Station)),"Station"]="D22"
D22f[which(is.na(D22f$Longitude)),"Longitude"]=D22f$Longitude[1]
D22f[which(is.na(D22f$Latitude)),"Latitude"]=D22f$Latitude[1]
D22f[which(is.na(D22f$date_dec)),"date_dec"]=as.numeric(dec_time(D22f[which(is.na(D22f$date_dec)),"Date"])$dec_time)
D22f[which(is.na(D22f$doy)),"doy"]=as.numeric(strftime(D22f[which(is.na(D22f$doy)),"Date"], format = "%j"))
D26f[which(is.na(D26f$Date)),"Date"]=paste(D26f[which(is.na(D26f$Date)),"yr"],D26f[which(is.na(D26f$Date)),"mon"],
"01",sep="-" )
D26f$Date=as.Date(D26f$Date)
D26f[which(is.na(D26f$Station)),"Station"]="D26"
D26f[which(is.na(D26f$Longitude)),"Longitude"]=D26f$Longitude[1]
D26f[which(is.na(D26f$Latitude)),"Latitude"]=D26f$Latitude[1]
D26f[which(is.na(D26f$date_dec)),"date_dec"]=as.numeric(dec_time(D26f[which(is.na(D26f$date_dec)),"Date"])$dec_time)
D26f[which(is.na(D26f$doy)),"doy"]=as.numeric(strftime(D26f[which(is.na(D26f$doy)),"Date"], format = "%j"))
D4f[which(is.na(D4f$Date)),"Date"]=paste(D4f[which(is.na(D4f$Date)),"yr"],D4f[which(is.na(D4f$Date)),"mon"],
"01",sep="-" )
D4f$Date=as.Date(D4f$Date)
D4f[which(is.na(D4f$Station)),"Station"]="D4"
D4f[which(is.na(D4f$Longitude)),"Longitude"]=D4f$Longitude[1]
D4f[which(is.na(D4f$Latitude)),"Latitude"]=D4f$Latitude[1]
D4f[which(is.na(D4f$date_dec)),"date_dec"]=as.numeric(dec_time(D4f[which(is.na(D4f$date_dec)),"Date"])$dec_time)
D4f[which(is.na(D4f$doy)),"doy"]=as.numeric(strftime(D4f[which(is.na(D4f$doy)),"Date"], format = "%j"))
```
```{r}
### now impute actual variables
#D10f[which(is.na(D10f$chl)),"chl"]
toImputeChl=which(is.na(D10f$chl))
toImputeDo=which(is.na(D10f$do))
toImputePheo=which(is.na(D10f$pheo))
toImputeSal=which(is.na(D10f$sal))
toImputeTemp=which(is.na(D10f$temp))
for(i in 1:length(toImputeChl)){
D10f$chl[toImputeChl[i]]=mean(c(D10f$chl[toImputeChl[i]-1],D10f$chl[toImputeChl[i]+1]),na.rm=T)
}
sum(is.na(D10f$chl))
for(i in 1:length(toImputeDo)){
D10f$do[toImputeDo[i]]=mean(c(D10f$do[toImputeDo[i]-1],D10f$do[toImputeDo[i]+1]),na.rm=T)
}
sum(is.na(D10f$do))
for(i in 1:length(toImputePheo)){
D10f$pheo[toImputePheo[i]]=mean(c(D10f$pheo[toImputePheo[i]-1],D10f$pheo[toImputePheo[i]+1]),na.rm=T)
}
sum(is.na(D10f$pheo))
for(i in 1:length(toImputeSal)){
D10f$sal[toImputeSal[i]]=mean(c(D10f$sal[toImputeSal[i]-1],D10f$sal[toImputeSal[i]+1]),na.rm=T)
}
sum(is.na(D10f$sal))
for(i in 1:length(toImputeTemp)){
D10f$temp[toImputeTemp[i]]=mean(c(D10f$temp[toImputeTemp[i]-1],D10f$temp[toImputeTemp[i]+1]),na.rm=T)
}
sum(is.na(D10f$temp))
###
toImputeChl=which(is.na(D12f$chl))
toImputeDo=which(is.na(D12f$do))
toImputePheo=which(is.na(D12f$pheo))
toImputeSal=which(is.na(D12f$sal))
toImputeTemp=which(is.na(D12f$temp))
for(i in 1:length(toImputeChl)){
D12f$chl[toImputeChl[i]]=mean(c(D12f$chl[toImputeChl[i]-1],D12f$chl[toImputeChl[i]+1]),na.rm=T)
}
sum(is.na(D12f$chl))
for(i in 1:length(toImputeDo)){
D12f$do[toImputeDo[i]]=mean(c(D12f$do[toImputeDo[i]-1],D12f$do[toImputeDo[i]+1]),na.rm=T)
}
sum(is.na(D12f$do))
for(i in 1:length(toImputePheo)){
D12f$pheo[toImputePheo[i]]=mean(c(D12f$pheo[toImputePheo[i]-1],D12f$pheo[toImputePheo[i]+1]),na.rm=T)
}
sum(is.na(D12f$pheo))
for(i in 1:length(toImputeSal)){
D12f$sal[toImputeSal[i]]=mean(c(D12f$sal[toImputeSal[i]-1],D12f$sal[toImputeSal[i]+1]),na.rm=T)
}
sum(is.na(D12f$sal))
for(i in 1:length(toImputeTemp)){
D12f$temp[toImputeTemp[i]]=mean(c(D12f$temp[toImputeTemp[i]-1],D12f$temp[toImputeTemp[i]+1]),na.rm=T)
}
sum(is.na(D12f$temp))
###
toImputeChl=which(is.na(D22f$chl))
toImputeDo=which(is.na(D22f$do))
toImputePheo=which(is.na(D22f$pheo))
toImputeSal=which(is.na(D22f$sal))
toImputeTemp=which(is.na(D22f$temp))
for(i in 1:length(toImputeChl)){
D22f$chl[toImputeChl[i]]=mean(c(D22f$chl[toImputeChl[i]-1],D22f$chl[toImputeChl[i]+1]),na.rm=T)
}
sum(is.na(D22f$chl))
for(i in 1:length(toImputeDo)){
D22f$do[toImputeDo[i]]=mean(c(D22f$do[toImputeDo[i]-1],D22f$do[toImputeDo[i]+1]),na.rm=T)
}
sum(is.na(D22f$do))
for(i in 1:length(toImputePheo)){
D22f$pheo[toImputePheo[i]]=mean(c(D22f$pheo[toImputePheo[i]-1],D22f$pheo[toImputePheo[i]+1]),na.rm=T)
}
sum(is.na(D22f$pheo))
for(i in 1:length(toImputeSal)){
D22f$sal[toImputeSal[i]]=mean(c(D22f$sal[toImputeSal[i]-1],D22f$sal[toImputeSal[i]+1]),na.rm=T)
}
sum(is.na(D22f$sal))
for(i in 1:length(toImputeTemp)){
D22f$temp[toImputeTemp[i]]=mean(c(D22f$temp[toImputeTemp[i]-1],D22f$temp[toImputeTemp[i]+1]),na.rm=T)
}
sum(is.na(D22f$temp))
###
toImputeChl=which(is.na(D26f$chl))
toImputeDo=which(is.na(D26f$do))
toImputePheo=which(is.na(D26f$pheo))
toImputeSal=which(is.na(D26f$sal))
toImputeTemp=which(is.na(D26f$temp))
for(i in 1:length(toImputeChl)){
D26f$chl[toImputeChl[i]]=mean(c(D26f$chl[toImputeChl[i]-1],D26f$chl[toImputeChl[i]+1]),na.rm=T)
}
sum(is.na(D26f$chl))
for(i in 1:length(toImputeDo)){
D26f$do[toImputeDo[i]]=mean(c(D26f$do[toImputeDo[i]-1],D26f$do[toImputeDo[i]+1]),na.rm=T)
}
sum(is.na(D26f$do))
for(i in 1:length(toImputePheo)){
D26f$pheo[toImputePheo[i]]=mean(c(D26f$pheo[toImputePheo[i]-1],D26f$pheo[toImputePheo[i]+1]),na.rm=T)
}
sum(is.na(D26f$pheo))
for(i in 1:length(toImputeSal)){
D26f$sal[toImputeSal[i]]=mean(c(D26f$sal[toImputeSal[i]-1],D26f$sal[toImputeSal[i]+1]),na.rm=T)
}
sum(is.na(D26f$sal))
for(i in 1:length(toImputeTemp)){
D26f$temp[toImputeTemp[i]]=mean(c(D26f$temp[toImputeTemp[i]-1],D26f$temp[toImputeTemp[i]+1]),na.rm=T)
}
sum(is.na(D26f$temp))
###
toImputeChl=which(is.na(D4f$chl))
toImputeDo=which(is.na(D4f$do))
toImputePheo=which(is.na(D4f$pheo))
toImputeSal=which(is.na(D4f$sal))
toImputeTemp=which(is.na(D4f$temp))
for(i in 1:length(toImputeChl)){
D4f$chl[toImputeChl[i]]=mean(c(D4f$chl[toImputeChl[i]-1],D4f$chl[toImputeChl[i]+1]),na.rm=T)
}
sum(is.na(D4f$chl))
for(i in 1:length(toImputeDo)){
D4f$do[toImputeDo[i]]=mean(c(D4f$do[toImputeDo[i]-1],D4f$do[toImputeDo[i]+1]),na.rm=T)
}
sum(is.na(D4f$do))
for(i in 1:length(toImputePheo)){
D4f$pheo[toImputePheo[i]]=mean(c(D4f$pheo[toImputePheo[i]-1],D4f$pheo[toImputePheo[i]+1]),na.rm=T)
}
sum(is.na(D4f$pheo))
for(i in 1:length(toImputeSal)){
D4f$sal[toImputeSal[i]]=mean(c(D4f$sal[toImputeSal[i]-1],D4f$sal[toImputeSal[i]+1]),na.rm=T)
}
sum(is.na(D4f$sal))
for(i in 1:length(toImputeTemp)){
D4f$temp[toImputeTemp[i]]=mean(c(D4f$temp[toImputeTemp[i]-1],D4f$temp[toImputeTemp[i]+1]),na.rm=T)
}
sum(is.na(D4f$temp))
###
tail(D10f,20)
## need to trim july on in 2015
D10f=D10f[1:which(D10f$yr=="2015" & D10f$mon=="6"),]
D12f=D12f[1:which(D12f$yr=="2015" & D12f$mon=="6"),]
D22f=D22f[1:which(D22f$yr=="2015" & D22f$mon=="6"),]
D26f=D26f[1:which(D26f$yr=="2015" & D26f$mon=="6"),]
D4f=D4f[1:which(D4f$yr=="2015" & D4f$mon=="6"),]
D22f$Longitude[1]=D22f$Longitude[2]
D22f$Latitude[1]=D22f$Latitude[2]
D22f$do[1]=D22f$do[2]
```
```{r,eval=F}
setwd("~/UC_Berkeley/Semester_4/timeSeries")
afterImputation=rbind(D10f,D12f,D22f,D26f,D4f)
write.csv(afterImputation,"sfeiDataForProject.csv",row.names=F)
```
## De-trend, de-seasonalize, variance stabilization
```{r}
setwd("~/UC_Berkeley/Semester_4/timeSeries")
sfeiData<-read.csv("sfeiDataForProject.csv",stringsAsFactors=FALSE)
names(sfeiData)
## "chl" "do" "pheo" "sal" "temp"
length(unique(sfeiData$Station)) ## 5
unique(sfeiData$Station) ## "D10" "D12" "D22" "D26" "D4"
D10<-subset(sfeiData,Station=="D10")
D12<-subset(sfeiData,Station=="D12")
D22<-subset(sfeiData,Station=="D22")
D26<-subset(sfeiData,Station=="D26")
D4<-subset(sfeiData,Station=="D4")
plot(D10$chl,type="l")
require(mgcv)
require(parallel)
nc <- 4 ## have up to 8
if (detectCores()>1) { ## no point otherwise
cl <- makeCluster(nc)
} else cl <- NULL
```
```{r}
#### chl ####
sfeiData$Station=as.factor(sfeiData$Station)
chlSeasonalTimeTrend=bam(chl~Station+s(date_dec,bs="cs",by=Station,k=25)+s(doy,bs="cs",by=Station,k=25),data=sfeiData,cluster=cl)
summary(chlSeasonalTimeTrend)
gam.check(chlSeasonalTimeTrend)
plot(chlSeasonalTimeTrend)
## datedec flat for D10, D12, D4
## increasing for D22
## curved updward for D26
## doy peak in 100s for D10, D12, D4
## plateau 100 to 250 for D22, D26
sfeiData$predGAMchl=chlSeasonalTimeTrend$fitted
sfeiData$residGAMchl=chlSeasonalTimeTrend$resid
D10<-subset(sfeiData,Station=="D10")
D12<-subset(sfeiData,Station=="D12")
D22<-subset(sfeiData,Station=="D22")
D26<-subset(sfeiData,Station=="D26")
D4<-subset(sfeiData,Station=="D4")
plot(D10$chl,type="l")
lines(D10$residGAMchl,col="red")
lines(D10$predGAMchl,col="blue")
par(mfrow=c(2,1))
plot(D10$residGAMchl,type="l") ## check for stationarity
plot(log(D10$residGAMchl+abs(min(D10$residGAMchl))),type="l")
plot(D12$residGAMchl,type="l")
plot(log(D12$residGAMchl+abs(min(D12$residGAMchl))),type="l")
plot(D22$residGAMchl,type="l")
plot(log(D22$residGAMchl+abs(min(D22$residGAMchl))),type="l")
plot(D26$residGAMchl,type="l")
plot(log(D26$residGAMchl+abs(min(D26$residGAMchl))),type="l")
plot(D4$residGAMchl,type="l")
plot(log(D4$residGAMchl+abs(min(D4$residGAMchl))),type="l")
D10$residGAMchlTransform=log(D10$residGAMchl+abs(min(D10$residGAMchl))+1)
D12$residGAMchlTransform=log(D12$residGAMchl+abs(min(D12$residGAMchl))+1)
D22$residGAMchlTransform=log(D22$residGAMchl+abs(min(D22$residGAMchl))+1)
D26$residGAMchlTransform=log(D26$residGAMchl+abs(min(D26$residGAMchl))+1)
D4$residGAMchlTransform=log(D4$residGAMchl+abs(min(D4$residGAMchl))+1)
sfeiData=rbind(D10,D12,D22,D26,D4)
```
```{r}
doSeasonalTimeTrend=bam(do~Station+s(date_dec,bs="cs",by=Station,k=25)+s(doy,bs="cs",by=Station,k=25),data=sfeiData,cluster=cl)
summary(doSeasonalTimeTrend)
gam.check(doSeasonalTimeTrend)
plot(doSeasonalTimeTrend)
## datedec slight concave D10, D12, D22 D4
## flatter D26
## doy peak 50, min peak 200 all
sfeiData$predGAMdo=doSeasonalTimeTrend$fitted
sfeiData$residGAMdo=doSeasonalTimeTrend$resid
D10<-subset(sfeiData,Station=="D10")
D12<-subset(sfeiData,Station=="D12")
D22<-subset(sfeiData,Station=="D22")
D26<-subset(sfeiData,Station=="D26")
D4<-subset(sfeiData,Station=="D4")
plot(D10$do,type="l")
lines(D10$residGAMdo,col="red")
lines(D10$predGAMdo,col="blue")
## these don't seem to help stick with original
par(mfrow=c(2,1))
plot(D10$residGAMdo,type="l") ## check for stationarity
plot(log(D10$residGAMdo+abs(min(D10$residGAMdo))),type="l")
##http://stackoverflow.com/questions/26617587/finding-optimal-lambda-for-box-cox-transform-in-r
require(MASS)
out <- boxcox(lm(D10$residGAMdo+abs(min(D10$residGAMdo))+1~1))
range(out$x[out$y > max(out$y)-qchisq(0.95,1)/2]) ## one is consistent, keep as is
plot(D12$residGAMdo,type="l")
plot(log(D12$residGAMdo+abs(min(D12$residGAMdo))),type="l")
out <- boxcox(lm(D12$residGAMdo+abs(min(D12$residGAMdo))+1~1))
range(out$x[out$y > max(out$y)-qchisq(0.95,1)/2]) ## one is consistent, keep as is
plot(D22$residGAMdo,type="l")
plot(log(D22$residGAMdo+abs(min(D22$residGAMdo))),type="l")
out <- boxcox(lm(D22$residGAMdo+abs(min(D22$residGAMdo))+1~1))
range(out$x[out$y > max(out$y)-qchisq(0.95,1)/2]) ## one is consistent, keep as is
plot(D26$residGAMdo,type="l")
plot(log(D26$residGAMdo+abs(min(D26$residGAMdo))),type="l")
out <- boxcox(lm(D26$residGAMdo+abs(min(D26$residGAMdo))+1~1))
range(out$x[out$y > max(out$y)-qchisq(0.95,1)/2]) ## one is consistent, keep as is
plot(D4$residGAMdo,type="l")
plot(log(D4$residGAMdo+abs(min(D4$residGAMdo))),type="l")
out <- boxcox(lm(D4$residGAMdo+abs(min(D4$residGAMdo))+1~1))
range(out$x[out$y > max(out$y)-qchisq(0.95,1)/2]) ##
require(forecast)
plot(D4$residGAMdo,type="l")
trans.vector = BoxCox( D4$residGAMdo+abs(min(D4$residGAMdo))+1, 1.5)
plot(trans.vector,type="l") ## basically the same
```
```{r}
#### pheo ####
pheoSeasonalTimeTrend=bam(pheo~Station+s(date_dec,bs="cs",by=Station,k=25)+s(doy,bs="cs",by=Station,k=25),data=sfeiData,cluster=cl)
summary(pheoSeasonalTimeTrend)
gam.check(pheoSeasonalTimeTrend)
plot(pheoSeasonalTimeTrend)
## date dec flat D10, D12, D4
## downward trend D22
## down and up D26
## doy, peak 125, low point 275 D10
## concave slight peak around 150 D12, D26, D4 (even slighter for D22)
sfeiData$predGAMpheo=pheoSeasonalTimeTrend$fitted
sfeiData$residGAMpheo=pheoSeasonalTimeTrend$resid
D10<-subset(sfeiData,Station=="D10")
D12<-subset(sfeiData,Station=="D12")
D22<-subset(sfeiData,Station=="D22")
D26<-subset(sfeiData,Station=="D26")
D4<-subset(sfeiData,Station=="D4")
plot(D10$pheo,type="l")
lines(D10$residGAMpheo,col="red")
lines(D10$predGAMpheo,col="blue")
par(mfrow=c(2,1))
plot(D10$residGAMpheo,type="l") ## check for stationarity
plot(log(D10$residGAMpheo+abs(min(D10$residGAMpheo))),type="l")
plot(D12$residGAMpheo,type="l")
plot(log(D12$residGAMpheo+abs(min(D12$residGAMpheo))),type="l")
plot(D22$residGAMpheo,type="l")
plot(log(D22$residGAMpheo+abs(min(D22$residGAMpheo))),type="l")
plot(D26$residGAMpheo,type="l")
plot(log(D26$residGAMpheo+abs(min(D26$residGAMpheo))),type="l")
plot(D4$residGAMpheo,type="l")
plot(log(D4$residGAMpheo+abs(min(D4$residGAMpheo))),type="l")
D10$residGAMpheoTransform=log(D10$residGAMpheo+abs(min(D10$residGAMpheo))+1)
D12$residGAMpheoTransform=log(D12$residGAMpheo+abs(min(D12$residGAMpheo))+1)
D22$residGAMpheoTransform=log(D22$residGAMpheo+abs(min(D22$residGAMpheo))+1)
D26$residGAMpheoTransform=log(D26$residGAMpheo+abs(min(D26$residGAMpheo))+1)
D4$residGAMpheoTransform=log(D4$residGAMpheo+abs(min(D4$residGAMpheo))+1)
sfeiData=rbind(D10,D12,D22,D26,D4)
```
```{r}
salSeasonalTimeTrend=bam(sal~Station+s(date_dec,bs="cs",by=Station,k=25)+s(doy,bs="cs",by=Station,k=25),data=sfeiData,cluster=cl)
summary(salSeasonalTimeTrend)
gam.check(salSeasonalTimeTrend)
plot(salSeasonalTimeTrend)
## date dec D10 wiggly peak 2008, same wiggles but dampened D12, D4
## concave plateau D22
## flat D26
## doy min peak 75, peak 325 D10, D4 same but dampened D12, D22
## flat D26
sfeiData$predGAMsal=salSeasonalTimeTrend$fitted
sfeiData$residGAMsal=salSeasonalTimeTrend$resid
D10<-subset(sfeiData,Station=="D10")
D12<-subset(sfeiData,Station=="D12")
D22<-subset(sfeiData,Station=="D22")
D26<-subset(sfeiData,Station=="D26")
D4<-subset(sfeiData,Station=="D4")
plot(D10$sal,type="l")
lines(D10$residGAMsal,col="red")
lines(D10$predGAMsal,col="blue")
## these don't seem to help, stick to original
par(mfrow=c(2,1))
plot(D10$residGAMsal,type="l") ## check for stationarity
plot(log(D10$residGAMsal+abs(min(D10$residGAMsal))),type="l")
out <- boxcox(lm(D10$residGAMsal+abs(min(D10$residGAMsal))+1~1))
range(out$x[out$y > max(out$y)-qchisq(0.95,1)/2]) ## one is consistent, keep this the same
plot(D12$residGAMsal,type="l")
plot(log(D12$residGAMsal+abs(min(D12$residGAMsal))),type="l")
out <- boxcox(lm(D12$residGAMsal+abs(min(D12$residGAMsal))+1~1))
range(out$x[out$y > max(out$y)-qchisq(0.95,1)/2]) ##
trans.vector = BoxCox( D12$residGAMsal+abs(min(D12$residGAMsal))+1, .5)
plot(D12$residGAMsal,type="l")
plot(trans.vector,type="l") ## looks the same
plot(D22$residGAMsal,type="l")
plot(log(D22$residGAMsal+abs(min(D22$residGAMsal))),type="l")
out <- boxcox(lm(D22$residGAMsal+abs(min(D22$residGAMsal))+1~1))
range(out$x[out$y > max(out$y)-qchisq(0.95,1)/2]) ## this suggest log is better, actually change
plot(D26$residGAMsal,type="l")
plot(log(D26$residGAMsal+abs(min(D26$residGAMsal))),type="l")
out <- boxcox(lm(D26$residGAMsal+abs(min(D26$residGAMsal))+1~1))
range(out$x[out$y > max(out$y)-qchisq(0.95,1)/2]) ##
trans.vector = BoxCox( D26$residGAMsal+abs(min(D26$residGAMsal))+1, -1.75)
plot(D26$residGAMsal,type="l")
plot(trans.vector,type="l") ## looks the same
plot(D4$residGAMsal,type="l")
plot(log(D4$residGAMsal+abs(min(D4$residGAMsal))),type="l")
out <- boxcox(lm(D4$residGAMsal+abs(min(D4$residGAMsal))+1~1))
range(out$x[out$y > max(out$y)-qchisq(0.95,1)/2]) ## 1 is consistent, keep
D22$residGAMsalTransform=log(D22$residGAMsal+abs(min(D22$residGAMsal))+1)
require(dplyr)
sfeiData=bind_rows(D10,D12,D22,D26,D4)
```
```{r}
tempSeasonalTimeTrend=bam(temp~Station+s(date_dec,bs="cs",by=Station,k=25)+s(doy,bs="cs",by=Station,k=25),data=sfeiData,cluster=cl)
summary(tempSeasonalTimeTrend)
gam.check(tempSeasonalTimeTrend)
plot(tempSeasonalTimeTrend)
## datedec nearly flat D10, D12, D26, D4
## flat D22
## doy peak 200 all
sfeiData$predGAMtemp=tempSeasonalTimeTrend$fitted
sfeiData$residGAMtemp=tempSeasonalTimeTrend$resid
D10<-subset(sfeiData,Station=="D10")
D12<-subset(sfeiData,Station=="D12")
D22<-subset(sfeiData,Station=="D22")
D26<-subset(sfeiData,Station=="D26")
D4<-subset(sfeiData,Station=="D4")
plot(D10$temp,type="l")
lines(D10$residGAMtemp,col="red")
lines(D10$predGAMtemp,col="blue")
## doesn't really help, stick with original
par(mfrow=c(2,1))
plot(D10$residGAMtemp,type="l") ## check for stationarity
plot(log(D10$residGAMtemp+abs(min(D10$residGAMtemp))),type="l")
out <- boxcox(lm(D10$residGAMtemp+abs(min(D10$residGAMtemp))+1~1))
range(out$x[out$y > max(out$y)-qchisq(0.95,1)/2]) ## 1 is consistent, keep
plot(D12$residGAMtemp,type="l")
plot(log(D12$residGAMtemp+abs(min(D12$residGAMtemp))),type="l")
out <- boxcox(lm(D12$residGAMtemp+abs(min(D12$residGAMtemp))+1~1))
range(out$x[out$y > max(out$y)-qchisq(0.95,1)/2]) ## 1 is consistent, keep
plot(D22$residGAMtemp,type="l")
plot(log(D22$residGAMtemp+abs(min(D22$residGAMtemp))),type="l")
out <- boxcox(lm(D22$residGAMtemp+abs(min(D22$residGAMtemp))+1~1))
range(out$x[out$y > max(out$y)-qchisq(0.95,1)/2]) ## 1 is consistent, keep
plot(D26$residGAMtemp,type="l")
plot(log(D26$residGAMtemp+abs(min(D26$residGAMtemp))),type="l")
out <- boxcox(lm(D26$residGAMtemp+abs(min(D26$residGAMtemp))+1~1))
range(out$x[out$y > max(out$y)-qchisq(0.95,1)/2]) ## 1 is consistent, keep
plot(D4$residGAMtemp,type="l")
plot(log(D4$residGAMtemp+abs(min(D4$residGAMtemp))),type="l")
out <- boxcox(lm(D4$residGAMtemp+abs(min(D4$residGAMtemp))+1~1))
range(out$x[out$y > max(out$y)-qchisq(0.95,1)/2]) ## 1 is consistent, keep
```
```{r,eval=F}
setwd("~/UC_Berkeley/Semester_4/timeSeries")
write.csv(D10,"D10data.csv",row.names=F)
write.csv(D12,"D12data.csv",row.names=F)
write.csv(D22,"D22data.csv",row.names=F)
write.csv(D26,"D26data.csv",row.names=F)
write.csv(D4,"D4data.csv",row.names=F)
```
## Frequency Domain
```{r}
acfTest=function(stationData,nutrient){
if(sum(grepl(paste(nutrient,"Transform",sep=""),names(stationData)))>0){
varName=paste("residGAM",nutrient,"Transform",sep="")
}else{
varName=paste("residGAM",nutrient,sep="")
}
empP<-c()
for(i in 2:nrow(stationData) ){
test1=stationData[c((i):nrow(stationData),1:(i-1)),varName]
test=acf(test1,lag.max=12,plot=F)
acfOfInterest=test$acf[2:13]
empP<-c( empP,acfOfInterest[which.max(abs(acfOfInterest))] )
# print(i)
}
test=acf(stationData[,varName],lag.max=12,plot=F)
acfOfInterest=test$acf[2:13]
lagOfInterest=test$lag[2:13]
maxLag=lagOfInterest[which.max(abs(acfOfInterest))]
if(acfOfInterest[which.max(abs(acfOfInterest))]<0){
pVal=length(which(empP<acfOfInterest[which.max(abs(acfOfInterest))]))/nrow(stationData)
}else{
pVal=length(which(empP>acfOfInterest[which.max(abs(acfOfInterest))]))/nrow(stationData)
}
minPval=1/nrow(stationData)
return(list(maxLag=maxLag,pVal=pVal,minPval=minPval))
}
acfTest(D10,"chl")
ccfTest=function(station1Data,station2Data,station1Nutrient,station2Nutrient){
if(sum(grepl(paste(station1Nutrient,"Transform",sep=""),names(station1Data)))>0){
varName=paste("residGAM",station1Nutrient,"Transform",sep="")
}else{
varName=paste("residGAM",station1Nutrient,sep="")
}
if(sum(grepl(paste(station2Nutrient,"Transform",sep=""),names(station2Data)))>0){
varName2=paste("residGAM",station2Nutrient,"Transform",sep="")
}else{
varName2=paste("residGAM",station2Nutrient,sep="")
}
empP<-c()
for(i in 2:nrow(station2Data) ){
test1=station2Data[c((i):nrow(station2Data),1:(i-1)),varName2]
test=ccf(station1Data[,varName],test1,lag.max=12,plot=F)
ccfOfInterest=test$acf[14:25]
empP<-c( empP,ccfOfInterest[which.max(abs(ccfOfInterest))] )
# print(i)
}
test=ccf(station1Data[,varName],station2Data[,varName2],lag.max=12,plot=F)
ccfOfInterest=test$acf[14:25]
lagOfInterest=test$lag[14:25]
maxLag=lagOfInterest[which.max(abs(ccfOfInterest))]
if(ccfOfInterest[which.max(abs(ccfOfInterest))]<0){
pVal=length(which(empP<ccfOfInterest[which.max(abs(ccfOfInterest))]))/nrow(station2Data)
}else{
pVal=length(which(empP>ccfOfInterest[which.max(abs(ccfOfInterest))]))/nrow(station2Data)
}
minPval=1/nrow(station2Data)
return(list(maxLag=maxLag,pVal=pVal,minPval=minPval))
}
ccfTest(D10,D12,"chl","chl")
```
## All possible combinations: do time analysis automatically for all pairs
```{r,eval=F}
stationNames<-c("D10","D12","D22","D26","D4")
varNames<-c("chl","do","pheo","sal","temp")
allCombo=expand.grid(stationNames,stationNames,varNames,varNames)
dim(allCombo)
head(allCombo)
names(allCombo)=c("station1","station2","var1","var2")
withinStation=allCombo[which(allCombo$station1==allCombo$station2),]
dim(withinStation) ## 125
withinStationSameVar=withinStation[which(withinStation$var1==withinStation$var2),]
dim(withinStationSameVar) ## 25
withinStationDiffVar=withinStation[which(withinStation$var1!=withinStation$var2),]
dim(withinStationDiffVar) ## 100
leftOver=allCombo[-which(allCombo$station1==allCombo$station2),]
acrossStationSameVar=leftOver[which(leftOver$var1==leftOver$var2),]
dim(acrossStationSameVar) ## 100
leftOver2=leftOver[-which(leftOver$var1==leftOver$var2),]
dim(leftOver2)
acrossStationDiffVar=leftOver2[which(leftOver2$var1!=leftOver2$var2),]
dim(acrossStationDiffVar) ## 400 same as leftOver2 as expected
setwd("~/UC_Berkeley/Semester_4/timeSeries")
D10<-read.csv("D10data.csv",stringsAsFactors=F)
D12<-read.csv("D12data.csv",stringsAsFactors=F)
D22<-read.csv("D22data.csv",stringsAsFactors=F)
D26<-read.csv("D26data.csv",stringsAsFactors=F)
D4<-read.csv("D4data.csv",stringsAsFactors=F)
storeData=vector("list",length(stationNames))
storeData[[1]]=D10
storeData[[2]]=D12
storeData[[3]]=D22
storeData[[4]]=D26
storeData[[5]]=D4
names(storeData)=stationNames
setwd("~/UC_Berkeley/Semester_4/timeSeries")
acrossStationSameVarResults<-c()
for(i in 1:nrow(acrossStationSameVar)){
res= ccfTest(storeData[[acrossStationSameVar$station1[i]]],storeData[[acrossStationSameVar$station2[i]]],
as.character(acrossStationSameVar$var1[i]),as.character(acrossStationSameVar$var2[i]))
acrossStationSameVarResults<-rbind(acrossStationSameVarResults,c(res$maxLag,res$pVal,res$minPval))
print(i)
}
write.csv(acrossStationSameVarResults,"acrossStationSameVarResults.csv",row.names=F)
acrossStationDiffVarResults<-c()
for(i in 1:nrow(acrossStationDiffVar)){
res= ccfTest(storeData[[acrossStationDiffVar$station1[i]]],storeData[[acrossStationDiffVar$station2[i]]],
as.character(acrossStationDiffVar$var1[i]),as.character(acrossStationDiffVar$var2[i]))
acrossStationDiffVarResults<-rbind(acrossStationDiffVarResults,c(res$maxLag,res$pVal,res$minPval))
print(i)
}
write.csv(acrossStationDiffVarResults,"acrossStationDiffVarResults.csv",row.names=F)
withinStationDiffVarResults<-c()
for(i in 1:nrow(withinStationDiffVar)){
res=ccfTest(storeData[[withinStationDiffVar$station1[i]]],storeData[[withinStationDiffVar$station2[i]]],
as.character(withinStationDiffVar$var1[i]),as.character(withinStationDiffVar$var2[i]))
withinStationDiffVarResults<-rbind(withinStationDiffVarResults,c(res$maxLag,res$pVal,res$minPval))
print(i)
}
write.csv(withinStationDiffVarResults,"withinStationDiffVarResults.csv",row.names=F)
## don't actually use this, not one of the research questions
withinStationSameVarResults<-c()
for(i in 1:nrow(withinStationSameVar)){
res=acfTest(storeData[[withinStationSameVar$station1[i]]],as.character(withinStationSameVar$var1[i]))
withinStationSameVarResults<-rbind(withinStationSameVarResults,c(res$maxLag,res$pVal,res$minPval))
print(i)
}
write.csv(withinStationSameVarResults,"withinStationSameVarResults.csv",row.names=F)
```
## Frequency domain
```{r}
require(psd)
ccfTestFreq=function(station1Data,station2Data,station1Nutrient,station2Nutrient){
if(sum(grepl(paste(station1Nutrient,"Transform",sep=""),names(station1Data)))>0){
varName=paste("residGAM",station1Nutrient,"Transform",sep="")
}else{
varName=paste("residGAM",station1Nutrient,sep="")
}
if(sum(grepl(paste(station2Nutrient,"Transform",sep=""),names(station2Data)))>0){
varName2=paste("residGAM",station2Nutrient,"Transform",sep="")
}else{
varName2=paste("residGAM",station2Nutrient,sep="")
}
## doesn't change results
#tryThis=prewhiten(station1Data[,varName],AR.max=2)
#tryThis2=prewhiten(station2Data[,varName2],AR.max=2)
#test=spectrum(cbind(tryThis$prew_ar,tryThis2$prew_ar),taper=.2,log="no",spans=c(16,16),demean=T,detrend=F,plot=F)
test=spectrum( cbind(station1Data[,varName],station2Data[,varName2]),taper=.2,log="no",spans=c(16,16),demean=T,detrend=F,plot=F)
pVal=1-pf(test$coh/(1-test$coh)*(test$df/2-1),2,test$df-2)[which.max(test$coh)]
maxPhase=test$phase[which.max(test$coh)]
maxCoh=test$coh[which.max(test$coh)]
maxFreq=1/test$freq[which.max(test$coh)]
return(list(maxPhase=maxPhase,maxCoh=maxCoh,maxFreq=maxFreq,pVal=pVal))
}
ccfTestFreq(D10,D12,"chl","pheo")
acfTestFreq=function(stationData,nutrient){
if(sum(grepl(paste(nutrient,"Transform",sep=""),names(stationData)))>0){
varName=paste("residGAM",nutrient,"Transform",sep="")
}else{
varName=paste("residGAM",nutrient,sep="")
}
test=spectrum(stationData[,varName],taper=.2,log="no",spans=c(16,16),demean=T,detrend=F,plot=F)
pVal=1-pchisq(test$spec,2)
maxSpec=test$spec[which.max(test$spec)]
maxFreq=1/test$freq[which.max(test$spec)]
pVal=pVal[which.max(test$spec)]
return(list(maxSpec=maxSpec,maxFreq=maxFreq,pVal=pVal))