SeaIce

library(repmis)

## Warning: package 'repmis' was built under R version 3.2.4

githubURL <- "https://github.com/AndyBunn/TeachingData/raw/master/climate_Time_Series_Extravaganza.Rdata"
source_data(githubURL) 

## Downloading data from: https://github.com/AndyBunn/TeachingData/raw/master/climate_Time_Series_Extravaganza.Rdata

## SHA-1 hash of the downloaded data file is:
## 48125039f27ef2efe9ea38ac221d894f640c2fa5

##  [1] "loti.zoo" "co2.zoo"  "ice.zoo"  "ohc.zoo"  "sl.zoo"   "loti.ts" 
##  [7] "co2.ts"   "ice.ts"   "ohc.ts"   "sl.ts"

Simple plotting and summary statistics

plot(ice.ts)

summary(ice.ts)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   3.566   8.871  12.210  11.580  14.400  16.350

class(ice.ts)

## [1] "ts"

Just looking at the plot, I can see a somewhat negative trend in the data over time.

library(moments)

## Warning: package 'moments' was built under R version 3.2.3

kt <-kurtosis(ice.ts)
sk <- skewness(ice.ts)
my.xlim <- range(ice.ts)
h<-hist(ice.ts, breaks=10, col="lightblue", xlab="ice extent (sq km)",main="",xlim=my.xlim) 
xfit<-seq(min(ice.ts),max(ice.ts),length=100) 
yfit<-dnorm(xfit,mean=mean(ice.ts),sd=sd(ice.ts)) 
yfit <- yfit*diff(h$mids[1:2])*length(ice.ts) 
lines(xfit, yfit, col="darkblue", lwd=2)
boxplot(ice.ts, horizontal=TRUE,  outline=TRUE,  axes=FALSE, ylim=my.xlim, col = "lightgreen", add = TRUE,boxwex=3)
text(x = 4, y=60, labels = paste("Kurtosis=",round(kt,2)),pos = 4)
text(x = 4, y=55, labels = paste("Skewness=",round(sk,2)),pos = 4)

The plot shows normal distribution with a very little skewness to the right.

Is there a linear trend through time?

icetime <- time(ice.ts)
ice.lm <- lm(ice.ts ~ icetime)
summary(ice.lm)

## 
## Call:
## lm(formula = ice.ts ~ icetime)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7.1893 -2.6979  0.6955  2.8952  4.4143 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 119.52096   27.23324   4.389 1.42e-05 ***
## icetime      -0.05404    0.01363  -3.964 8.58e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.131 on 448 degrees of freedom
## Multiple R-squared:  0.03388,    Adjusted R-squared:  0.03173 
## F-statistic: 15.71 on 1 and 448 DF,  p-value: 8.585e-05

The results show that there was an annual decrease in sea ice of 0.05, or 5%.

I used a moving average filtering method in order to smooth the data.

ma10 <- filter(x=ice.ts, filter=rep(x=1/10,times=10), sides=2)
ma5 <- filter(x=ice.ts, filter=rep(x=1/5,times=5), sides=2)
plot(ice.ts,col="grey")
lines(ma10,col="red",lwd=2)
lines(ma5,col="blue",lwd=2)
abline(ice.lm, col="black",lwd=2, lty="dashed") 

##Decomposing by season In order to remove the seasonal component of the data, I decomposed the data

ice.ts<- decompose(ice.ts) 
plot(ice.ts)