Work01
Faythe
April 1, 2016
Sea Ice Summary
load("C:/Users/duranf/Downloads/climate_Time_Series_Extravaganza.Rdata")
summary(ice.ts)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.566 8.871 12.210 11.580 14.400 16.350tsp(ice.ts)## [1] 1978.750 2016.167 12.000Preliminary Plots
plot(ice.ts)
boxplot(ice.ts~cycle(ice.ts),xlab="Month",ylab="Millions of sq km")#see the seasons
my.xlim <- range(ice.ts)
h<-hist(ice.ts, breaks=12, col="chartreuse3", xlab="Sea Ice (millions of sq km)",
main="",xlim=my.xlim)
xfit<-seq(min(ice.ts),max(ice.ts),length=15)
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="bisque1", lwd=2)
boxplot(ice.ts, horizontal=TRUE, outline=TRUE, axes=FALSE,
ylim=my.xlim, col = "lightblue4", add = TRUE, boxwex=3)
The first plot above is all the sea ice data over time. We can see that there is seasonality to the data, but a trend is not apparent. To see the season more clearly I made a boxplot of the sea ice by month (I think). We can see that sea ice increases from October to March and decreases April through September. Next I made a histogram of the data. We can see that the data are not evenly distributed (not verified by tests).
Linear model
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-05Moving averages and trend line
I chose to use 2 and 15 years as my smoothing intervals because I wanted to see the stark difference in smoothing over short and longer intervals.
ma3 <- filter(x=ice.ts, filter=rep(x=1/3,times=3), sides=2)
ma15 <- filter(x=ice.ts, filter=rep(x=1/15,times=15), sides=2)
plot(ice.ts,col="azure3")
lines(ma3,col="sandybrown",lwd=2)
lines(ma15,col="turquoise2",lwd=2)
abline(ice.lm, col="navy",lwd=2, lty="dashed")
Decomposition
ice.d <- decompose(ice.ts)
plot(ice.d)
Look at that downward trend in sea ice!
New data
From the Time Series Data Library, I chose the Personal savings as % of disposable income 1955-1979 data set.
setwd("E:/")
read.csv("save.csv",header=T)## Quarter persave
## 1 1955Q1 4.9
## 2 1955Q2 5.2
## 3 1955Q3 5.7
## 4 1955Q4 5.7
## 5 1956Q1 6.2
## 6 1956Q2 6.7
## 7 1956Q3 6.9
## 8 1956Q4 7.1
## 9 1957Q1 6.6
## 10 1957Q2 7.0
## 11 1957Q3 6.9
## 12 1957Q4 6.4
## 13 1958Q1 6.6
## 14 1958Q2 6.4
## 15 1958Q3 7.0
## 16 1958Q4 7.3
## 17 1959Q1 6.0
## 18 1959Q2 6.3
## 19 1959Q3 4.8
## 20 1959Q4 5.3
## 21 1960Q1 5.4
## 22 1960Q2 4.7
## 23 1960Q3 4.9
## 24 1960Q4 4.4
## 25 1961Q1 5.1
## 26 1961Q2 5.3
## 27 1961Q3 6.0
## 28 1961Q4 5.9
## 29 1962Q1 5.9
## 30 1962Q2 5.6
## 31 1962Q3 5.3
## 32 1962Q4 4.5
## 33 1963Q1 4.7
## 34 1963Q2 4.6
## 35 1963Q3 4.3
## 36 1963Q4 5.0
## 37 1964Q1 5.2
## 38 1964Q2 6.2
## 39 1964Q3 5.8
## 40 1964Q4 6.7
## 41 1965Q1 5.7
## 42 1965Q2 6.1
## 43 1965Q3 7.2
## 44 1965Q4 6.5
## 45 1966Q1 6.1
## 46 1966Q2 6.3
## 47 1966Q3 6.4
## 48 1966Q4 7.0
## 49 1967Q1 7.6
## 50 1967Q2 7.2
## 51 1967Q3 7.5
## 52 1967Q4 7.0
## 53 1968Q1 7.6
## 54 1968Q2 7.2
## 55 1968Q3 7.5
## 56 1968Q4 7.8
## 57 1969Q1 7.2
## 58 1969Q2 7.5
## 59 1969Q3 5.6
## 60 1969Q4 5.7
## 61 1970Q1 4.9
## 62 1970Q2 5.1
## 63 1970Q3 6.2
## 64 1970Q4 6.0
## 65 1971Q1 6.1
## 66 1971Q2 7.5
## 67 1971Q3 7.8
## 68 1971Q4 8.0
## 69 1972Q1 8.0
## 70 1972Q2 8.1
## 71 1972Q3 7.6
## 72 1972Q4 7.1
## 73 1973Q1 6.6
## 74 1973Q2 5.6
## 75 1973Q3 5.9
## 76 1973Q4 6.6
## 77 1974Q1 6.8
## 78 1974Q2 7.8
## 79 1974Q3 7.9
## 80 1974Q4 8.7
## 81 1975Q1 7.7
## 82 1975Q2 7.3
## 83 1975Q3 6.7
## 84 1975Q4 7.5
## 85 1976Q1 6.4
## 86 1976Q2 9.7
## 87 1976Q3 7.5
## 88 1976Q4 7.1
## 89 1977Q1 6.4
## 90 1977Q2 6.0
## 91 1977Q3 5.7
## 92 1977Q4 5.0
## 93 1978Q1 4.2
## 94 1978Q2 5.1
## 95 1978Q3 5.4
## 96 1978Q4 5.1
## 97 1979Q1 5.3
## 98 1979Q2 5.0
## 99 1979Q3 4.8
## 100 1979Q4 4.7
## 101 1980Q1 5.0
## 102 1980Q2 5.4
## 103 1980Q3 4.3
## 104 1980Q4 3.5
## 105 NA
## 106 Personal savings as % of disposable income 1955-1979 NAS<-read.csv("save.csv",header=T)
SAVE<-S$persave
save<- ts(SAVE,start=c(1955,4),end=c(1979,4),frequency=4)
plot(save,ylab="Personal savings as a % of disposable income")
my.xlim <- range(save)
h<-hist(save, breaks=7, col="chartreuse3", xlab="% Savings",
main="",xlim=my.xlim)
xfit<-seq(min(save),max(save),length=5)
yfit<-dnorm(xfit,mean=mean(save),sd=sd(save))
yfit <- yfit*diff(h$mids[1:2])*length(save)
lines(xfit, yfit, col="bisque1", lwd=2)
boxplot(save, horizontal=TRUE, outline=TRUE, axes=FALSE,
ylim=my.xlim, col = "lightblue4", add = TRUE, boxwex=3)
Linear model
savetime <- time(save)
save.lm <- lm(save ~ savetime)
summary(save.lm)##
## Call:
## lm(formula = save ~ savetime)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.5709 -0.7931 0.0011 0.8641 2.9999
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -73.29710 30.37382 -2.413 0.0177 *
## savetime 0.04046 0.01544 2.621 0.0102 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.064 on 95 degrees of freedom
## Multiple R-squared: 0.06746, Adjusted R-squared: 0.05764
## F-statistic: 6.872 on 1 and 95 DF, p-value: 0.0102There seems to be a downward trend.
Moving averages and trend line
ma3 <- filter(x=save, filter=rep(x=1/3,times=3), sides=2)
ma12 <- filter(x=save, filter=rep(x=1/9,times=9), sides=2)
plot(save,col="azure3")
lines(ma3,col="sandybrown",lwd=2)
lines(ma12,col="turquoise2",lwd=2)
abline(save.lm, col="navy",lwd=2, lty="dashed")
These data are much less pretty than the ice data. Lets see what happens when I decompose…
Decomposition
save.d<-decompose(save)
plot(save.d)
I do not see an obvious trend. What I see is a very strong seasonal pattern. I may be doing this incorrectly, but when I try to pull out the season in a box plot, I do not see an evident pattern (see below).
boxplot(save~cycle(save),xlab="Quarter",ylab="Personal savings")
Trouble shooting
I tried to import the data using the “rdatamarket” library, and read a bit about how the data are imported if you use the dmseries function. It was my understanding that it brings it in as a zoo timeseries. I was able to do most of the above functions except for making a boxplot and using the decompose function. I tried to troubleshoot for a bit, but decide to import my data the way Matt did (Thanks Matt!!) and continued my analysis.How did you guys import your other data?