library(smooth)

## Warning: package 'smooth' was built under R version 4.0.2

## Loading required package: greybox

## Warning: package 'greybox' was built under R version 4.0.2

## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo

## Package "greybox", v0.6.0 loaded.

## This is package "smooth", v2.6.0

Importing dataset “Global Temperatures”, attaching it and reading the names of columns present in it.

globaltemp=read.csv(file = "C://temp//GlobalTemperatures.csv", header = TRUE)
attach(globaltemp)
names(globaltemp)

## [1] "dt"                                       
## [2] "LandAverageTemperature"                   
## [3] "LandAverageTemperatureUncertainty"        
## [4] "LandMaxTemperature"                       
## [5] "LandMaxTemperatureUncertainty"            
## [6] "LandMinTemperature"                       
## [7] "LandMinTemperatureUncertainty"            
## [8] "LandAndOceanAverageTemperature"           
## [9] "LandAndOceanAverageTemperatureUncertainty"

Removing all columns showing “uncertainty” as well as “landmintemperature” as we do not intend to use them in our analysis.

globaltemp=subset(globaltemp, select = -c(LandAndOceanAverageTemperatureUncertainty, LandAverageTemperatureUncertainty, LandMaxTemperatureUncertainty, LandMinTemperatureUncertainty, LandMinTemperature))

Reading names of remaining columns.

names(globaltemp)

## [1] "dt"                             "LandAverageTemperature"        
## [3] "LandMaxTemperature"             "LandAndOceanAverageTemperature"

Creating time-series objects for the 3 types of temperature readings.

tslandavg=ts(data = LandAverageTemperature, start = c(1850, 1), end = c(2015,12), frequency = 12)
tslandmax=ts(data = LandMaxTemperature, start = c(1850, 1), end = c(2015,12), frequency = 12)
tslandoceanavg=ts(data = LandAndOceanAverageTemperature, start = c(1850, 1), end = c(2015,12), frequency = 12)

Plotting timeseries objects.

plot(tslandavg)

plot(tslandmax)

plot(tslandoceanavg)

We see an overall positive trend for all 3 quantities. However, to be able to comment any further, we need to break down each time-series into 3 components - trend, seasonality, and residual.

plot(decompose(tslandavg))

plot(decompose(tslandmax))

plot(decompose(tslandoceanavg))

Above graphs shows a positive trend for all 3 quantities. We also see the presence of a seasonal variation where each block repeats itself every ~20 years. Random variation is seen for all as well.

10-year moving average on Land and Ocean Average Temperature

sma(tslandoceanavg, order = 10)

## Time elapsed: 0.03 seconds
## Model estimated: SMA(10)
## Initial values were produced using backcasting.
## 
## Loss function type: MSE; Loss function value: 2.1596
## Error standard deviation: 1.4703
## Sample size: 1992
## Number of estimated parameters: 2
## Number of degrees of freedom: 1990
## Information criteria:
##      AIC     AICc      BIC     BICc 
## 7190.693 7190.699 7201.887 7201.910