library(tseries)
library(zoom)
library(zoo)

## 
## Attaching package: 'zoo'

## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric

library(moments)
library(ggplot2)
library(fBasics)

## Loading required package: timeDate

## 
## Attaching package: 'timeDate'

## The following objects are masked from 'package:moments':
## 
##     kurtosis, skewness

## Loading required package: timeSeries

## 
## Attaching package: 'timeSeries'

## The following object is masked from 'package:zoo':
## 
##     time<-

data <- read.csv("C:\\Users\\t420\\Desktop\\lauda.csv")

str(data)

## 'data.frame':    172 obs. of  3 variables:
##  $ ly : num  -0.001027 -0.003155 -0.000281 0.000808 0.003094 ...
##  $ lu : num  8.4 8.92 8.57 8.34 7.87 ...
##  $ lpi: num  1.49 1.49 1.5 1.51 1.51 ...

pi <- data[,3]

summary(pi)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.486   1.761   1.885   1.853   1.986   2.058

pi1 <- ts(pi)

par(mfcol=c(2,1))
plot(pi)
plot(pi1)

acf(pi, lag=12)

pacf(pi,lag=12)

sd(pi)

## [1] 0.152973

mean(pi)

## [1] 1.853205

range(pi)

## [1] 1.485736 2.057936

skewness(pi)

## [1] -0.7091381
## attr(,"method")
## [1] "moment"

kurtosis(pi)

## [1] -0.4013097
## attr(,"method")
## [1] "excess"

qplot(pi,geom= 'histogram', binwidth=20)+ xlab('Time')

s1 <- skewness(pi)

t1<-s1/sqrt(3/173)
t1

## [1] -5.385094
## attr(,"method")
## [1] "moment"

pv <- 2*(1-pnorm(t1))
pv

## [1] 2
## attr(,"method")
## [1] "moment"

lpi <- log(pi+1)*100
t.test(lpi)

## 
##  One Sample t-test
## 
## data:  lpi
## t = 250.54, df = 171, p-value < 2.2e-16
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  103.8723 105.5221
## sample estimates:
## mean of x 
##  104.6972

The result shows that we fail to reject null hypothesis. That means true mean is zero.

normalTest(lpi, method='jb')

## 
## Title:
##  Jarque - Bera Normalality Test
## 
## Test Results:
##   STATISTIC:
##     X-squared: 19.0228
##   P VALUE:
##     Asymptotic p Value: 7.4e-05 
## 
## Description:
##  Wed Mar 28 19:56:03 2018 by user: t420

The result shows the normality for inflation is rejected.