Question 1.

require(fpp2)
## Loading required package: fpp2
## Warning: package 'fpp2' was built under R version 3.5.2
## Loading required package: ggplot2
## Warning: package 'ggplot2' was built under R version 3.5.2
## Loading required package: forecast
## Warning: package 'forecast' was built under R version 3.5.2
## Loading required package: fma
## Warning: package 'fma' was built under R version 3.5.2
## Loading required package: expsmooth
## Warning: package 'expsmooth' was built under R version 3.5.2
time_series <-ts(rnorm(365*2),start =c( 2019,1),frequency=365)
autoplot(time_series)

require(timeDate)
## Loading required package: timeDate
## Warning: package 'timeDate' was built under R version 3.5.2
ts<- timeSequence(as.Date("2019-01-01"),as.Date("2019-06-30"))
ts;
## GMT
##   [1] [2019-01-01] [2019-01-02] [2019-01-03] [2019-01-04] [2019-01-05]
##   [6] [2019-01-06] [2019-01-07] [2019-01-08] [2019-01-09] [2019-01-10]
##  [11] [2019-01-11] [2019-01-12] [2019-01-13] [2019-01-14] [2019-01-15]
##  [16] [2019-01-16] [2019-01-17] [2019-01-18] [2019-01-19] [2019-01-20]
##  [21] [2019-01-21] [2019-01-22] [2019-01-23] [2019-01-24] [2019-01-25]
##  [26] [2019-01-26] [2019-01-27] [2019-01-28] [2019-01-29] [2019-01-30]
##  [31] [2019-01-31] [2019-02-01] [2019-02-02] [2019-02-03] [2019-02-04]
##  [36] [2019-02-05] [2019-02-06] [2019-02-07] [2019-02-08] [2019-02-09]
##  [41] [2019-02-10] [2019-02-11] [2019-02-12] [2019-02-13] [2019-02-14]
##  [46] [2019-02-15] [2019-02-16] [2019-02-17] [2019-02-18] [2019-02-19]
##  [51] [2019-02-20] [2019-02-21] [2019-02-22] [2019-02-23] [2019-02-24]
##  [56] [2019-02-25] [2019-02-26] [2019-02-27] [2019-02-28] [2019-03-01]
##  [61] [2019-03-02] [2019-03-03] [2019-03-04] [2019-03-05] [2019-03-06]
##  [66] [2019-03-07] [2019-03-08] [2019-03-09] [2019-03-10] [2019-03-11]
##  [71] [2019-03-12] [2019-03-13] [2019-03-14] [2019-03-15] [2019-03-16]
##  [76] [2019-03-17] [2019-03-18] [2019-03-19] [2019-03-20] [2019-03-21]
##  [81] [2019-03-22] [2019-03-23] [2019-03-24] [2019-03-25] [2019-03-26]
##  [86] [2019-03-27] [2019-03-28] [2019-03-29] [2019-03-30] [2019-03-31]
##  [91] [2019-04-01] [2019-04-02] [2019-04-03] [2019-04-04] [2019-04-05]
##  [96] [2019-04-06] [2019-04-07] [2019-04-08] [2019-04-09] [2019-04-10]
## ...
##  [ reached getRmetricsOption('max.print') | getOption('max.print') -- omitted 81 rows ]]
years.included <- unique( as.integer( format( x=ts, format="%Y" ) ) );
holidays <- holidayLONDON(years.included) 

business.days <- ts[isBizday(ts, holidays)]; 
business.days
## GMT
##   [1] [2019-01-02] [2019-01-03] [2019-01-04] [2019-01-07] [2019-01-08]
##   [6] [2019-01-09] [2019-01-10] [2019-01-11] [2019-01-14] [2019-01-15]
##  [11] [2019-01-16] [2019-01-17] [2019-01-18] [2019-01-21] [2019-01-22]
##  [16] [2019-01-23] [2019-01-24] [2019-01-25] [2019-01-28] [2019-01-29]
##  [21] [2019-01-30] [2019-01-31] [2019-02-01] [2019-02-04] [2019-02-05]
##  [26] [2019-02-06] [2019-02-07] [2019-02-08] [2019-02-11] [2019-02-12]
##  [31] [2019-02-13] [2019-02-14] [2019-02-15] [2019-02-18] [2019-02-19]
##  [36] [2019-02-20] [2019-02-21] [2019-02-22] [2019-02-25] [2019-02-26]
##  [41] [2019-02-27] [2019-02-28] [2019-03-01] [2019-03-04] [2019-03-05]
##  [46] [2019-03-06] [2019-03-07] [2019-03-08] [2019-03-11] [2019-03-12]
##  [51] [2019-03-13] [2019-03-14] [2019-03-15] [2019-03-18] [2019-03-19]
##  [56] [2019-03-20] [2019-03-21] [2019-03-22] [2019-03-25] [2019-03-26]
##  [61] [2019-03-27] [2019-03-28] [2019-03-29] [2019-04-01] [2019-04-02]
##  [66] [2019-04-03] [2019-04-04] [2019-04-05] [2019-04-08] [2019-04-09]
##  [71] [2019-04-10] [2019-04-11] [2019-04-12] [2019-04-15] [2019-04-16]
##  [76] [2019-04-17] [2019-04-18] [2019-04-23] [2019-04-24] [2019-04-25]
##  [81] [2019-04-26] [2019-04-29] [2019-04-30] [2019-05-01] [2019-05-02]
##  [86] [2019-05-03] [2019-05-07] [2019-05-08] [2019-05-09] [2019-05-10]
##  [91] [2019-05-13] [2019-05-14] [2019-05-15] [2019-05-16] [2019-05-17]
##  [96] [2019-05-20] [2019-05-21] [2019-05-22] [2019-05-23] [2019-05-24]
## ...
##  [ reached getRmetricsOption('max.print') | getOption('max.print') -- omitted 24 rows ]]

Question 2.

require(fpp2)
help(chicken)
## starting httpd help server ... done
autoplot(chicken)

require(fpp2)

frequency(chicken)
## [1] 1
which.max(chicken)
## [1] 22

This is a yearly based data on the price of chicken in the US

Overall, there is a decreasing trend starting from 1945 to the following year.

1973 seems to be an outlier

help(dole)
autoplot(dole)

frequency(dole)
## [1] 12
which.max(dole)
## [1] 439

this is a monthly unemployment benefits in Astralia (Jan 1965 -July 1992)

Overall, there is steep increase from 1975 to 1984, from 1990 to the following year

there is no seasonality or cyclicity or trend during this period

no obvious outliers found

help(usdeaths)
autoplot(usdeaths)

frequency(usdeaths)
## [1] 12
which.max(usdeaths)
## [1] 7

This is a monthly accidental deaths in USA

There is seasonality for each year with higher death in summer and lower death in winter

no obvious outlier found

It seems to be consistent seasonality

help(gold)
autoplot(gold)

frequency(gold)
## [1] 1
which.max(gold)
## [1] 770

This time series is daily morning gold prices

Overall, there is an increasing trend from 0 to 800 and a decreasing trend from 800 to the rest

There is an outlier at day 780

help(h02)
autoplot(h02)

frequency(h02)
## [1] 12
which.max(h02)
## [1] 162

This is monthly drug sales in Australia

This is yearly seasonality with bottom at the beginning of the year and peak at the year end

overall, there is an increasing trend

no obvious outliers

library(fpp2)
help(gasoline)
autoplot(gasoline)

frequency(gasoline)
## [1] 52.17857
which.max(gasoline)
## [1] 1324

This is weekly gas supply

This is yearly seasonality with an overall increasing trend

no obvious outlier found

Question 3.

retaildata <- readxl::read_excel("retail.xlsx", skip = 1)
mytimeseries <- ts(retaildata[,"A3349873A"], frequency=12, start=c(1982,4))
ownstr <- colnames(retaildata)[20]
mytimeseries <- ts(retaildata[,ownstr], frequency=12, start=c(1982,4))
autoplot(mytimeseries)

## There is a clear and increasing trend with strong seasonal pattern that increases in sales as the level of the series increases.

Question 4.

ddj<-diff(dj)
autoplot(ddj)

ggAcf(ddj)

## The changes in the Dow Jones Index looks white noise, because the autocorrelation is close to zero. In addtion, 95% of the spikes in the ACF lie within the bounds of the graph.

Question 5.

autoplot(arrivals)

## The arrivals from New Zealand and UK has clear seasonal patterns with an overall increasing trend. ## The arrivals from Janpan decrease a lot in the 2nd quarter compared to the other quarters. ## The arrivals from New Zealand are highest in 3rd quarter and lowest in 1st quarter. ## The arrivals from UK and US are low in 2nd and 3rd quarters and high in 1st and 4th quarter.

R Markdown

When you click the Knit button a document will be generated that includes both content as well as the output of any embedded R code chunks within the document. You can embed an R code chunk like this:

summary(cars)
##      speed           dist       
##  Min.   : 4.0   Min.   :  2.00  
##  1st Qu.:12.0   1st Qu.: 26.00  
##  Median :15.0   Median : 36.00  
##  Mean   :15.4   Mean   : 42.98  
##  3rd Qu.:19.0   3rd Qu.: 56.00  
##  Max.   :25.0   Max.   :120.00

Including Plots

You can also embed plots, for example:

Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot.