stat481/581: introductiontotime seriesanalysis - math.unm.edu
TRANSCRIPT
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STAT481/581:Introduction to TimeSeries Analysis
Ch2. Time series graphics
OTexts.org/fpp3/
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Outline
1 Time series in R
2 Time plots
3 Seasonal plots
4 Seasonal or cyclic?
5 Lag plots and autocorrelation
6 White noise
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Outline
1 Time series in R
2 Time plots
3 Seasonal plots
4 Seasonal or cyclic?
5 Lag plots and autocorrelation
6 White noise
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Class packages
# Data manipulation and plotting functionslibrary(tidyverse)# Forecasting functionslibrary(fable)# Time series manipulationlibrary(tsibble)# Time series graphics and statisticslibrary(feasts)# Functions to work with date-timeslibrary(lubridate)# Tidy time series datalibrary(tsibbledata)
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tsibbledata datasets
1 anasett: Passenger numbers on Anasett airline flights2 aus_livestock: Meat production in Australia for human
consumption from Q3 1965 to Q4 2018.3 aus_production: Quarterly estimates of manufacturing
production of selected commodities in Australia.4 aus_retail: Australian retail trade turnover (total value
of retail traded).5 gafa_stock: GAFA stock prices.6 global_economy: Global economic indicators.
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tsibbledata datasets
7 hh_budget: Household budget characteristics.8 nyc_bikes: A sample from NYC Citi Bike usage of 10
bikes throughout 2018.9 olympic_running: Fastest running times for Olympic
races.10 PBS: Monthly Medicare Australia prescription data.11 pelt: Pelt trading records.12 vic_elec: Half-hourly electricity demand for Victoria,
Australia
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tsibble objects
A tsibble allows storage and manipulation of time series in R.A tsibble is a data- and model-oriented object.
It contains:
Measured variable(s): numbers of interestKey variable(s): identifiers for each seriesAn index: time information about the observationA tsibble is sorted by its key first and then indexKey variable(s) together with the index uniquely identifieseach record
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tsibble objects example
#Creating a tsibble objectlibrary(tsibble)e1 <- tsibble(year = 2012:2016, x = c(1,2,1,2,2),y = c(123,39,78,52,110), index = year, key = x)
e1
## # A tsibble: 5 x 3 [1Y]## # Key: x [2]## year x y## <int> <dbl> <dbl>## 1 2012 1 123## 2 2014 1 78## 3 2013 2 39## 4 2015 2 52## 5 2016 2 110
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tsibble objects example
# yearquarter returns a numeric value that can be addede2<- tsibble(
qtr = rep(yearquarter("2010 Q1") + 0:9, 3),group = rep(c("x", "y", "z"), each = 10),value = rnorm(30),key = group, index = qtr)
e2
## # A tsibble: 30 x 3 [1Q]## # Key: group [3]## qtr group value## <qtr> <chr> <dbl>## 1 2010 Q1 x 0.449## 2 2010 Q2 x 0.702## 3 2010 Q3 x -0.732## 4 2010 Q4 x 0.284## 5 2011 Q1 x -1.39## 6 2011 Q2 x 0.895## 7 2011 Q3 x -1.47## 8 2011 Q4 x 1.21## 9 2012 Q1 x -1.28## 10 2012 Q2 x -0.621## # ... with 20 more rows
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The tsibble index
Common time index variables can be created withthese functions:
Frequency Function
Annual start year:end yearQuarterly yearquarter()Monthly yearmonth()Weekly yearweek()Daily as_Date(), ymd()Sub-daily as_datetime()
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Example for time index variables
2015:2020
## [1] 2015 2016 2017 2018 2019 2020
yearquarter("2010 Q1")+0:3
## [1] "2010 Q1" "2010 Q2" "2010 Q3" "2010 Q4"
yearmonth("2010 1")+0:3
## [1] "2010 Jan" "2010 Feb" "2010 Mar" "2010 Apr"
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Example for time index variables
yearweek("2010 1")+0:3
## [1] "2009 W53" "2010 W01" "2010 W02" "2010 W03"
as.Date("2020-01-22") + 0:3
## [1] "2020-01-22" "2020-01-23" "2020-01-24"## [4] "2020-01-25"
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Example for time index variables
ymd("2020-01-22")+0:3
## [1] "2020-01-22" "2020-01-23" "2020-01-24"## [4] "2020-01-25"
as_datetime("2020-01-22 00:50:50")+0:3
## [1] "2020-01-22 00:50:50 UTC"## [2] "2020-01-22 00:50:51 UTC"## [3] "2020-01-22 00:50:52 UTC"## [4] "2020-01-22 00:50:53 UTC"
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Coerce a dataset to be an tsibbledata ob-ject
olympic_running %>% as_tsibble(key = c(Length, Sex), index = Year)
## # A tsibble: 312 x 4 [4Y]## # Key: Length, Sex [14]## Year Length Sex Time## <dbl> <fct> <chr> <dbl>## 1 1896 100m men 12## 2 1900 100m men 11## 3 1904 100m men 11## 4 1908 100m men 10.8## 5 1912 100m men 10.8## 6 1916 100m men NA## 7 1920 100m men 10.8## 8 1924 100m men 10.6## 9 1928 100m men 10.8## 10 1932 100m men 10.3## # ... with 302 more rows
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The key to many time series
tsibbledata::olympic_running %>%group_by_key() %>%slice(1) %>%head(6) %>%knitr::kable(booktabs=TRUE)
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The key to many time series
Year Length Sex Time
1896 100m men 12.01928 100m women 12.21900 200m men 22.21948 200m women 24.41896 400m men 54.21964 400m women 52.0
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Australian GDP
#filter is to select a subset in rowsaus_economy <- global_economy %>%
filter(Code == "AUS")
## # A tsibble: 58 x 9 [1Y]## # Key: Country [1]## Country Code Year GDP Growth CPI## <fct> <fct> <dbl> <dbl> <dbl> <dbl>## 1 Austra~ AUS 1960 1.86e10 NA 7.96## 2 Austra~ AUS 1961 1.96e10 2.49 8.14## 3 Austra~ AUS 1962 1.99e10 1.30 8.12## 4 Austra~ AUS 1963 2.15e10 6.21 8.17## 5 Austra~ AUS 1964 2.38e10 6.98 8.40## 6 Austra~ AUS 1965 2.59e10 5.98 8.69## 7 Austra~ AUS 1966 2.73e10 2.38 8.98## 8 Austra~ AUS 1967 3.04e10 6.30 9.29## 9 Austra~ AUS 1968 3.27e10 5.10 9.52## 10 Austra~ AUS 1969 3.66e10 7.04 9.83## # ... with 48 more rows, and 3 more variables:## # Imports <dbl>, Exports <dbl>,## # Population <dbl>
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Outline
1 Time series in R
2 Time plots
3 Seasonal plots
4 Seasonal or cyclic?
5 Lag plots and autocorrelation
6 White noise
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Australian GDP
aus_economy %>% autoplot(GDP)
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Time plots
ansett %>%filter(Airports=="MEL-SYD", Class=="Economy") %>%autoplot(Passengers)
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Time plots
# Taking a subset of the time series according to timea10.subset <- PBS %>% filter(ATC2 == "A10")%>%
filter_index("2008 Jan")a10.subset
## # A tsibble: 4 x 9 [1M]## # Key: Concession, Type, ATC1, ATC2 [4]## Month Concession Type ATC1 ATC1_desc## <mth> <chr> <chr> <chr> <chr>## 1 2008 Jan Concessio~ Co-p~ A Alimenta~## 2 2008 Jan Concessio~ Safe~ A Alimenta~## 3 2008 Jan General Co-p~ A Alimenta~## 4 2008 Jan General Safe~ A Alimenta~## # ... with 4 more variables: ATC2 <chr>,## # ATC2_desc <chr>, Scripts <dbl>, Cost <dbl>
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Time plots
a10 <- PBS %>%filter(ATC2 == "A10") %>%summarise(Cost = sum(Cost)/1e6)
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Time plots
a10 %>% autoplot(Cost) +ylab("$ million") + xlab("Year") +ggtitle("Antidiabetic drug sales")
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Your turn
Create plots of the following time series: Bricksfrom aus_production, Lynx from pelt,Google from gafa_stockUse help() to find out about the data in eachseries.For the last plot, modify the axis labels and title.
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Are time plots the best?
maxtemp %>%autoplot(Temperature) +xlab("Week") + ylab("Max temperature")
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Are time plots the best?
maxtemp %>%ggplot(aes(x = Day, y = Temperature)) + geom_point() +xlab("Week") + ylab("Max temperature")
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Are time plots the best?
2012 2013 2014 2015Day
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Temperature
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Are time plots the best?
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Outline
1 Time series in R
2 Time plots
3 Seasonal plots
4 Seasonal or cyclic?
5 Lag plots and autocorrelation
6 White noise
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Seasonal plots
a10 %>% gg_season(Cost, labels = "both") +ylab("$ million") + ggtitle("Seasonal plot: antidiabetic drug sales")
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Seasonal plot: antidiabetic drug sales
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Seasonal plots
Data plotted against the individual “seasons” inwhich the data were observed. (In this case a“season” is a month.)Something like a time plot except that the datafrom each season are overlapped.Enables the underlying seasonal pattern to beseen more clearly, and also allows anysubstantial departures from the seasonal patternto be easily identified.In R: gg_season()
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Seasonal subseries plots
a10 %>%gg_subseries(Cost) + ylab("$ million") +ggtitle("Subseries plot: antidiabetic drug sales")
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Subseries plot: antidiabetic drug sales
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Seasonal subseries plots
Data for each season collected together in timeplot as separate time series.Enables the underlying seasonal pattern to beseen clearly, and changes in seasonality overtime to be visualized.In R: gg_subseries()
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Quarterly Australian Beer Production
beer <- aus_production %>%select(Quarter, Beer) %>%filter(year(Quarter) >= 1992)
beer %>% autoplot(Beer)
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Quarterly Australian Beer Production
beer %>% gg_season(Beer, labels="right")
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Quarterly Australian Beer Production
beer %>% gg_subseries(Beer)
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Your turn
Look at the quarterly tourism data for the SnowyMountains
snowy <- filter(tourism,Region == "Snowy Mountains",Purpose == "Holiday")
Use autoplot(), gg_season() andgg_subseries() to explore the data.What do you learn?
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Outline
1 Time series in R
2 Time plots
3 Seasonal plots
4 Seasonal or cyclic?
5 Lag plots and autocorrelation
6 White noise
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Time series patterns
Trend pattern exists when there is a long-termincrease or decrease in the data.
Seasonal pattern exists when a series is influencedby seasonal factors (e.g., the quarter ofthe year, the month, or day of the week).
Cyclic pattern exists when data exhibit rises andfalls that are not of fixed period.
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Time series components
Differences between seasonal and cyclicpatterns:
seasonal pattern constant length; cyclic patternvariable lengthaverage length of cycle longer than length ofseasonal patternmagnitude of cycle more variable thanmagnitude of seasonal pattern
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Time series patterns
as_tsibble(fma::elec) %>%filter(index >= 1980) %>% # or filter_index("1980 Jan" ~.)autoplot(value) + xlab("Year") + ylab("GWh") +ggtitle("Australian electricity production")
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Time series patterns
as_tsibble(fma::elec) %>%filter(index >= 1980) %>% gg_subseries(value)+xlab("Year") + ylab("GWh") +ggtitle("Australian electricity production")
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Australian electricity production
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Time series patterns
as_tsibble(fma::elec) %>%filter(index >= 1980) %>% gg_season(value)+xlab("Year") + ylab("GWh") +ggtitle("Australian electricity production")
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Time series patterns
aus_production %>%autoplot(Bricks) +ggtitle("Australian clay brick production") +xlab("Year") + ylab("million units")
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Time series patterns
aus_production %>%gg_subseries(Bricks) +ggtitle("Australian clay brick production") +xlab("Year") + ylab("million units")
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Time series patterns
aus_production %>%gg_season(Bricks) +ggtitle("Australian clay brick production") +xlab("Year") + ylab("million units")
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Time series patterns
as_tsibble(fma::hsales) %>%autoplot(value) +ggtitle("Sales of new one-family houses, USA") +xlab("Year") + ylab("Total sales")
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Time series patterns
as_tsibble(fma::hsales) %>%gg_subseries(value) +ggtitle("Sales of new one-family houses, USA") +xlab("Year") + ylab("Total sales")
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
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Sales of new one−family houses, USA
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Time series patterns
as_tsibble(fma::hsales) %>%gg_season(value) +ggtitle("Sales of new one-family houses, USA") +xlab("Year") + ylab("Total sales")
40
60
80
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecYear
Tota
l sal
es
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Sales of new one−family houses, USA
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Time series patterns
as_tsibble(fma::ustreas) %>%autoplot(value) +ggtitle("US Treasury Bill Contracts") +xlab("Day") + ylab("price")
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0 25 50 75 100Day
pric
e
US Treasury Bill Contracts
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Time series patterns
pelt %>%autoplot(Lynx) +ggtitle("Annual Canadian Lynx Trappings") +xlab("Year") + ylab("Number trapped")
0
20000
40000
60000
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1860 1880 1900 1920Year
Num
ber
trap
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Annual Canadian Lynx Trappings
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Seasonal or cyclic?
Differences between seasonal and cyclic patterns:
seasonal pattern constant length; cyclic patternvariable lengthaverage length of cycle longer than length ofseasonal patternmagnitude of cycle more variable thanmagnitude of seasonal pattern
The timing of peaks and troughs is predictable withseasonal data, but unpredictable in the long termwith cyclic data.
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Seasonal or cyclic?
Differences between seasonal and cyclic patterns:
seasonal pattern constant length; cyclic patternvariable lengthaverage length of cycle longer than length ofseasonal patternmagnitude of cycle more variable thanmagnitude of seasonal pattern
The timing of peaks and troughs is predictable withseasonal data, but unpredictable in the long termwith cyclic data.
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Outline
1 Time series in R
2 Time plots
3 Seasonal plots
4 Seasonal or cyclic?
5 Lag plots and autocorrelation
6 White noise
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Example: Beer production
new_production <- aus_production %>%filter(year(Quarter) >= 1992) # or filter_index("1992 Q1"~.)
new_production
## # A tsibble: 74 x 7 [1Q]## Quarter Beer Tobacco Bricks Cement## <qtr> <dbl> <dbl> <dbl> <dbl>## 1 1992 Q1 443 5777 383 1289## 2 1992 Q2 410 5853 404 1501## 3 1992 Q3 420 6416 446 1539## 4 1992 Q4 532 5825 420 1568## 5 1993 Q1 433 5724 394 1450## 6 1993 Q2 421 6036 462 1668## 7 1993 Q3 410 6570 475 1648## 8 1993 Q4 512 5675 443 1863## 9 1994 Q1 449 5311 421 1468## 10 1994 Q2 381 5717 475 1755## # ... with 64 more rows, and 2 more variables:## # Electricity <dbl>, Gas <dbl>
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Lagged scatterplots
Each graph shows yt plotted against yt−k fordifferent values of k .Vertical axis: lagged observationHorizontal axis: current observationColors: points are colored by the current quarter
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Example: Beer production
new_production %>% gg_lag(Beer, geom='point')
lag 7 lag 8 lag 9
lag 4 lag 5 lag 6
lag 1 lag 2 lag 3
400 450 500 400 450 500 400 450 500
400
450
500
400
450
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Beer
lag(
Bee
r, n)
season
Q1
Q2
Q3
Q4
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Lagged scatterplots
The autocorrelations are the correlationsassociated with these scatterplots.
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Autocorrelation
Covariance and correlation: measure extent oflinear relationship between two variables (y andX ).
Autocovariance and autocorrelation: measurelinear relationship between lagged values of a timeseries y .We measure the relationship between:
yt and yt−1
yt and yt−2
yt and yt−3
etc.
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Autocorrelation
Covariance and correlation: measure extent oflinear relationship between two variables (y andX ).Autocovariance and autocorrelation: measurelinear relationship between lagged values of a timeseries y .
We measure the relationship between:
yt and yt−1
yt and yt−2
yt and yt−3
etc.
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Autocorrelation
Covariance and correlation: measure extent oflinear relationship between two variables (y andX ).Autocovariance and autocorrelation: measurelinear relationship between lagged values of a timeseries y .We measure the relationship between:
yt and yt−1
yt and yt−2
yt and yt−3
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Autocorrelation
We denote the sample autocovariance at lag k by ck
and the sample autocorrelation at lag k by rk . Thendefine
ck = 1T
T∑t=k+1
(yt − y)(yt−k − y)
and rk = ck/c0
r1 indicates how successive values of y relate to each otherr2 indicates how y values two periods apart relate to eachotherrk is almost the same as the sample correlation betweenyt and yt−k .
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Autocorrelation
We denote the sample autocovariance at lag k by ck
and the sample autocorrelation at lag k by rk . Thendefine
ck = 1T
T∑t=k+1
(yt − y)(yt−k − y)
and rk = ck/c0
r1 indicates how successive values of y relate to each otherr2 indicates how y values two periods apart relate to eachotherrk is almost the same as the sample correlation betweenyt and yt−k .
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Autocorrelation
Results for first 9 lags for beer data:new_production %>% ACF(Beer, lag_max = 9)
## # A tsibble: 9 x 2 [1Q]## lag acf## <lag> <dbl>## 1 1Q -0.102## 2 2Q -0.657## 3 3Q -0.0603## 4 4Q 0.869## 5 5Q -0.0892## 6 6Q -0.635## 7 7Q -0.0542## 8 8Q 0.832## 9 9Q -0.108
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Autocorrelation
Results for first 9 lags for beer data:new_production %>% ACF(Beer, lag_max = 9) %>% autoplot()
−0.5
0.0
0.5
2 4 6 8lag [1Q]
acf
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Autocorrelation
r4 higher than for the other lags. This is due tothe seasonal pattern in the data: the peakstend to be 4 quarters apart and the troughstend to be 2 quarters apart.r2 is more negative than for the other lagsbecause troughs tend to be 2 quarters behindpeaks.Together, the autocorrelations at lags 1, 2, . . . ,make up the autocorrelation or ACF.The plot is known as a correlogram
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ACF
new_production %>% ACF(Beer) %>% autoplot()
−0.5
0.0
0.5
2 4 6 8 10 12 14 16 18lag [1Q]
acf
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Trend and seasonality in ACF plots
When data have a trend, the autocorrelationsfor small lags tend to be large and positive.When data are seasonal, the autocorrelationswill be larger at the seasonal lags (i.e., atmultiples of the seasonal frequency)When data are trended and seasonal, you see acombination of these effects.
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Aus monthly electricity production
elec2 <- as_tsibble(fma::elec) %>%filter(year(index) >= 1980)
elec2 %>% autoplot(value)
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1980 1985 1990 1995index [1M]
valu
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Aus monthly electricity production
elec2 %>% ACF(value, lag_max=48) %>%autoplot()
0.00
0.25
0.50
0.75
6 12 18 24 30 36 42 48lag [1M]
acf
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Aus monthly electricity production
Time plot shows clear trend and seasonality.
The same features are reflected in the ACF.
The slowly decaying ACF indicates trend.The ACF peaks at lags 12, 24, 36, . . . , indicateseasonality of length 12.
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Google stock price
google_2015 <- gafa_stock %>%filter(Symbol == "GOOG", year(Date) == 2015) %>%select(Date, Close)
google_2015
## # A tsibble: 252 x 2 [!]## Date Close## <date> <dbl>## 1 2015-01-02 522.## 2 2015-01-05 511.## 3 2015-01-06 499.## 4 2015-01-07 498.## 5 2015-01-08 500.## 6 2015-01-09 493.## 7 2015-01-12 490.## 8 2015-01-13 493.## 9 2015-01-14 498.## 10 2015-01-15 499.## # ... with 242 more rows
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Google stock price
google_2015 %>% autoplot(Close)
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Jan 2015 Apr 2015 Jul 2015 Oct 2015 Jan 2016Date [!]
Clo
se
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Google stock price
google_2015 %>%
ACF(Close, lag_max=100)# Error: Can't handle tsibble of irregular interval.
google_2015
## # A tsibble: 252 x 2 [!]## Date Close## <date> <dbl>## 1 2015-01-02 522.## 2 2015-01-05 511.## 3 2015-01-06 499.## 4 2015-01-07 498.## 5 2015-01-08 500.## 6 2015-01-09 493.## 7 2015-01-12 490.## 8 2015-01-13 493.## 9 2015-01-14 498.## 10 2015-01-15 499.## # ... with 242 more rows
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Google stock price
google_2015 %>%
ACF(Close, lag_max=100)# Error: Can't handle tsibble of irregular interval.
google_2015
## # A tsibble: 252 x 2 [!]## Date Close## <date> <dbl>## 1 2015-01-02 522.## 2 2015-01-05 511.## 3 2015-01-06 499.## 4 2015-01-07 498.## 5 2015-01-08 500.## 6 2015-01-09 493.## 7 2015-01-12 490.## 8 2015-01-13 493.## 9 2015-01-14 498.## 10 2015-01-15 499.## # ... with 242 more rows
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Google stock price
#mutate is to create a new variablegoogle_2015 <- google_2015 %>%
mutate(trading_day = row_number()) %>%update_tsibble(index=trading_day, regular=TRUE)
google_2015
## # A tsibble: 252 x 3 [1]## Date Close trading_day## <date> <dbl> <int>## 1 2015-01-02 522. 1## 2 2015-01-05 511. 2## 3 2015-01-06 499. 3## 4 2015-01-07 498. 4## 5 2015-01-08 500. 5## 6 2015-01-09 493. 6## 7 2015-01-12 490. 7## 8 2015-01-13 493. 8## 9 2015-01-14 498. 9## 10 2015-01-15 499. 10## # ... with 242 more rows
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Google stock price
google_2015 %>%ACF(Close, lag_max=100) %>% autoplot()
0.00
0.25
0.50
0.75
1.00
25 50 75 100lag [1]
acf
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Your turn
We have introduced the following functions:
gg_lagACF
Explore the following time series using thesefunctions. Can you spot any seasonality, cyclicity andtrend? What do you learn about the series?
Bricks from aus_productionLynx from peltVictorian Electricity Demand from aus_elec
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Which is which?
40
60
80
0 20 40 60
chir
ps p
er m
inut
e
1. Daily temperature of cow
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8000
9000
10000
11000
1974 1976 1978
thou
sand
s
2. Monthly accidental deaths
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400
600
1950 1955 1960
thou
sand
s
3. Monthly air passengers
30000
60000
90000
1860 1880 1900
thou
sand
s
4. Annual mink trappings
0.0
0.5
1.0
6 12 18
acf
A
0.0
0.5
1.0
5 10 15
acf
B
0.0
0.5
1.0
5 10 15
acf
C
0.0
0.5
1.0
6 12 18
acf
D
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Outline
1 Time series in R
2 Time plots
3 Seasonal plots
4 Seasonal or cyclic?
5 Lag plots and autocorrelation
6 White noise
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Example: White noise
wn <- tsibble(t = seq_len(36), y = rnorm(36),index = t)
wn %>% autoplot(y)
−2
−1
0
1
2
0 10 20 30t [1]
y
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Example: White noise
wn %>% ACF(y, lag_max = 10) %>%
as_tibble() %>%
tidyr::spread(lag, acf) %>%
rename_all(function(x){paste("$r_{",x,"}$",sep="")}) %>%
knitr::kable(booktabs=TRUE,
escape=FALSE, align="c", digits=3,
format.args=list(nsmall=3))
r1 r2 r3 r4 r5 r6 r7 r8 r9 r10
0.177 -0.071 -0.250 -0.020 -0.370 0.007 0.022 0.142 0.015 0.036
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Example: White noise
−0.4
−0.2
0.0
0.2
5 10 15lag [1]
acf
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Sampling distribution of autocorrelations
Sampling distribution of rk for white noise data isasymptotically N(0,1/T ).
95% of all rk for white noise must lie within±1.96/
√T .
If this is not the case, the series is probably notWN.Common to plot lines at ±1.96/
√T when
plotting ACF. These are the critical values.
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Sampling distribution of autocorrelations
Sampling distribution of rk for white noise data isasymptotically N(0,1/T ).
95% of all rk for white noise must lie within±1.96/
√T .
If this is not the case, the series is probably notWN.Common to plot lines at ±1.96/
√T when
plotting ACF. These are the critical values.
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Example: Pigs slaughtered
pigs <- aus_livestock %>%filter(State == "Victoria", Animal == "Pigs",
year(Month) >= 2014)pigs %>% autoplot(Count/1e3) +
xlab("Year") + ylab("Thousands") +ggtitle("Number of pigs slaughtered in Victoria")
80
90
100
110
2014 2016 2018Year
Tho
usan
ds
Number of pigs slaughtered in Victoria
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Example: Pigs slaughtered
pigs %>% ACF(Count) %>% autoplot()
−0.2
0.0
0.2
6 12lag [1M]
acf
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Example: Pigs slaughtered
Monthly total number of pigs slaughtered in the stateof Victoria, Australia, from January 2014 throughDecember 2018 (Source: Australian Bureau ofStatistics.)
Difficult to detect pattern in time plot.ACF shows significant autocorrelation for lag 2and 12.Indicate some slight seasonality.
These show the series is not a white noise series.
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Example: Pigs slaughtered
Monthly total number of pigs slaughtered in the stateof Victoria, Australia, from January 2014 throughDecember 2018 (Source: Australian Bureau ofStatistics.)
Difficult to detect pattern in time plot.ACF shows significant autocorrelation for lag 2and 12.Indicate some slight seasonality.
These show the series is not a white noise series.
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Example: Pigs slaughtered
Monthly total number of pigs slaughtered in the stateof Victoria, Australia, from January 2014 throughDecember 2018 (Source: Australian Bureau ofStatistics.)
Difficult to detect pattern in time plot.ACF shows significant autocorrelation for lag 2and 12.Indicate some slight seasonality.
These show the series is not a white noise series.82
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Your turn
You can compute the daily changes in the Googlestock price in 2018 using
dgoog <- gafa_stock %>%
filter(Symbol == "GOOG", year(Date) >= 2018) %>%
mutate(trading_day = row_number()) %>%
update_tsibble(index=trading_day, regular=TRUE) %>%
mutate(diff = difference(Close))
Does diff look like white noise?
83