library(fpp3) # Explore some rich tsibbles ---------------------------------------- ## Olympics --------------------------------------------------------- olympic_running olympic_running |> distinct(Length) olympic_running$Year |> range() olympic_running |> filter(Length=="100") |> autoplot(Time) + geom_point() # Why the missing observations? # Just to show you what you can do olympic_running |> ggplot(aes(x=Year, y = Time, colour = Sex)) + geom_line() + geom_point(size = 1) + facet_wrap(~ Length, scales = "free_y", nrow = 2) + theme_minimal() + scale_color_brewer(palette = "Dark2") + theme(legend.position = "bottom", legend.title = element_blank()) + labs(title = "Olympic running times", y="Seconds") # Back to slides ## PBS -------------------------------------------------------------- # Let's sum Cost of A10 across Concession and Type, i.e., total A10 cost a10 <- PBS |> filter(ATC2 == "A10") |> select(Month, Concession, Type, Cost) |> summarise(TotalC = sum(Cost)) |> mutate(Cost = TotalC / 1e6) a10 # Time Series patterns ---------------------------------------- a10 |> autoplot(Cost) + #Cost labs( title = "Australian antidiabetic drug sales", y = "Cost $ (millions)" ) # Note - it will pick the first variable it sees - hence select appropriate variable # I could do it with ggplot() a10 |> ggplot(aes(x=Month, y=Cost)) + geom_line() + #geom_point() + labs( title = "Australian antidiabetic drug sales", y = "$ (millions)" ) a10 |> autoplot() + geom_point() + labs( title = "Australian antidiabetic drug sales", y = "$ (millions)" ) # What patterns do we see? aus_production |> filter(year(Quarter) >= 1980) |> autoplot(Electricity) + geom_point() + labs( title = "Australian electricity production", y = "GWh" ) # Switch in production due to cooling us_employment |> filter(Title == "Retail Trade", year(Month) >= 1980) |> autoplot(Employed / 1e3) + labs( y = "Million people", title = "Retail employment, USA" ) # A mistake in the video - peak in December - Xmas # 1991-1992 - Gulf War # 2009-2010 - GFC ## Google, Apple, Facebook, Amazon gafa_stock |> filter(Symbol == "AMZN", year(Date) >= 2014) |> autoplot(Close) + labs( title = "Amazon closing stock price", y="$" ) # No seasonality in stock prices - especially if market is efficient # Seems no trend or cycle because only looking at 1-year # Change year(Date) >= 2014 to see what happens ## Explore the pelt tsibble pelt #fur help(pelt) ?pelt #https://en.wikipedia.org/wiki/Hudson%27s_Bay_Company pelt |> autoplot(Lynx) # A bit of a plotting trick/lesson that may be useful later on pelt |> autoplot() # Add some axis labels and title pelt |> pivot_longer(2:3, names_to = "Animal") |> autoplot() + labs(title="Lynx eating Hare", y="No. of animals") # Note this is annual data - talk about population cycle # Lynx eating Hare ### BACK TO SLIDES # ACF ------------- ## Aus beer - you have seen this in the video aus_production |> filter(year(Quarter) >= 1979) |> autoplot(Beer) + geom_point() + labs( title = "Australian beer production", y="megalitres" ) aus_production |> filter(year(Quarter) >= 1979) |> gg_season(Beer, labels = "right") aus_production |> filter(year(Quarter) >= 1979) |> gg_subseries(Beer) aus_production |> filter(year(Quarter) >= 1979) |> gg_lag(Beer, geom = "point", lags = 1:12) aus_production |> filter(year(Quarter) >= 1979) |> ACF(Beer, lag_max = 20) aus_production |> filter(year(Quarter) >= 1979) |> ACF(Beer) |> autoplot() ## Contrast this with Brick production aus_production |> autoplot(Bricks) + labs( title = "Australian clay brick production", y="million units" ) aus_production |> ACF(Bricks, lag_max = 48) |> autoplot() ## An even more pronounced trend a10 |> autoplot(Cost) + geom_point() + labs( title = "Australian antidiabetic drug sales", y = "$ (millions)" ) a10 |> ACF(Cost, lag_max = 48) |> autoplot() ## Lynx ACF pelt |> autoplot(Lynx) pelt |> ACF(Lynx) |> autoplot() # you'll see plenty of examples in the tutes. # White noise and random walks --------------- # White noise set.seed(100) T=100 # Change to 1000 my_data <- tsibble(t = seq(T), y = rnorm(T), index = t) my_data |> autoplot(y) my_data |> ACF(y) |> autoplot() my_data |> gg_tsdisplay(y, plot_type = "histogram") # Random walks T=100 # Change to 1000 tsibble(t = seq(T), y = cumsum(rnorm(T)), index = t) |> gg_tsdisplay(y, plot_type = "histogram") # Lectorial activity 1 ---------------------------------------------------------- ## Snowy mountains tourism -------------------------------------------- snowy <- tourism |> filter(Region == "Snowy Mountains") |> summarise(Trips = sum(Trips)) # Notice there are 4 purposes of travel # hence sum over all four of them before you continue # Use autoplot(), gg_season(), gg_subseries() and ACF() to explore feature of the time series ## Completed --------------------------------------------------------- snowy |> autoplot(Trips) + geom_point() snowy |> gg_season(Trips, labels="both") snowy |> gg_subseries(Trips) snowy |> ACF(Trips) |> autoplot() ## Snowy (more on tourism) ----------------------------------------------------- # Or in the same way dat <- filter(tourism, Region %in% c("Snowy Mountains","Gold Coast") ) |> group_by(Region) |> summarise(Trips=sum(Trips)) dat |> autoplot(Trips) + geom_point() # Very different patterns between the two # Let's see it better dat |> gg_season(Trips,labels="right") # Very different patterns between the two dat |> gg_subseries(Trips) ## Australian state tourism # We explored this in the lecture video # If we have time we will go through it # Just quickly show plotting on the log-scale # skip the rest holidays <- tourism |> filter(Purpose == "Holiday") |> group_by(State) |> summarise(Trips = sum(Trips)) # original scale holidays |> autoplot(Trips) + labs( title= "Australian domestic holiday nights", y = "thousands of trips", x= "Year" ) # log scale holidays |> autoplot(Trips) + scale_y_log10()+ labs( title= "Australian domestic holiday nights", y = "thousands of trips", x= "Year" ) # let's filter the top three top3_tourism <- tourism |> filter(Purpose == "Holiday") |> group_by(State) |> filter(State %in% c("New South Wales", "Victoria", "Queensland")) |> summarise(Trips = sum(Trips)) # Show these and comment here - slides are a little too squashed top3_tourism |> gg_season(Trips) + labs( title= "Australian domestic holiday nights", y = "thousands of trips", x= "Year" ) top3_tourism |> gg_subseries(Trips) + labs( title= "Australian domestic holiday nights", y = "thousands of trips", x= "Year" ) # Lectorial Activity 3 ----------------------------------------------------- ## Differencing Amazon closing price ------------------------------ # You can compute and plot the daily changes in the Amazon stock price # in 2018 using the code below. Do the daily changes look like white noise? dAMZN <- gafa_stock |> filter(Symbol == "AMZN", year(Date) >= 2018) |> mutate(trading_day = row_number()) |> update_tsibble(index=trading_day, regular=TRUE) |> mutate(diff = difference(Close)) ## Completed ------------------------------------------------------ gafa_stock |> filter(Symbol == "AMZN", year(Date) >= 2018) |> autoplot() dAMZN <- gafa_stock |> filter(Symbol == "AMZN", year(Date) >= 2018) |> mutate(trading_day = row_number()) |> update_tsibble(index=trading_day, regular=TRUE) |> mutate(diff = difference(Close)) dAMZN |> autoplot(Close) dAMZN |> ACF(Close) |> autoplot() dAMZN |> autoplot(diff) dAMZN |> ACF(diff) |> autoplot() # A random walk accumulates random shocks over time. # If we remove the accumulation by taking the difference # between consecutive values, what remains are just # the random shocks themselves, i.e., the white noise. # Pigs ------------------------------------------------------------- pigs <- aus_livestock |> filter(State == "Victoria", Animal == "Pigs", year(Month) >= 2014) pigs |> autoplot(Count/1e3) + labs(title = "Number of pigs slaughtered in Victoria", y="Thousands") pigs |> gg_season() pigs |> ACF() |> autoplot()