lab_timeseriesgraphics – BAN430 Forecasting

Time series graphics

Before you start

This is an in-class lab: work through the material below at your own pace (in pairs or small groups is fine) — I’ll walk around to help, and we’ll stop along the way to discuss as a group.

The lecture covered the theory — trend, seasonality, cycles, autocorrelation, white noise, stationarity. Today you apply it: load real data, produce the graphics yourself, and interpret what you see. Don’t just make the plots — for every plot, write down (in the text, or on paper) what it tells you.

library(fpp3)
library(tidyverse)

Cheat sheet: turning a date/time column into a tsibble index

Frequency	Function
Annual	`start:end`
Quarterly	`yearquarter()`
Monthly	`yearmonth()`
Weekly	`yearweek()`
Daily	`as_date()`, `ymd()`
Sub-daily	`as_datetime()`, `ymd_hms()`

A tsibble is created with as_tsibble(index = <time column>, key = <grouping column(s)>). To re-aggregate an existing tsibble to a coarser time scale, use group_by_key() %>% index_by(<new time column> = ~<function of the old one>) %>% summarise(...).

Cheat sheet: graphics functions

Plot	Function
Time plot	`autoplot(data, variable)`
Seasonal plot	`gg_season(data, variable, period = ...)`
Seasonal subseries plot	`gg_subseries(data, variable)`
Scatter plot	`ggplot(data, aes(x, y)) + geom_point()`
Lag plot	`gg_lag(data, variable, lags = 1:k)`
Autocorrelation plot	`ACF(data, variable) %>% autoplot()`
Distribution	`geom_histogram()`, `geom_boxplot()`, `stat_density()`

Warm-up: city temperatures across Norway

A quick warm-up before the main case, using daily temperature data for four Norwegian cities — a first taste of the key argument on something familiar.

citytemp <- readr::read_csv2("https://raw.githubusercontent.com/holleland/BAN430/master/data/citytemp.csv",
                              show_col_types = FALSE)

ℹ Using "','" as decimal and "'.'" as grouping mark. Use `read_delim()` for more control.

citytemp_ts <- citytemp %>%
  mutate(date = as_date(date, format = "%d.%m.%Y")) %>%
  filter(!is.na(date)) %>%
  as_tsibble(index = date, key = name) %>%
  fill_gaps()

citytemp_ts

# A tsibble: 35,068 x 4 [1D]
# Key:       name [4]
   name             station date       meanTemp
   <chr>            <chr>   <date>        <dbl>
 1 Bergen - Florida SN50540 2000-01-01      6.3
 2 Bergen - Florida SN50540 2000-01-02      6.3
 3 Bergen - Florida SN50540 2000-01-03      6.7
 4 Bergen - Florida SN50540 2000-01-04      4.6
 5 Bergen - Florida SN50540 2000-01-05      4.6
 6 Bergen - Florida SN50540 2000-01-06      6.5
 7 Bergen - Florida SN50540 2000-01-07      6.3
 8 Bergen - Florida SN50540 2000-01-08      6.4
 9 Bergen - Florida SN50540 2000-01-09      4.1
10 Bergen - Florida SN50540 2000-01-10      5.3
# ℹ 35,058 more rows

Q: How many series are in citytemp_ts? What’s the key, and what’s the index? (fill_gaps() is there because there are a few missing days per station; gg_season() below won’t run without it.)

Now make these three plots:

# Time plot: one line per city

# Seasonal plot (period = "year")

# Seasonal subseries plot — hint: aggregate to monthly means first with
# group_by_key() %>% index_by() %>% summarise(), same as wp_month later

Now put a number on what you saw in the plots. For each city, compute the average temperature per calendar month (Jan, Feb, …, Dec, pooling across all years — not year-month), then the minimum, maximum, and range of those 12 monthly averages.

# Hint: mutate(month = month(date, label = TRUE)) %>% group_by(name, month)
# %>% summarise(...) to get the 12 monthly averages per city, then
# group_by(name) %>% summarise(min = ___, max = ___, range = ___)

Q: Do all four cities have roughly the same seasonal shape? Do they have the same seasonal amplitude (range)? Does the ranking from your table match what the seasonal plot suggested? Any guesses why the amplitudes differ, geographically?

The case: offshore wind power

You have five years (2015–2019) of hourly simulated power production data (in MW) for two proposed Norwegian offshore wind farm locations: Utsira Nord and Sørlig Nordsjø 2.

You work as an analyst asked to give an initial, purely data-driven, recommendation on where to build the first offshore wind farm. You have no cost or grid-connection information — only five years of production data. What can the data alone tell you?

Keep that question in mind as you work through the tasks below — you’ll return to it at the end.

Task 0: Load the data

The data lives in the ban430data package as windpower — install it if you haven’t already.

# install.packages("remotes")
remotes::install_github("holleland/ban430data")

library(ban430data)
data(windpower)

wp_hour <- windpower
wp_hour

# A tsibble: 87,648 x 3 [1h] <?>
# Key:       Place [2]
   Place            powerprod datetime           
   <chr>                <dbl> <dttm>             
 1 Sørlig Nordsjø 2        15 2015-01-01 00:00:00
 2 Sørlig Nordsjø 2        15 2015-01-01 01:00:00
 3 Sørlig Nordsjø 2        15 2015-01-01 02:00:00
 4 Sørlig Nordsjø 2        15 2015-01-01 03:00:00
 5 Sørlig Nordsjø 2        15 2015-01-01 04:00:00
 6 Sørlig Nordsjø 2        15 2015-01-01 05:00:00
 7 Sørlig Nordsjø 2        15 2015-01-01 06:00:00
 8 Sørlig Nordsjø 2        15 2015-01-01 07:00:00
 9 Sørlig Nordsjø 2        15 2015-01-01 08:00:00
10 Sørlig Nordsjø 2        15 2015-01-01 09:00:00
# ℹ 87,638 more rows

Q: What is the index variable, and what is the key? Why do we need a key here — for the same reason citytemp needed one above?

Task 1: Aggregate to other time scales

Hourly data is hard to read as a time plot over five years. Create three new tsibbles — wp_day, wp_week and wp_month — by aggregating wp_hour with the mean production. The daily version is done for you; use the cheat sheet above (and the fact that a datetime can be turned into a date with as.Date()) to complete the other two.

wp_day <- wp_hour %>%
  group_by_key() %>%
  index_by(date = ~as.Date(.)) %>%
  summarise(powerprod = mean(powerprod, na.rm = TRUE))

wp_day

# A tsibble: 3,654 x 3 [1D]
# Key:       Place [2]
   Place            date       powerprod
   <chr>            <date>         <dbl>
 1 Sørlig Nordsjø 2 2014-12-31     15   
 2 Sørlig Nordsjø 2 2015-01-01     13.1 
 3 Sørlig Nordsjø 2 2015-01-02     12.5 
 4 Sørlig Nordsjø 2 2015-01-03     15   
 5 Sørlig Nordsjø 2 2015-01-04     14.8 
 6 Sørlig Nordsjø 2 2015-01-05      4.81
 7 Sørlig Nordsjø 2 2015-01-06     14.2 
 8 Sørlig Nordsjø 2 2015-01-07     14.4 
 9 Sørlig Nordsjø 2 2015-01-08     15   
10 Sørlig Nordsjø 2 2015-01-09      7.26
# ℹ 3,644 more rows

wp_week <- wp_hour %>%
  group_by_key() %>%
  index_by(yearweek = ___) %>%
  summarise(powerprod = ___)

wp_month <- wp_hour %>%
  group_by_key() %>%
  index_by(yearmonth = ___) %>%
  summarise(powerprod = ___)

Task 2: Time plots at every scale

Produce autoplot() time plots for wp_hour, wp_day, wp_week and wp_month.

Q: At which scale(s) can you see a trend? A cycle? Seasonality? Does the picture change as you aggregate more?

Task 3: Seasonal plots

Use gg_season() on an appropriate aggregate (or several) to check for seasonality at different periods: within a day, within a week, within a year.

Q: Is there a daily pattern? A weekly pattern? An annual pattern? Is it the same at both locations?

Task 4: Seasonal subseries plots

Pick the time scale and period where you found the clearest seasonal pattern in Task 3, and use gg_subseries() to look at it more closely.

Q: Does gg_subseries() show you anything gg_season() didn’t — e.g. is the seasonal pattern stable across the five years, or changing?

Task 5: Relationship between the two locations

So far you’ve looked at each location separately. Now compare them directly.

# Hint: pivot_wider(names_from = Place, values_from = powerprod) first,
# then ggplot() + geom_point() + geom_smooth()

Q: Do the two locations move together? Is the relationship linear? Does your answer change depending on which time scale (hourly/daily/weekly/monthly) you use? Why might that be?

Task 6: Lag plots and autocorrelation

Choose one location (filter(Place == ...)) and one time scale, and produce a lag plot and an ACF plot.

Q: At which lag(s) is the autocorrelation strongest? Does that match the seasonal period you found in Task 3? Would you say this series looks like white noise, or not — why?

Task 7 (if time permits): Distribution

Use geom_histogram(), stat_density() or geom_boxplot() to look at the distribution of production values (e.g. split by month, or by location).

Q: Is the distribution symmetric? Are there a lot of hours/days at or near zero production? What might that mean physically?

Wrap-up discussion

Come back to the opening question:

If you were to decide where to build the first offshore wind farm based solely on the data you have explored today, which location would you choose, and why? What are you not able to say from this data alone? Does your recommendation depend on which time scale you looked at?

Discuss with your neighbors, then we’ll compare answers across the room.