Applications to resilience assesments
zoo: supports irregular time series (Zeileis’s ordered observations)
NAs and rolling windowsSource: Foley, 2021
library(tsibbledata)
library(fpp3)
library(patchwork)
library(feasts)
a <- vic_elec %>% gg_season(Demand, period = "week") +
scale_colour_gradient(breaks = NULL, labels = NULL) +
theme(legend.position = "none") +
labs(y="MWh", title="Daily")
b <- vic_elec %>% gg_season(Demand, period = "week") +
scale_colour_gradient(breaks = NULL, labels = NULL) +
theme(legend.position = "none") +
labs(y="MWh", title="Weekly")
c <- vic_elec %>% gg_season(Demand, period = "year") +
scale_colour_gradient(breaks = NULL, labels = NULL) +
labs(y="MWh", title="Annual")
(a+b+c) + plot_layout(guides= "collect") & theme_light(base_size = 14) Measures the linear relationship between lagged values of time series
# A tsibble: 9 x 2 [1Q]
lag acf
<cf_lag> <dbl>
1 1Q -0.0530
2 2Q -0.758
3 3Q -0.0262
4 4Q 0.802
5 5Q -0.0775
6 6Q -0.657
7 7Q 0.00119
8 8Q 0.707
9 9Q -0.0888 ACF is the autocorrelation function and it is useful to study the autocorrelation structure of the data
Decompose a time series into its seasonal, trend, and remainder parts:
\[y_t = S_t + T_t + R_t \] or \[y_t = S_t * T_t * R_t \]
Choice depends of case, but note that:
\[y_t = S_t * T_t * R_t \] is equivalent to \[logy_t = logS_t + logT_t + logR_t\]
Decompose a time series into its seasonal, trend, and remainder parts:
dcmp <- us_retail_employment %>%
# seasonal trend decomposition using loess
model(stl = STL(Employed))
components(dcmp)# A dable: 357 x 7 [1M]
# Key: .model [1]
# : Employed = trend + season_year + remainder
.model Month Employed trend season_year remainder season_adjust
<chr> <mth> <dbl> <dbl> <dbl> <dbl> <dbl>
1 stl 1990 Jan 13256. 13288. -33.0 0.836 13289.
2 stl 1990 Feb 12966. 13269. -258. -44.6 13224.
3 stl 1990 Mar 12938. 13250. -290. -22.1 13228.
4 stl 1990 Apr 13012. 13231. -220. 1.05 13232.
5 stl 1990 May 13108. 13211. -114. 11.3 13223.
6 stl 1990 Jun 13183. 13192. -24.3 15.5 13207.
7 stl 1990 Jul 13170. 13172. -23.2 21.6 13193.
8 stl 1990 Aug 13160. 13151. -9.52 17.8 13169.
9 stl 1990 Sep 13113. 13131. -39.5 22.0 13153.
10 stl 1990 Oct 13185. 13110. 61.6 13.2 13124.
# ℹ 347 more rows
swe_exports <- global_economy |>
filter(Country == "Sweden") |>
mutate(
`5-MA` = slider::slide_dbl(Exports, mean,
.before = 2, .after=2, .complete = TRUE),
`7-MA` = slider::slide_dbl(Exports, mean,
.before = 3, .after=3, .complete = TRUE),
`9-MA` = slider::slide_dbl(Exports, mean,
.before = 4, .after=4, .complete = TRUE)
)
swe_exports# A tsibble: 58 x 12 [1Y]
# Key: Country [1]
Country Code Year GDP Growth CPI Imports Exports Population `5-MA`
<fct> <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Sweden SWE 1960 1.48e10 NA 9.21 23.4 23.0 7484656 NA
2 Sweden SWE 1961 1.61e10 5.68 9.41 21.7 22.3 7519998 NA
3 Sweden SWE 1962 1.75e10 4.26 9.86 21.4 21.9 7561588 22.3
4 Sweden SWE 1963 1.90e10 5.33 10.1 21.5 21.9 7604328 22.1
5 Sweden SWE 1964 2.11e10 6.82 10.5 21.9 22.3 7661354 21.9
6 Sweden SWE 1965 2.33e10 3.82 11.0 22.5 21.9 7733853 21.7
7 Sweden SWE 1966 2.53e10 2.09 11.7 21.9 21.4 7807797 21.7
8 Sweden SWE 1967 2.75e10 3.37 12.2 21.0 21.1 7867931 21.8
9 Sweden SWE 1968 2.91e10 3.64 12.5 21.6 21.6 7912273 21.9
10 Sweden SWE 1969 3.16e10 5.01 12.8 23.0 22.8 7968072 22.2
# ℹ 48 more rows
# ℹ 2 more variables: `7-MA` <dbl>, `9-MA` <dbl>
The generic resilience indicators do not necessarily align with critical slowing down or speeding up theories
In the absence of ground truth, if \(\Delta\) is > 95% or < 5% of the distribution is considered a signal of resilience loss
~30% of ecosystem show symptoms of resilience loss, boreal forest and tundra particularly strong signals
~25% of ecosystem show symptoms of resilience loss, Easter Indo-Pacific and Tropical Eastern Pacific Oceans particularly strong signals
Low-hanging fruit
Challenge
