Временные ряды

class: center, middle, inverse, title-slide

.title[
# Временные ряды
]
.subtitle[
## Визуализация и анализ географических данных на языке R
]
.author[
### Тимофей Самсонов
]
.institute[
### МГУ имени Ломоносова, Географический факультет
]
.date[
### 2023-10-24
]

---

## Используемые пакеты:

.pull-left[
__tidyverse__

```r
# tidyverse
library(tidyverse)
library(readxl)
library(googlesheets4)
```

__Данные__

```r
library(tsibbledata)
library(nasapower)
```
]

.pull-right[
__Временные данные__

```r
# пакеты для временных данных
library(gganimate)
library(zoo)
library(trend)
library(tsibble)
library(feasts)
library(fable)
```
]

---

## Основные аспекты работы с временными рядами

1. Типы данных времени
2. Структуры данных для временных рядов
3. Преобразования времени и временных рядов
4. Декомпозиция временных рядов
5. Анализ трендов и автокорреляции
6. Построение моделей и прогнозирование
7. Визуализация и анимация

---

## Создание и преобразование дат и времени

Текущее время и дата:

```r
(date = Sys.Date())
## [1] "2023-10-24"
(time = Sys.time())
## [1] "2023-10-24 11:31:54 MSK"
```

Полученные объекты имеют типы `Date` и `POSIXct`:

```r
class(date)
## [1] "Date"
class(time)
## [1] "POSIXct" "POSIXt"
```

---

## Система счета времени

Время `POSIXct` хранится в целочисленном формате и отсчитывается начиная с начала эпохи UNIX — `$1$` января `$1970$` года по гринвичскому (_UTC_) времени:

```r
as.integer(date)
## [1] 19654
difftime(date, as.Date('1970-01-01'))
## Time difference of 19654 days

as.integer(time)
## [1] 1698136314
difftime(time, as.POSIXct('1970-01-01 00:00:00', tz = 'UTC'), units = 'secs')
## Time difference of 1698136315 secs
```

---

## Работа с данными в lubridate

__Создание__ дат возможно на основе целочисленных и строковых значений:

```r
ymd(20150515)
## [1] "2015-05-15"
dmy('15052015')
## [1] "2015-05-15"
```

Для создания отметки времени необходимо сформировать строку, которая может быть интерпретирована должным образом. Часовой пояс указывается в `tz`:

```r
ymd_hms('2015-05-15 22:15:34') # по умолчанию Гринвичское время
## [1] "2015-05-15 22:15:34 UTC"
ymd_hms('2015-05-15 22:15:34', tz = "Europe/Moscow")
## [1] "2015-05-15 22:15:34 MSK"
```

---

## Работа с данными в lubridate

.pull-left[
__Извлечение__ компоненты даты/времени:

```r
year(time)
## [1] 2023
month(time)
## [1] 10
week(time)
## [1] 43
day(time)
## [1] 24
hour(time)
## [1] 11
second(time)
## [1] 54.60705
```

> Недели отсчитываются от начала года, а не месяца.

]

.pull-right[
__Замена__ компонент даты/времени:

```r
year(time) = 2015
month(time) = 01
time
## [1] "2015-01-24 11:31:54 MSK"
```

__Округление__ даты/времени. Например, получить первый день в текущем году можно так:

```r
floor_date(Sys.Date(), 
           unit = 'year')
## [1] "2023-01-01"
```
]
 
---

## Работа с данными в lubridate

__Периоды__  (_periods_) — это промежутки дат с точностью до _дня_. С помощью периода можно, например, к дате прибавить 1 год, 4 месяца, 3 недели и 2 дня:

```r
date
## [1] "2023-10-24"
date + years(1) + months(4) + weeks(3) + days(2)
## [1] "2025-03-19"
```

__Длительности__ (_durations_) — это промежутки времени с точностью до _секунды_. Работают они в целом аналогично периодам:

```r
dweeks(1)
## [1] "604800s (~1 weeks)"
time
## [1] "2015-01-24 11:31:54 MSK"
time + dweeks(1)
## [1] "2015-01-31 11:31:54 MSK"
time + weeks(1)
## [1] "2015-01-31 11:31:54 MSK"
```

---

## Работа с данными в lubridate

__Интервалы__ — это отрезки между двумя датами. Интервал можно преобразовывать в периоды и длительности:

```r
int = lubridate::interval(Sys.time(), time)
int
## [1] 2023-10-24 11:31:54 MSK--2015-01-24 11:31:54 MSK
as.period(int, 'days')
## [1] "-3195d 0H 0M -0.139196157455444S"
as.duration(int)
## [1] "-276048000.139196s (~-8.75 years)"
```

---

## Восстановление пропусков

В качестве источника данных будем использовать данные об уровне воды на гидропосте Паялка (р. Умба, Мурманская область) с 1932 по 2014 год. Отсутствие информации в файле данных закодировано числом `9999`:

```r
src = read_delim('../r-geo-course/data/in_Umba.txt', delim = ' ', 
      col_names = c('day', 'month', 'year', 'level'), na = '9999')
head(src)
## # A tibble: 6 × 4
##     day month  year level
##   <dbl> <dbl> <dbl> <dbl>
## 1     1     1  1932  49.4
## 2     2     1  1932  NA  
## 3     3     1  1932  NA  
## 4     4     1  1932  NA  
## 5     5     1  1932  NA  
## 6     6     1  1932  NA
```

---

## Восстановление пропусков

Сформируем даты на основе первых трёх столбцов и проверим, все ли из них корректны. Если компоненты даты некорректны, то функция `yms()` вернет `NA`:

.left-60[

```r
tab = src |>
    mutate(Date = ymd(paste(year, 
                            month, 
                            day)))
tab |> 
  filter(is.na(Date))
## # A tibble: 1 × 5
##     day month  year level Date  
##   <dbl> <dbl> <dbl> <dbl> <date>
## 1    29     2  1941  27.4 NA
```
]

.right-40[
<br>
Проверка показала, что преобразование в дату оказалось невозможно только для одной строки. В этой строке оператором была введена несуществующая дата — 29 февраля 1941 года.

Для дальнейшей работы необходимо избавиться от некорректных дат.
]

---

## Создание временного фрейма данных (tsibble)

__tsibble__ — это временной фрейм данных, у которого есть индекс в виде временного столбца:

```r
tsbl = tab |> 
  filter(!is.na(Date)) |> 
  distinct(Date, .keep_all = T) |> 
  as_tsibble(index = Date)

tsbl
## # A tsibble: 30,314 x 5 [1D]
##      day month  year level Date      
##    <dbl> <dbl> <dbl> <dbl> <date>    
##  1     1     1  1932  49.4 1932-01-01
##  2     2     1  1932  NA   1932-01-02
##  3     3     1  1932  NA   1932-01-03
##  4     4     1  1932  NA   1932-01-04
##  5     5     1  1932  NA   1932-01-05
##  6     6     1  1932  NA   1932-01-06
##  7     7     1  1932  NA   1932-01-07
##  8     8     1  1932  NA   1932-01-08
##  9     9     1  1932  NA   1932-01-09
## 10    10     1  1932  47   1932-01-10
## # ℹ 30,304 more rows
```

---

## Восстановление пропусков

Для того чтобы выяснить, есть ли пропуски, можно использовать `scan_gaps()` (индивидуальные пропуски) или `count_gaps()` (периоды пропусков)

```r
scan_gaps(tsbl)
## # A tsibble: 2 x 1 [1D]
##   Date      
##   <date>    
## 1 1941-12-31
## 2 1942-01-01
count_gaps(tsbl)
## # A tibble: 1 × 3
##   .from      .to           .n
##   <date>     <date>     <int>
## 1 1941-12-31 1942-01-01     2
```

---

## Восстановление пропусков

Для устранения пропусков дат используем `fill_gaps()`:

```r
tsbl = fill_gaps(tsbl)
scan_gaps(tsbl)
## # A tsibble: 0 x 1 [?]
## # ℹ 1 variable: Date <date>
```

---

## Заполнение пропусков данных

Создание таблицы пропусков:

```r
find_gaps = function(df, variable) {
  df |> 
    as_tibble() |>
    mutate(type = if_else(is.na(df[variable]), 'gap', 'data'),
           num = with(rle(type), rep(seq_along(lengths), lengths))) |> 
    group_by(num) |> 
    summarise(start_date = min(Date),
              end_date = max(Date),
              duration = end_date - start_date + 1,
              type = first(type))
}
timerep = find_gaps(tab, 'level')
```

---

## Заполнение пропусков

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---

## Автокорреляция

Критическую длину пропуска, заполняемого интерполяцией, можно связать с пороговым значением __автокорреляции__ — коэффициента корреляции исходного ряда данных и его копии, полученной со сдвигом `$\tau$`.

.pull-left[

```r
acorr = tsbl |> ACF(level)
acorr
## # A tsibble: 41 x 2 [1D]
##         lag   acf
##    <cf_lag> <dbl>
##  1       1D 0.994
##  2       2D 0.982
##  3       3D 0.964
##  4       4D 0.943
##  5       5D 0.919
##  6       6D 0.893
##  7       7D 0.866
##  8       8D 0.839
##  9       9D 0.812
## 10      10D 0.786
## # ℹ 31 more rows
```

]

.pull-right[

```r
autoplot(acorr)
```

![](08_TemporalStats_files/figure-html/unnamed-chunk-22-1.png)
]

---

## Анализ АКФ

За допустимую величину автокорреляции при восстановлении рядов данных принято брать некоторое значение. Например, гидрологи часто используют `$0.7$`. Найдем индекс первого элемента менее данной величины, используя функцию `detect_index()` из пакета __purrr__:

```r
max_dur = purrr::detect_index(acorr$acf, ~ .x < 0.7)
max_dur
## [1] 14
```

Полученное значение говорит нам о том, что при заданном допуске допустимо интерполировать значения в пропусках данных короче, чем 14 дней.

---

## Интерполяция по времени

Для начала визуализируем участок в окрестности одного из пробелов

```r
autoplot(tsbl, level, size = 1) +
  scale_x_date(limits = c(ymd(19320101), ymd(19360101)))
```

![](08_TemporalStats_files/figure-html/unnamed-chunk-24-1.png)

---

## Интерполяция по времени (линейная)

Для выполнения обычной линейной интерполяции между пропускаи воспользуемся функцией `na.approx()` из пакета __zoo__ и округлим полученные значения до одного знака после запятой (что соответствует точности исходных данных):

```r
(tsbl_int = tsbl |> 
  mutate(level_interp = 
           zoo::na.approx(level, maxgap = max_dur) |> round(1)))
## # A tsibble: 30,316 x 6 [1D]
##      day month  year level Date       level_interp
##    <dbl> <dbl> <dbl> <dbl> <date>            <dbl>
##  1     1     1  1932  49.4 1932-01-01         49.4
##  2     2     1  1932  NA   1932-01-02         49.1
##  3     3     1  1932  NA   1932-01-03         48.9
##  4     4     1  1932  NA   1932-01-04         48.6
##  5     5     1  1932  NA   1932-01-05         48.3
##  6     6     1  1932  NA   1932-01-06         48.1
##  7     7     1  1932  NA   1932-01-07         47.8
##  8     8     1  1932  NA   1932-01-08         47.5
##  9     9     1  1932  NA   1932-01-09         47.3
## 10    10     1  1932  47   1932-01-10         47  
## # ℹ 30,306 more rows
```

---

## Интерполяция по времени (линейная)

Визуализируем результат:

```r
autoplot(tsbl_int, level_interp, color = 'red', size = 1) +
  geom_line(aes(Date, level), tsbl, size = 1) +
  scale_x_date(limits = c(ymd(19320101), ymd(19360101)))
```

![](08_TemporalStats_files/figure-html/unnamed-chunk-26-1.png)

---

## Интерполяция по времени (с авторегрессией)

Ту же задачу можно решить с применением модели [ARIMA](https://ru.wikipedia.org/wiki/ARIMA), которая подыскивает интерполятор с учетом авторегрессии и сглаживающего среднего.

```r
tsbl_int2 = tsbl |> 
  model(mdl = ARIMA(level ~ 0 + pdq(0,1,0) + PDQ(0,0,0))) |> 
  interpolate(tsbl)
```

---

## Интерполяция по времени (с авторегрессией)

Однако в простейшем случае здесь есть проблемы с немонотонными участками (начало 1935 года).

```r
autoplot(tsbl_int2, level, color = 'magenta', size = 1) +
  geom_line(aes(Date, level), tsbl, size = 1) +
  scale_x_date(limits = c(ymd(19320101), ymd(19360101)))
```

![](08_TemporalStats_files/figure-html/unnamed-chunk-28-1.png)
---

## Интерполяция с учетом предикторов

Используем данные по температуре и осадкам и посчитаем по ним скользящее среднее за 10 и 5 дней соответственно:

```r
meteo = read_delim('../r-geo-course/data/in_Umba_meteo.txt', delim = ' ', 
                 col_names = c('day', 'month', 'year', 'temp', 'prec'), na = '9999') |> 
  mutate(Date = ymd(paste(year, month, day)),
         tempsm = zoo::rollmean(temp, 10, fill = NA, align = 'center'),
         precsum = zoo::rollsum(prec, 5, fill = NA, align = 'center')) |> 
  select(Date, temp, tempsm, prec, precsum)

tsbl_all = left_join(tsbl_int, meteo, by = 'Date')
tsbl_all
## # A tsibble: 30,316 x 10 [1D]
##      day month  year level Date       level_interp   temp tempsm  prec precsum
##    <dbl> <dbl> <dbl> <dbl> <date>            <dbl>  <dbl>  <dbl> <dbl>   <dbl>
##  1     1     1  1932  49.4 1932-01-01         49.4 -14.9   NA    0.184   NA   
##  2     2     1  1932  NA   1932-01-02         49.1 -15.1   NA    0.578   NA   
##  3     3     1  1932  NA   1932-01-03         48.9 -10.4   NA    0.942    3.97
##  4     4     1  1932  NA   1932-01-04         48.6  -7.58  NA    1.44     4.07
##  5     5     1  1932  NA   1932-01-05         48.3  -8.46 -11.3  0.826    4.42
##  6     6     1  1932  NA   1932-01-06         48.1 -13.0  -10.7  0.288    4.64
##  7     7     1  1932  NA   1932-01-07         47.8 -13.3   -9.72 0.925    3.95
##  8     8     1  1932  NA   1932-01-08         47.5 -10.4   -8.83 1.16     3.79
##  9     9     1  1932  NA   1932-01-09         47.3 -10.4   -8.33 0.75     4.53
## 10    10     1  1932  47   1932-01-10         47    -9.16  -7.62 0.662    4.49
## # ℹ 30,306 more rows
```

---

## Интерполяция с учетом предикторов

Выполним интерполяцию методом ARIMA с внешними предикторами:

```r
tsbl_int_met = tsbl_all |> 
  model(mdl = ARIMA(level_interp ~ tempsm + precsum)) |> 
  interpolate(tsbl_all)
```

---

## Интерполяция с учетом предикторов

Визуализируем результат:

```r
autoplot(tsbl_int_met, level_interp, color = 'green', size = 1) +
  geom_line(aes(Date, level_interp), tsbl_all, size = 1) +
  scale_x_date(limits = c(ymd(19320101), ymd(19360101)))
```

![](08_TemporalStats_files/figure-html/unnamed-chunk-31-1.png)

---

## Пересчет на другую временную сетку

Загрузим в качестве примера данные по метеостанции __NETATMO__:

```r
tab = read_csv('../r-geo-course/data/70_ee_50_00_8e_1a.csv')
```
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---

## Пересчет на другую временную сетку

Определим расчетные интервалы, кратные 30 минутам:

```r
tab = tab |> select(id, temperature, time_temperature)

tmin = ceiling_date(min(tab$time_temperature), 
                    unit = '30 minutes')
tmax = floor_date(max(tab$time_temperature), 
                  unit = '30 minutes')
```

---

## Пересчет на другую временную сетку

Проинтерполуруем данные на единую регулярную временную сетку через `$30$` минут, используя функцию [`approx()`](https://stat.ethz.ch/R-manual/R-devel/library/stats/html/approxfun.html) из базового __R__:

```r
time_interp = tibble(
  datetime = seq(tmin, tmax, by = '30 min'),
  temp = round(approx(tab$time_temperature, 
                      tab$temperature, 
                      xout = datetime)$y, 1)
)
```

---

## Пересчет на другую временную сетку

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---

## Обеспеченность данными

Надежность каждого интерполированного значения можно оценить, задав максимальную продолжительность интерполируемого интервала. Предположим, что она не должна превышать `$60$` минут:

```r
idx = sapply(time_interp$datetime, \(x) match(TRUE, tab$time_temperature >= x))

time_interp = time_interp |> 
  mutate(before_time = datetime - tab$time_temperature[idx-1],
         after_time = tab$time_temperature[idx] - datetime,
         valid = after_time - before_time <= minutes(60))

cat('Valid are ', round(100 * sum(time_interp$valid) / nrow(time_interp), 1), 
    '% of interpolated values', sep = '')
## Valid are 86.3% of interpolated values
```

---

## Обеспеченность данными

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class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>datetime<\/th>\n      <th>temp<\/th>\n      <th>before_time<\/th>\n      <th>after_time<\/th>\n      <th>valid<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"columnDefs":[{"className":"dt-right","targets":2},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>

---

## Прогнозирование по времени

Рассмотрим задачу прогнозирования количества [потребляемой электроэнергии](https://otexts.com/fpp3/forecasting.html#example-forecasting-electricity-demand) в штате Виктория (Австралия) в зависимости от температуры воздуха.

.code-small[

```r
data(vic_elec, package = 'tsibbledata')

vic_elec_daily = vic_elec |> 
  filter(year(Time) == 2014) |> 
  index_by(Date = date(Time)) |> 
  summarise(
    Demand = sum(Demand) / 1e3,
    Temperature = max(Temperature),
    Holiday = any(Holiday)
  ) |> 
  mutate(Day_Type = case_when(
    Holiday ~ "Holiday",
    wday(Date) %in% 2:6 ~ "Weekday",
    TRUE ~ "Weekend"
  ))
```
]

---

## Прогнозирование по времени

Визуализируем исходные данные:

```r
vic_elec_daily |> 
  pivot_longer(c(Demand, Temperature)) |> 
    ggplot(aes(x = Date, y = value)) +
    geom_line() +
    facet_grid(name ~ ., scales = "free_y") + ylab("")
```

![](08_TemporalStats_files/figure-html/unnamed-chunk-40-1.png)

---

## Прогнозирование по времени

Выполним построение модели и сформируем прогнозные данные по температуре:

```r
fit = vic_elec_daily |> 
  model(ARIMA(Demand ~ Temperature + I(Temperature^2) +
                (Day_Type == "Weekday")))

vic_elec_future = new_data(vic_elec_daily, 14) |> 
  mutate(
    Temperature = 26,
    Holiday = c(TRUE, rep(FALSE, 13)),
    Day_Type = case_when(
      Holiday ~ "Holiday",
      wday(Date) %in% 2:6 ~ "Weekday",
      TRUE ~ "Weekend"
    )
  )
```

---

## Прогнозирование по времени

Выполним прогнозирование:

```r
forecast(fit, vic_elec_future) |> 
  autoplot(vic_elec_daily) +
  labs(title="Daily electricity demand: Victoria",
       y="GW") +
  scale_x_date(limits = c(ymd(20141001), ymd(20150115)))
```

![](08_TemporalStats_files/figure-html/unnamed-chunk-42-1.png)

---

## Аппроксимация по времени

В качестве примера возьмем данные межгодичных изменений характеристик стока реки Мезень на посту Малонисогорская:

```r
(tab = read_csv('../r-geo-course/data/Mezen.csv'))
## # A tibble: 75 × 57
##    year_number Year1 Year2 datestart  datepolend    Qy  Qmax datemax     Qygr
##          <dbl> <dbl> <dbl> <date>     <date>     <dbl> <dbl> <date>     <dbl>
##  1           1  1938  1939 2000-03-23 2000-06-08  98.1   747 2000-04-03  19.9
##  2           2  1939  1940 2000-03-16 2000-07-11  66.9   487 2000-04-28  14.8
##  3           3  1940  1941 2000-03-09 2000-07-12  97.4   995 2000-04-28  18.9
##  4           4  1941  1942 2000-03-24 2000-07-21 214.   2030 2000-05-01  31.4
##  5           5  1942  1943 2000-04-02 2000-07-31 242.   2790 2000-05-08  26.9
##  6           6  1943  1944 2000-03-24 2000-06-15  71.3   451 2000-05-02  26.5
##  7           7  1944  1945 2000-02-26 2000-06-30  89.0   530 2000-04-28  27.0
##  8           8  1945  1946 2000-03-25 2000-07-13 128.   1220 2000-04-27  33.9
##  9           9  1946  1947 2000-03-15 2000-06-30 179.   2150 2000-04-28  25.8
## 10          10  1947  1948 2000-03-06 2000-07-15 153.   1720 2000-04-16  31.3
## # ℹ 65 more rows
## # ℹ 48 more variables: Qmmsummer <dbl>, monmmsummer <date>, Qmmwin <dbl>,
## #   nommwin <date>, Q30s <dbl>, date30s1 <date>, date30s2 <date>, Q30w <dbl>,
## #   date30w1 <date>, date30w2 <date>, Q10s <dbl>, date10s1 <date>,
## #   date10s2 <date>, Q10w <dbl>, date10w1 <date>, date10w2 <date>, Q5s <dbl>,
## #   date5s1 <date>, date5s2 <date>, Q5w <dbl>, date5w1 <date>, date5w2 <date>,
## #   Wy <dbl>, Wgr <dbl>, Wpol1 <dbl>, Wpol2 <dbl>, Wpol3 <dbl>, Wpavs1 <dbl>, …
```

---

## Аппроксимация по времени

Построим график межгодичной изменчивости объема грунтового стока (переменная `Wgr` в `$км^3$`). Для того чтобы нанести линию глобального тренда, добавим грамматику `geom_smooth(method = 'lm')`:

.pull-left[
.code-small[

```r
ggplot(
  tab, 
  mapping = aes(Year1, Wgr)
) +
  geom_line() +
  geom_area(alpha = 0.5) +
  geom_smooth(method = 'lm') +
  labs(
    title = 'Объем грунтового стока',
    x = 'Год',
    y = expression(км^3)
  )
```
]
]

.pull-right[
![](08_TemporalStats_files/figure-html/wgr-out-1.png)
]

---

## Аппроксимация по времени

Добавим линию локальной регрессии `geom_smooth(method = 'loess')`:

.pull-left[
.code-small[

```r
ggplot(
  tab, 
  mapping = aes(Year1, Wgr)
) +
  geom_line() +
  geom_area(alpha = 0.5) +
  geom_smooth(method = 'lm') +
  geom_smooth(
    method = 'loess',
    color = 'orangered', 
    span = 0.2
  ) +
  labs(
    title = 'Объем грунтового стока',
    x = 'Год',
    y = expression(км^3)
  )
```
]
]

.pull-right[
![](08_TemporalStats_files/figure-html/wgr2-out-1.png)
]

---

## Локальная регрессия

Нанесем несколько кривых локальной регрессии, используя разный охват данных:

.pull-left[
.code-small[

```r
ggplot(
  tab, 
  mapping = aes(Year1, Wgr)
) +
  geom_line() +
  geom_area(alpha = 0.5) +
  geom_smooth(color = 'yellow', 
              span = 0.1) +
  geom_smooth(color = 'orangered', 
              span = 0.2) +
  geom_smooth(color = 'darkred', 
              span = 0.4) +
  labs(
    title = 'Объем грунтового стока',
    x = 'Год',
    y = expression(км^3)
  )
```
]
]

.pull-right[
![](08_TemporalStats_files/figure-html/loess-out-1.png)
]

---

## Статистики

При анализе временных рядов часто используются:

- Тест Манна-Кендалла на значимость линейного тренда
- Тест Петтитт на точку перелома
- Оценка величины тренда по методу Тейла-Сена

Эти тесты доступны в пакете __trend__:

.code-small[

```r
(mk = mk.test(tab$Wgr))
## 
## 	Mann-Kendall trend test
## 
## data:  tab$Wgr
## z = 7.8129, n = 75, p-value = 5.589e-15
## alternative hypothesis: true S is not equal to 0
## sample estimates:
##            S         varS          tau 
## 1.709000e+03 4.779167e+04 6.158559e-01
```
]

---

## Статистики

.code-small[

```r
(pt = pettitt.test(tab$Wgr))
## 
## 	Pettitt's test for single change-point detection
## 
## data:  tab$Wgr
## U* = 1324, p-value = 4.131e-11
## alternative hypothesis: two.sided
## sample estimates:
## probable change point at time K 
##                              38
(ts = sens.slope(tab$Wgr))
## 
## 	Sen's slope
## 
## data:  tab$Wgr
## z = 7.8129, n = 75, p-value = 5.589e-15
## alternative hypothesis: true z is not equal to 0
## 95 percent confidence interval:
##  0.01378903 0.02202750
## sample estimates:
## Sen's slope 
##  0.01810404
```
]

---

## Статистики

.pull-left[
.code-small[

```r
ggplot(tab, aes(Year1, Wgr)) +
  geom_line() +
  geom_area(alpha = 0.5) +
  geom_smooth(method = 'lm') +
  geom_vline(
    xintercept = tab$Year1[pt$estimate], 
    color = "red", size = 0.5
  ) +
  annotate(
    "text", 
    label = tab$Year1[pt$estimate], 
    x = tab$Year1[pt$estimate] + 4, 
    y = max(tab$Wgr), 
    size = 4, colour = "red"
  ) +
  labs(
    title = 'Объем грунтового стока',
    x = 'Год',
    y = expression(км^3)
  )
```
]
]

.pull-right[
Для наглядности нанесем полученную точку перелома на график:
![](08_TemporalStats_files/figure-html/pt-out-1.png)
]

---

## Анимация

Возможности анимаций в __gganimate__ реализуются посредством добавления новых грамматик к построенному графику __ggplot2__. К числу этих грамматик относятся:

- `transition_*()` — распределение данных по времени;
- `view_*()` — поведение осей координат во времени;
- `shadow_*()` — отображение данных, не относящихся к текущему временному срезу;
- `enter_*()/exit_*()` — характер появления/исчезновения данных в процессе анимации;
- `ease_aes()` — порядок смягчения (интерполяции) графических переменных в моменты перехода.

---

## Анимация

В качестве первого примера используем данные реанализа NASA POWER суточного осреднения, выгрузив информацию по точкам в трех городах (Мурманск, Москва, Краснодар) за 2018 год:

```r
cities = list(Мурманск = c(33, 69), 
              Москва = c(38, 56), Краснодар = c(39, 45))

tab = purrr::imap(cities, function(coords, city){
  get_power(
    community = "AG",
    lonlat = coords,
    pars = c("RH2M", "T2M", "PRECTOT"),
    dates = c("2018-01-01", "2018-12-31"),
    temporal_average = "DAILY"
  ) |> mutate(CITY = city,
               MONTH = month(YYYYMMDD))
}) |> bind_rows()
```

---

## Переход по времени

```r
ggplot(tab, aes(CITY, T2M)) +
  geom_boxplot() +
  labs(title = "Температура воздуха",
*   subtitle = 'Месяц: {round(frame_time)}') +
  xlab('Город') + ylab('Т, °С') +
* transition_time(MONTH)
```

---

## Переход по времени

.pull-left[

```r
ggplot(tab, aes(T2M, fill = CITY)) +
* geom_density(alpha = 0.5) +
  labs(
    title = "Температура воздуха",
    subtitle = 'Месяц: {round(frame_time)}',
    fill = 'Город'
  ) +
  xlab('Т, °С') +
  ylab('Плотность распределения') +
  transition_time(MONTH)
```
]

.pull-right[
Плотность распределения:
![](img/density_anim.gif)
]

---

## Переход по времени

Данные Gapminder по соотношению продолжительности жизни и ВВП:
.code-small[

```r
countries = read_excel('../r-geo-course/data/gapminder.xlsx', 2) |>
  select(Country = name, Region = eight_regions) |>
  mutate(Country = factor(Country, levels = Country[order(.$Region)]))
# ВВП на душу населения
gdpdf_tidy = read_sheet('1cxtzRRN6ldjSGoDzFHkB8vqPavq1iOTMElGewQnmHgg') |> 
  pivot_longer(cols = `1764`:`2018`, names_to = 'year', values_to = 'gdp') |> 
  rename(Country = 1)
# численность населения
popdf_tidy = read_sheet('1IbDM8z5XicMIXgr93FPwjgwoTTKMuyLfzU6cQrGZzH8') |> 
  pivot_longer(cols = `1800`:`2015`, names_to = 'year', values_to = 'pop') |> 
  rename(Country = 1)
```
]

---

## Переход по времени

Данные Gapminder по соотношению продолжительности жизни и ВВП:

.code-small[

```r
# продолжительность жизни
lifedf_tidy = read_sheet('1H3nzTwbn8z4lJ5gJ_WfDgCeGEXK3PVGcNjQ_U5og8eo') |>
  pivot_longer(cols = `1800`:`2016`, names_to = 'year', values_to = 'lifexp') |> 
  rename(Country = 1)

---

## Переход по времени

.pull-left[
.code-small[

```r
options(scipen = 999)
ggplot(
  tab, aes(
    gdp, lifexp, 
    size = pop, 
    color = Region
  )
) +
  geom_point(alpha = 0.5) +
  scale_x_log10() +
  labs(title = 
       'Year: {round(frame_time)}') +
  theme_bw() +
  transition_time(year)
```
]
]

.pull-right[
![](img/scatter_anim.gif)
]

---

# Переход по состояниям

- В ряде случаев вместо перехода по времени целесообразно использовать __переход по состояниям__. В частности, такой подход оказывается удобен, когда сопоставляются данные за аналогичные временные срезы разных периодов.

- Подобную стратегию можно использовать для визуализации изменений внутригодичного распределения величины между годами.

- Чтобы обеспечить сопоставимость аналогичных дат за разные года, необходимо сохранить у них только месяц и день.

- Поскольку такого формата даты не существует, в качестве "трюка" можно просто заменить года всех дат на `$2000$` и записать результат в новое поле.

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# Переход по состояниям

Необходимые преобразования реализуются следующим образом:

# фиктивное поле, в котором аналогичные даты за разные года совпадают
year(flt_tab$yDate) <- 2000 
```

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# Переход по состояниям

```r
anim = ggplot(flt_tab, mapping = aes(x = yDate, y = level_interp)) +
    geom_ribbon(aes(ymin = 0, ymax = level_interp), alpha = 0.5) +
    geom_line() +
    scale_x_date(date_breaks = "1 month", date_labels = "%b") +
    labs(title = "Расход воды на гидропосту Паялка",
         subtitle = 'Год: {closest_state}') +
    xlab('Дата') +
    ylab('куб.м/с') +
    theme(text = element_text(size = 18, family = 'Open Sans')) +
*   transition_states(year, state_length = 0) +
*   view_follow(fixed_y = TRUE)

animate(anim, 
        fps = 20,                                    # число кадров в секунду
        nframes = 10 * length(unique(flt_tab$year)), # общее число кадров
        width = 800, 
        height = 600)
```

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# Переход по состояниям

> Текущий срез при выполнении анимации по состояниям доступен в переменной окружения `closest_state`.

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