Time Adjustments by Bill Smith is licensed under
CC BY
2.0
introduction
prerequisites
time series in Date class
time series in ts class
convert ts to data frame
tsibble
references
In time series data, dates and times are the typically independent variable and the quantitative observation is the dependent variable.
In many cases, the quantitative variables IA a column in a data frame
encoded as class Date or POSIXct (these classes are discussed in the
time and dates tutorial). In other cases,
the quantitative variable is a vector encoded as an R Time-Series
object. I will use “time series” (lowercase) to denote time-dependent
data in general and “Time-Series” to denote the R object of class ts.
Project setup
- Start every work session by launching the RStudio Project file for
the course, e.g.,
portfolio.Rproj - Ensure your project directory structure satisfies the course requirements
Ensure you have installed the following packages. See install packages for instructions if needed.
- tidyverse
- lubridate
- tsbox
- astsa
Scripts to initialize
explore/ 0603-time-series-explore.R
And start with a minimal header
# your name
# date
# load packages
library("tidyverse")
library("lubridate")
library("tsbox")
library("astsa")Consider the economics data set that comes bundled with ggplot2. It
has five quantitative variables and one date variable of class Date.
View the data help page by running ? economics.
data(economics, package = "ggplot2")
economics
#> # A tibble: 574 x 6
#> date pce pop psavert uempmed unemploy
#> <date> <dbl> <int> <dbl> <dbl> <int>
#> 1 1967-07-01 507. 198712 12.5 4.5 2944
#> 2 1967-08-01 510. 198911 12.5 4.7 2945
#> 3 1967-09-01 516. 199113 11.7 4.6 2958
#> 4 1967-10-01 513. 199311 12.5 4.9 3143
#> 5 1967-11-01 518. 199498 12.5 4.7 3066
#> 6 1967-12-01 526. 199657 12.1 4.8 3018
#> 7 1968-01-01 532. 199808 11.7 5.1 2878
#> 8 1968-02-01 534. 199920 12.2 4.5 3001
#> 9 1968-03-01 545. 200056 11.6 4.1 2877
#> 10 1968-04-01 545. 200208 12.2 4.6 2709
#> # ... with 564 more rows
class(economics$date)
#> [1] "Date"In this form, we can go right to the graph. I’ll graph the number of unemployed (in 1000s) by date.
ggplot(data = economics, mapping = aes(x = date, y = unemploy)) +
geom_line()
Class ts is fundamentally different from date-time classes Date and
POSIXct. The date-time classes represent date and time values. The
ts class represents Time-Series objects, typically numeric data
vectors, that are observed at equally-spaced time intervals in time.
Examples of possible Time-Series objects: unemployment rate observed every month, CO2 levels observed every day, temperature observed every hour, etc.
For illustrating the ts class, we’ll examine the LakeHuron data
set—a time series in base R, recording annual measurements of the lake
level, in feet, from 1875 to 1972.
data(LakeHuron)Printing Time-Series shows the data vector plus additional information that identifies the object as a Time-Series. “Frequency = 1” indicates that the constant interval between observations is 1 year; the start and end years are also printed. Note that time is not printed as a vector.
print(LakeHuron)
#> Time Series:
#> Start = 1875
#> End = 1972
#> Frequency = 1
#> [1] 580.38 581.86 580.97 580.80 579.79 580.39 580.42 580.82 581.40 581.32
#> [11] 581.44 581.68 581.17 580.53 580.01 579.91 579.14 579.16 579.55 579.67
#> [21] 578.44 578.24 579.10 579.09 579.35 578.82 579.32 579.01 579.00 579.80
#> [31] 579.83 579.72 579.89 580.01 579.37 578.69 578.19 578.67 579.55 578.92
#> [41] 578.09 579.37 580.13 580.14 579.51 579.24 578.66 578.86 578.05 577.79
#> [51] 576.75 576.75 577.82 578.64 580.58 579.48 577.38 576.90 576.94 576.24
#> [61] 576.84 576.85 576.90 577.79 578.18 577.51 577.23 578.42 579.61 579.05
#> [71] 579.26 579.22 579.38 579.10 577.95 578.12 579.75 580.85 580.41 579.96
#> [81] 579.61 578.76 578.18 577.21 577.13 579.10 578.25 577.91 576.89 575.96
#> [91] 576.80 577.68 578.38 578.52 579.74 579.31 579.89 579.96The structure reveals that the vector is a Time-Series object.
str(LakeHuron)
#> Time-Series [1:98] from 1875 to 1972: 580 582 581 581 580 ...The class is ts. The tsp attribute gives the start time in time
units, the end time, and the frequency (the number of observations per
unit of time). Run ? tsp for its help page.
attributes(LakeHuron)
#> $tsp
#> [1] 1875 1972 1
#>
#> $class
#> [1] "ts"The data are numeric.
typeof(LakeHuron)
#> [1] "double"We could use the base R plot() function to graph the data. This will
not be our usual procedure, but it makes the point that Time-Series
objects do actually encode both a data value and a time value.
plot(LakeHuron)
To use our usual ggplot functions, we need the data in a data frame.
Example 1. Level of Lake Huron 1875–1972
In this firs example, the class of the data object is ts.
class(LakeHuron)
#> [1] "ts"tsbox::ts_df()to convert to data frame
df <- ts_df(LakeHuron) %>%
glimpse()
#> Observations: 98
#> Variables: 2
#> $ time <date> 1875-01-01, 1876-01-01, 1877-01-01, 1878-01-01, 1879-01...
#> $ value <dbl> 580.38, 581.86, 580.97, 580.80, 579.79, 580.39, 580.42, ...
class(df)
#> [1] "data.frame"In this case, however, the conversion has introduced a month and day in the date variable that was not present in the original data. I would therefore extract the years only.
year()to extract year from date, result is numeric
df <- df %>%
mutate(time = year(time)) %>%
glimpse()
#> Observations: 98
#> Variables: 2
#> $ time <dbl> 1875, 1876, 1877, 1878, 1879, 1880, 1881, 1882, 1883, 18...
#> $ value <dbl> 580.38, 581.86, 580.97, 580.80, 579.79, 580.39, 580.42, ...rename()the variables
df <- df %>%
dplyr::rename("lake_year" = "time", "lake_level" = "value") %>%
glimpse()
#> Observations: 98
#> Variables: 2
#> $ lake_year <dbl> 1875, 1876, 1877, 1878, 1879, 1880, 1881, 1882, 188...
#> $ lake_level <dbl> 580.38, 581.86, 580.97, 580.80, 579.79, 580.39, 580...In the graph, we assign the date to the x-scale.
ggplot(data = df, mapping = aes(x = lake_year, y = lake_level)) +
geom_line()
Example 2. Monthly Federal Reserve Board Production Index
In the second example, we use a Time-Series with data every month.
data(prodn, package = "astsa")
class(prodn)
#> [1] "ts"
prodn
#> Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov
#> 1948 40.6 41.1 40.5 40.1 40.4 41.2 39.3 41.6 42.3 43.2 41.8
#> 1949 40.0 40.1 39.3 38.5 37.7 37.9 36.0 39.0 40.0 39.2 39.0
#> 1950 39.8 40.3 41.6 42.6 43.0 44.7 43.4 48.3 48.7 50.0 48.3
#> 1951 48.5 49.6 50.0 49.4 48.6 49.1 45.5 48.0 49.1 49.5 48.9
#> 1952 49.0 50.1 50.4 49.1 48.3 48.4 44.9 50.6 53.4 54.5 54.5
#> 1953 54.2 55.6 56.3 55.8 55.8 55.9 53.2 55.8 55.5 55.8 53.2
#> 1954 51.3 52.0 51.8 51.2 51.3 51.9 48.8 51.3 52.3 53.5 53.6
#> 1955 54.7 56.2 57.5 57.9 58.4 59.1 55.8 58.6 60.1 61.9 61.3
#> 1956 60.5 61.1 61.2 61.6 60.7 61.0 55.2 60.4 62.6 63.8 62.6
#> 1957 62.0 63.5 63.6 62.3 61.8 63.1 59.4 62.8 63.0 62.6 60.4
#> 1958 57.0 56.4 55.8 54.7 55.0 57.6 59.4 58.7 60.7 61.3 62.1
#> 1959 61.9 63.8 65.2 66.4 67.2 68.5 62.9 63.3 64.5 64.6 63.6
#> 1960 67.8 68.2 68.0 67.5 67.3 67.5 63.4 65.6 66.6 66.9 64.5
#> 1961 62.0 62.7 63.5 65.1 66.1 68.0 64.6 67.9 69.5 71.1 70.5
#> 1962 68.9 71.0 72.1 72.4 72.4 73.4 69.7 71.9 74.7 75.0 73.6
#> 1963 72.4 74.7 75.7 76.4 77.1 78.6 73.4 75.5 78.9 80.2 78.7
#> 1964 77.5 79.8 80.2 81.5 81.9 83.2 78.3 81.3 84.6 83.9 84.5
#> 1965 84.8 87.0 88.8 88.8 89.5 91.7 86.7 89.4 92.4 94.5 93.0
#> 1966 92.7 95.3 97.3 97.1 97.8 100.0 93.8 97.2 101.7 102.8 100.0
#> 1967 98.1 99.1 99.0 99.6 98.7 100.9 94.4 99.6 102.7 103.4 103.1
#> 1968 101.8 104.5 105.6 104.9 106.5 109.3 102.5 105.5 109.6 110.1 109.6
#> 1969 107.3 110.4 111.6 110.6 110.5 114.0 107.3 111.6 115.1 115.1 112.0
#> 1970 106.5 109.1 109.4 108.8 108.6 110.8 104.5 108.0 110.4 108.0 105.1
#> 1971 105.5 108.3 108.6 108.8 109.5 112.5 105.4 108.8 113.5 113.9 111.6
#> 1972 111.5 115.6 116.8 118.7 118.4 121.8 114.2 120.5 125.5 126.8 125.2
#> 1973 122.7 128.1 128.8 128.6 129.6 133.0 126.4 130.3 134.8 135.3 132.9
#> 1974 126.3 129.8 130.8 129.9 131.7 135.3 127.3 131.4 135.5 133.1 125.5
#> 1975 111.8 113.0 111.8 113.0 113.8 119.2 114.5 121.4 125.9 125.4 123.8
#> 1976 122.2 128.3 128.6 128.7 130.0 133.2 126.5 131.7 134.3 133.8 132.1
#> 1977 128.8 133.6 135.7 136.2 137.2 141.5 134.1 138.2 142.4 142.7 139.5
#> 1978 134.8 139.6 141.4 144.2 144.2 148.8 141.9 146.9 152.0 152.6 149.7
#> Dec
#> 1948 40.5
#> 1949 38.8
#> 1950 48.2
#> 1951 48.2
#> 1952 53.6
#> 1953 51.0
#> 1954 53.4
#> 1955 60.4
#> 1956 62.0
#> 1957 57.8
#> 1958 60.8
#> 1959 65.9
#> 1960 61.7
#> 1961 69.4
#> 1962 71.8
#> 1963 76.5
#> 1964 83.4
#> 1965 91.4
#> 1966 97.5
#> 1967 101.4
#> 1968 106.2
#> 1969 108.3
#> 1970 104.1
#> 1971 108.5
#> 1972 121.8
#> 1973 126.7
#> 1974 114.9
#> 1975 119.8
#> 1976 128.3
#> 1977 134.9
#> 1978 145.0tsbox::ts_df()to create a data frame
df <- ts_df(prodn) %>%
glimpse()
#> Observations: 372
#> Variables: 2
#> $ time <date> 1948-01-01, 1948-02-01, 1948-03-01, 1948-04-01, 1948-05...
#> $ value <dbl> 40.6, 41.1, 40.5, 40.1, 40.4, 41.2, 39.3, 41.6, 42.3, 43...rename()the variables
df <- df %>%
dplyr::rename("date" = "time", "production_index" = "value") %>%
glimpse()
#> Observations: 372
#> Variables: 2
#> $ date <date> 1948-01-01, 1948-02-01, 1948-03-01, 1948-04-...
#> $ production_index <dbl> 40.6, 41.1, 40.5, 40.1, 40.4, 41.2, 39.3, 41....Graph
ggplot(data = df, mapping = aes(x = date, y = production_index)) +
geom_line()
Example 3. LA Pollution-Mortality Study
In this example, the original data is a Time-Series matrix, with multiple measurements taken at the same time.
data(lap, package = "astsa")
class(lap)
#> [1] "mts" "ts"
summary(lap)
#> tmort rmort cmort tempr
#> Min. :142.1 Min. : 4.150 Min. : 68.11 Min. :50.91
#> 1st Qu.:159.6 1st Qu.: 6.668 1st Qu.: 81.90 1st Qu.:67.23
#> Median :166.7 Median : 7.760 Median : 87.33 Median :74.06
#> Mean :169.0 Mean : 8.387 Mean : 88.70 Mean :74.26
#> 3rd Qu.:176.4 3rd Qu.: 9.182 3rd Qu.: 94.36 3rd Qu.:81.49
#> Max. :231.7 Max. :30.430 Max. :132.04 Max. :99.88
#> rh co so2 no2
#> Min. :17.65 Min. : 2.520 Min. :0.860 Min. : 4.140
#> 1st Qu.:51.84 1st Qu.: 4.970 1st Qu.:2.050 1st Qu.: 8.258
#> Median :60.46 Median : 6.865 Median :2.740 Median :10.555
#> Mean :58.83 Mean : 7.909 Mean :2.844 Mean :11.221
#> 3rd Qu.:67.12 3rd Qu.:10.080 3rd Qu.:3.465 3rd Qu.:13.510
#> Max. :93.01 Max. :22.390 Max. :6.570 Max. :25.180
#> hycarb o3 part
#> Min. : 21.57 Min. : 1.140 Min. :20.25
#> 1st Qu.: 40.21 1st Qu.: 4.588 1st Qu.:35.85
#> Median : 48.23 Median : 7.850 Median :44.25
#> Mean : 50.48 Mean : 8.334 Mean :47.41
#> 3rd Qu.: 59.69 3rd Qu.:11.255 3rd Qu.:57.54
#> Max. :100.12 Max. :22.050 Max. :97.94tsbox::ts_df()to create a data frame, adds the variableidto capture the original column names
df <- ts_df(lap) %>%
glimpse()
#> Observations: 5,588
#> Variables: 3
#> $ id <chr> "tmort", "tmort", "tmort", "tmort", "tmort", "tmort", "t...
#> $ time <dttm> 1970-01-01 00:00:00, 1970-01-08 00:33:22, 1970-01-15 01...
#> $ value <dbl> 183.63, 191.05, 180.09, 184.67, 173.60, 183.73, 171.79, ...rename()the variables
df <- df %>%
dplyr::rename("date" = "time", "mortality" = "value") %>%
glimpse()
#> Observations: 5,588
#> Variables: 3
#> $ id <chr> "tmort", "tmort", "tmort", "tmort", "tmort", "tmort"...
#> $ date <dttm> 1970-01-01 00:00:00, 1970-01-08 00:33:22, 1970-01-1...
#> $ mortality <dbl> 183.63, 191.05, 180.09, 184.67, 173.60, 183.73, 171....From the original ts object, the frequency is 52, hence the data are
weekly. Thus the times shown are spurious.
as_date()to convertdttmtoDate.
df <- df %>%
mutate(date = as_date(date)) %>%
glimpse()
#> Observations: 5,588
#> Variables: 3
#> $ id <chr> "tmort", "tmort", "tmort", "tmort", "tmort", "tmort"...
#> $ date <date> 1970-01-01, 1970-01-08, 1970-01-15, 1970-01-22, 197...
#> $ mortality <dbl> 183.63, 191.05, 180.09, 184.67, 173.60, 183.73, 171....Retain the mortality data only,
df_subset <- df %>%
filter(id %in% c("cmort", "rmort", "tmort"))Graph, faceting on id
ggplot(data = df_subset, mapping = aes(x = date, y = mortality)) +
geom_line() +
facet_wrap(vars(reorder(id, mortality)), as.table = FALSE, ncol = 3)
Have a look at package tsibble that extends the tidyverse to temporal data. Built on top of the tibble, a tsibble (or tbl_ts) is a data-centric format that preserves time indices as the essential data column and makes heterogeneous data structures possible.
Wickham H and Grolemund G (2017) R for Data Science. O’Reilly Media, Inc., Sebastopol, CA https://r4ds.had.co.nz/