healthyverse_tsa
Time Series Analysis and Nested Modeling of the Healthyverse Packages
Steven P. Sanderson II, MPH - Date: 25 April, 2025
This analysis follows a Nested Modeltime Workflow.
Get Data
glimpse(downloads_tbl)
## Rows: 137,962
## Columns: 11
## $ date <date> 2020-11-23, 2020-11-23, 2020-11-23, 2020-11-23, 2020-11-23,…
## $ time <Period> 15H 36M 55S, 11H 26M 39S, 23H 34M 44S, 18H 39M 32S, 9H 0M…
## $ date_time <dttm> 2020-11-23 15:36:55, 2020-11-23 11:26:39, 2020-11-23 23:34:…
## $ size <int> 4858294, 4858294, 4858301, 4858295, 361, 4863722, 4864794, 4…
## $ r_version <chr> NA, "4.0.3", "3.5.3", "3.5.2", NA, NA, NA, NA, NA, NA, NA, N…
## $ r_arch <chr> NA, "x86_64", "x86_64", "x86_64", NA, NA, NA, NA, NA, NA, NA…
## $ r_os <chr> NA, "mingw32", "mingw32", "linux-gnu", NA, NA, NA, NA, NA, N…
## $ package <chr> "healthyR.data", "healthyR.data", "healthyR.data", "healthyR…
## $ version <chr> "1.0.0", "1.0.0", "1.0.0", "1.0.0", "1.0.0", "1.0.0", "1.0.0…
## $ country <chr> "US", "US", "US", "GB", "US", "US", "DE", "HK", "JP", "US", …
## $ ip_id <int> 2069, 2804, 78827, 27595, 90474, 90474, 42435, 74, 7655, 638…
The last day in the data set is 2025-04-23 23:50:51, the file was birthed on: 2024-08-07 07:35:44, and at report knit time is -6228.25 hours old. Happy analyzing!
Now that we have our data lets take a look at it using the skimr
package.
skim(downloads_tbl)
| Name | downloads_tbl |
| Number of rows | 137962 |
| Number of columns | 11 |
| _______________________ | |
| Column type frequency: | |
| character | 6 |
| Date | 1 |
| numeric | 2 |
| POSIXct | 1 |
| Timespan | 1 |
| ________________________ | |
| Group variables | None |
Data summary
Variable type: character
| skim_variable | n_missing | complete_rate | min | max | empty | n_unique | whitespace |
|---|---|---|---|---|---|---|---|
| r_version | 99291 | 0.28 | 5 | 5 | 0 | 46 | 0 |
| r_arch | 99291 | 0.28 | 3 | 7 | 0 | 5 | 0 |
| r_os | 99291 | 0.28 | 7 | 15 | 0 | 22 | 0 |
| package | 0 | 1.00 | 7 | 13 | 0 | 8 | 0 |
| version | 0 | 1.00 | 5 | 17 | 0 | 60 | 0 |
| country | 11652 | 0.92 | 2 | 2 | 0 | 163 | 0 |
Variable type: Date
| skim_variable | n_missing | complete_rate | min | max | median | n_unique |
|---|---|---|---|---|---|---|
| date | 0 | 1 | 2020-11-23 | 2025-04-23 | 2023-06-08 | 1613 |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| size | 0 | 1 | 1135390.77 | 1521900.90 | 355 | 14701 | 278019.5 | 2367773.00 | 5677952 | ▇▁▂▁▁ |
| ip_id | 0 | 1 | 10378.68 | 18424.62 | 1 | 298 | 3064.0 | 11717.25 | 209747 | ▇▁▁▁▁ |
Variable type: POSIXct
| skim_variable | n_missing | complete_rate | min | max | median | n_unique |
|---|---|---|---|---|---|---|
| date_time | 0 | 1 | 2020-11-23 09:00:41 | 2025-04-23 23:50:51 | 2023-06-08 02:45:25 | 84062 |
Variable type: Timespan
| skim_variable | n_missing | complete_rate | min | max | median | n_unique |
|---|---|---|---|---|---|---|
| time | 0 | 1 | 0 | 59 | 30 | 60 |
We can see that the following columns are missing a lot of data and for
us are most likely not useful anyways, so we will drop them
c(r_version, r_arch, r_os)
Plots
Now lets take a look at a time-series plot of the total daily downloads by package. We will use a log scale and place a vertical line at each version release for each package.
Now lets take a look at some time series decomposition graphs.
Feature Engineering
Now that we have our basic data and a shot of what it looks like, let’s
add some features to our data which can be very helpful in modeling.
Lets start by making a tibble that is aggregated by the day and
package, as we are going to be interested in forecasting the next 4
weeks or 28 days for each package. First lets get our base data.
##
## Call:
## stats::lm(formula = .formula, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -147.92 -35.72 -10.66 26.64 813.81
##
## Coefficients:
## Estimate Std. Error
## (Intercept) -1.840e+02 7.203e+01
## date 1.121e-02 3.821e-03
## lag(value, 1) 1.058e-01 2.469e-02
## lag(value, 7) 9.542e-02 2.557e-02
## lag(value, 14) 9.707e-02 2.568e-02
## lag(value, 21) 6.904e-02 2.573e-02
## lag(value, 28) 6.623e-02 2.570e-02
## lag(value, 35) 6.757e-02 2.576e-02
## lag(value, 42) 4.931e-02 2.587e-02
## lag(value, 49) 6.769e-02 2.570e-02
## month(date, label = TRUE).L -1.018e+01 5.133e+00
## month(date, label = TRUE).Q 2.787e+00 5.195e+00
## month(date, label = TRUE).C -1.244e+01 5.195e+00
## month(date, label = TRUE)^4 -6.501e+00 5.197e+00
## month(date, label = TRUE)^5 -1.227e+01 5.199e+00
## month(date, label = TRUE)^6 -3.097e+00 5.250e+00
## month(date, label = TRUE)^7 -6.236e+00 5.167e+00
## month(date, label = TRUE)^8 -4.383e+00 5.167e+00
## month(date, label = TRUE)^9 5.302e+00 5.168e+00
## month(date, label = TRUE)^10 4.595e+00 5.251e+00
## month(date, label = TRUE)^11 -5.912e+00 5.334e+00
## fourier_vec(date, type = "sin", K = 1, period = 7) -1.155e+01 2.378e+00
## fourier_vec(date, type = "cos", K = 1, period = 7) 8.072e+00 2.505e+00
## t value Pr(>|t|)
## (Intercept) -2.555 0.010711 *
## date 2.934 0.003395 **
## lag(value, 1) 4.285 1.94e-05 ***
## lag(value, 7) 3.732 0.000197 ***
## lag(value, 14) 3.780 0.000163 ***
## lag(value, 21) 2.683 0.007371 **
## lag(value, 28) 2.577 0.010060 *
## lag(value, 35) 2.623 0.008804 **
## lag(value, 42) 1.906 0.056804 .
## lag(value, 49) 2.634 0.008527 **
## month(date, label = TRUE).L -1.982 0.047609 *
## month(date, label = TRUE).Q 0.536 0.591745
## month(date, label = TRUE).C -2.395 0.016737 *
## month(date, label = TRUE)^4 -1.251 0.211140
## month(date, label = TRUE)^5 -2.360 0.018400 *
## month(date, label = TRUE)^6 -0.590 0.555352
## month(date, label = TRUE)^7 -1.207 0.227677
## month(date, label = TRUE)^8 -0.848 0.396391
## month(date, label = TRUE)^9 1.026 0.305066
## month(date, label = TRUE)^10 0.875 0.381628
## month(date, label = TRUE)^11 -1.108 0.267919
## fourier_vec(date, type = "sin", K = 1, period = 7) -4.858 1.31e-06 ***
## fourier_vec(date, type = "cos", K = 1, period = 7) 3.223 0.001297 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 58.77 on 1541 degrees of freedom
## (49 observations deleted due to missingness)
## Multiple R-squared: 0.2464, Adjusted R-squared: 0.2357
## F-statistic: 22.91 on 22 and 1541 DF, p-value: < 2.2e-16
NNS Forecasting
This is something I have been wanting to try for a while. The NNS
package is a great package for forecasting time series data.
library(NNS)
data_list <- base_data |>
select(package, value) |>
group_split(package)
data_list |>
imap(
\(x, idx) {
obj <- x
x <- obj |> pull(value) |> tail(7*52)
train_set_size <- length(x) - 56
pkg <- obj |> pluck(1) |> unique()
sf <- NNS.seas(x, modulo = 7, plot = FALSE)$periods
cat(paste0("Package: ", pkg, "\n"))
NNS.ARMA.optim(
variable = x,
h = 28,
training.set = train_set_size,
#seasonal.factor = seq(12, 60, 7),
seasonal.factor = sf,
pred.int = 0.95,
plot = TRUE
)
title(
sub = paste0("\n",
"Package: ", pkg, " - NNS Optimization")
)
}
)
## Package: healthyR
## [1] "CURRNET METHOD: lin"
## [1] "COPY LATEST PARAMETERS DIRECTLY FOR NNS.ARMA() IF ERROR:"
## [1] "NNS.ARMA(... method = 'lin' , seasonal.factor = c( 70 ) ...)"
## [1] "CURRENT lin OBJECTIVE FUNCTION = 3.94315090938525"
## [1] "NNS.ARMA(... method = 'lin' , seasonal.factor = c( 70, 63 ) ...)"
## [1] "CURRENT lin OBJECTIVE FUNCTION = 3.42511996893374"
## [1] "BEST method = 'lin', seasonal.factor = c( 70, 63 )"
## [1] "BEST lin OBJECTIVE FUNCTION = 3.42511996893374"
## [1] "CURRNET METHOD: nonlin"
## [1] "COPY LATEST PARAMETERS DIRECTLY FOR NNS.ARMA() IF ERROR:"
## [1] "NNS.ARMA(... method = 'nonlin' , seasonal.factor = c( 70, 63 ) ...)"
## [1] "CURRENT nonlin OBJECTIVE FUNCTION = 5.18142554228718"
## [1] "BEST method = 'nonlin' PATH MEMBER = c( 70, 63 )"
## [1] "BEST nonlin OBJECTIVE FUNCTION = 5.18142554228718"
## [1] "CURRNET METHOD: both"
## [1] "COPY LATEST PARAMETERS DIRECTLY FOR NNS.ARMA() IF ERROR:"
## [1] "NNS.ARMA(... method = 'both' , seasonal.factor = c( 70, 63 ) ...)"
## [1] "CURRENT both OBJECTIVE FUNCTION = 4.08806747552172"
## [1] "BEST method = 'both' PATH MEMBER = c( 70, 63 )"
## [1] "BEST both OBJECTIVE FUNCTION = 4.08806747552172"
## Package: healthyR.ai
## [1] "CURRNET METHOD: lin"
## [1] "COPY LATEST PARAMETERS DIRECTLY FOR NNS.ARMA() IF ERROR:"
## [1] "NNS.ARMA(... method = 'lin' , seasonal.factor = c( 28 ) ...)"
## [1] "CURRENT lin OBJECTIVE FUNCTION = 2.99075230277401"
## [1] "NNS.ARMA(... method = 'lin' , seasonal.factor = c( 28, 63 ) ...)"
## [1] "CURRENT lin OBJECTIVE FUNCTION = 2.85541805450539"
## [1] "NNS.ARMA(... method = 'lin' , seasonal.factor = c( 28, 63, 84 ) ...)"
## [1] "CURRENT lin OBJECTIVE FUNCTION = 2.75122004274312"
## [1] "NNS.ARMA(... method = 'lin' , seasonal.factor = c( 28, 63, 84, 91 ) ...)"
## [1] "CURRENT lin OBJECTIVE FUNCTION = 2.66803166786165"
## [1] "NNS.ARMA(... method = 'lin' , seasonal.factor = c( 28, 63, 84, 91, 70 ) ...)"
## [1] "CURRENT lin OBJECTIVE FUNCTION = 2.6266006097587"
## [1] "BEST method = 'lin', seasonal.factor = c( 28, 63, 84, 91, 70 )"
## [1] "BEST lin OBJECTIVE FUNCTION = 2.6266006097587"
## [1] "CURRNET METHOD: nonlin"
## [1] "COPY LATEST PARAMETERS DIRECTLY FOR NNS.ARMA() IF ERROR:"
## [1] "NNS.ARMA(... method = 'nonlin' , seasonal.factor = c( 28, 63, 84, 91, 70 ) ...)"
## [1] "CURRENT nonlin OBJECTIVE FUNCTION = 3.59715096569321"
## [1] "BEST method = 'nonlin' PATH MEMBER = c( 28, 63, 84, 91, 70 )"
## [1] "BEST nonlin OBJECTIVE FUNCTION = 3.59715096569321"
## [1] "CURRNET METHOD: both"
## [1] "COPY LATEST PARAMETERS DIRECTLY FOR NNS.ARMA() IF ERROR:"
## [1] "NNS.ARMA(... method = 'both' , seasonal.factor = c( 28, 63, 84, 91, 70 ) ...)"
## [1] "CURRENT both OBJECTIVE FUNCTION = 3.00299333204891"
## [1] "BEST method = 'both' PATH MEMBER = c( 28, 63, 84, 91, 70 )"
## [1] "BEST both OBJECTIVE FUNCTION = 3.00299333204891"
## Package: healthyR.data
## [1] "CURRNET METHOD: lin"
## [1] "COPY LATEST PARAMETERS DIRECTLY FOR NNS.ARMA() IF ERROR:"
## [1] "NNS.ARMA(... method = 'lin' , seasonal.factor = c( 91 ) ...)"
## [1] "CURRENT lin OBJECTIVE FUNCTION = 3.23480235802104"
## [1] "NNS.ARMA(... method = 'lin' , seasonal.factor = c( 91, 98 ) ...)"
## [1] "CURRENT lin OBJECTIVE FUNCTION = 2.62385437324976"
## [1] "NNS.ARMA(... method = 'lin' , seasonal.factor = c( 91, 98, 63 ) ...)"
## [1] "CURRENT lin OBJECTIVE FUNCTION = 2.33624578602086"
## [1] "BEST method = 'lin', seasonal.factor = c( 91, 98, 63 )"
## [1] "BEST lin OBJECTIVE FUNCTION = 2.33624578602086"
## [1] "CURRNET METHOD: nonlin"
## [1] "COPY LATEST PARAMETERS DIRECTLY FOR NNS.ARMA() IF ERROR:"
## [1] "NNS.ARMA(... method = 'nonlin' , seasonal.factor = c( 91, 98, 63 ) ...)"
## [1] "CURRENT nonlin OBJECTIVE FUNCTION = 2.81572359284023"
## [1] "BEST method = 'nonlin' PATH MEMBER = c( 91, 98, 63 )"
## [1] "BEST nonlin OBJECTIVE FUNCTION = 2.81572359284023"
## [1] "CURRNET METHOD: both"
## [1] "COPY LATEST PARAMETERS DIRECTLY FOR NNS.ARMA() IF ERROR:"
## [1] "NNS.ARMA(... method = 'both' , seasonal.factor = c( 91, 98, 63 ) ...)"
## [1] "CURRENT both OBJECTIVE FUNCTION = 2.37001724046608"
## [1] "BEST method = 'both' PATH MEMBER = c( 91, 98, 63 )"
## [1] "BEST both OBJECTIVE FUNCTION = 2.37001724046608"
## Package: healthyR.ts
## [1] "CURRNET METHOD: lin"
## [1] "COPY LATEST PARAMETERS DIRECTLY FOR NNS.ARMA() IF ERROR:"
## [1] "NNS.ARMA(... method = 'lin' , seasonal.factor = c( 63 ) ...)"
## [1] "CURRENT lin OBJECTIVE FUNCTION = 3.57532066442321"
## [1] "NNS.ARMA(... method = 'lin' , seasonal.factor = c( 63, 70 ) ...)"
## [1] "CURRENT lin OBJECTIVE FUNCTION = 3.13114014026799"
## [1] "BEST method = 'lin', seasonal.factor = c( 63, 70 )"
## [1] "BEST lin OBJECTIVE FUNCTION = 3.13114014026799"
## [1] "CURRNET METHOD: nonlin"
## [1] "COPY LATEST PARAMETERS DIRECTLY FOR NNS.ARMA() IF ERROR:"
## [1] "NNS.ARMA(... method = 'nonlin' , seasonal.factor = c( 63, 70 ) ...)"
## [1] "CURRENT nonlin OBJECTIVE FUNCTION = 4.75301423941003"
## [1] "BEST method = 'nonlin' PATH MEMBER = c( 63, 70 )"
## [1] "BEST nonlin OBJECTIVE FUNCTION = 4.75301423941003"
## [1] "CURRNET METHOD: both"
## [1] "COPY LATEST PARAMETERS DIRECTLY FOR NNS.ARMA() IF ERROR:"
## [1] "NNS.ARMA(... method = 'both' , seasonal.factor = c( 63, 70 ) ...)"
## [1] "CURRENT both OBJECTIVE FUNCTION = 3.75421457231103"
## [1] "BEST method = 'both' PATH MEMBER = c( 63, 70 )"
## [1] "BEST both OBJECTIVE FUNCTION = 3.75421457231103"
## Package: healthyverse
## [1] "CURRNET METHOD: lin"
## [1] "COPY LATEST PARAMETERS DIRECTLY FOR NNS.ARMA() IF ERROR:"
## [1] "NNS.ARMA(... method = 'lin' , seasonal.factor = c( 35 ) ...)"
## [1] "CURRENT lin OBJECTIVE FUNCTION = 5.60205444188786"
## [1] "BEST method = 'lin', seasonal.factor = c( 35 )"
## [1] "BEST lin OBJECTIVE FUNCTION = 5.60205444188786"
## [1] "CURRNET METHOD: nonlin"
## [1] "COPY LATEST PARAMETERS DIRECTLY FOR NNS.ARMA() IF ERROR:"
## [1] "NNS.ARMA(... method = 'nonlin' , seasonal.factor = c( 35 ) ...)"
## [1] "CURRENT nonlin OBJECTIVE FUNCTION = 11.8973605516513"
## [1] "BEST method = 'nonlin' PATH MEMBER = c( 35 )"
## [1] "BEST nonlin OBJECTIVE FUNCTION = 11.8973605516513"
## [1] "CURRNET METHOD: both"
## [1] "COPY LATEST PARAMETERS DIRECTLY FOR NNS.ARMA() IF ERROR:"
## [1] "NNS.ARMA(... method = 'both' , seasonal.factor = c( 35 ) ...)"
## [1] "CURRENT both OBJECTIVE FUNCTION = 8.87836943844484"
## [1] "BEST method = 'both' PATH MEMBER = c( 35 )"
## [1] "BEST both OBJECTIVE FUNCTION = 8.87836943844484"
## Package: RandomWalker
## [1] "CURRNET METHOD: lin"
## [1] "COPY LATEST PARAMETERS DIRECTLY FOR NNS.ARMA() IF ERROR:"
## [1] "NNS.ARMA(... method = 'lin' , seasonal.factor = c( 42 ) ...)"
## [1] "CURRENT lin OBJECTIVE FUNCTION = 2.94454882162532"
## [1] "BEST method = 'lin', seasonal.factor = c( 42 )"
## [1] "BEST lin OBJECTIVE FUNCTION = 2.94454882162532"
## [1] "CURRNET METHOD: nonlin"
## [1] "COPY LATEST PARAMETERS DIRECTLY FOR NNS.ARMA() IF ERROR:"
## [1] "NNS.ARMA(... method = 'nonlin' , seasonal.factor = c( 42 ) ...)"
## [1] "CURRENT nonlin OBJECTIVE FUNCTION = 3.99374106966977"
## [1] "BEST method = 'nonlin' PATH MEMBER = c( 42 )"
## [1] "BEST nonlin OBJECTIVE FUNCTION = 3.99374106966977"
## [1] "CURRNET METHOD: both"
## [1] "COPY LATEST PARAMETERS DIRECTLY FOR NNS.ARMA() IF ERROR:"
## [1] "NNS.ARMA(... method = 'both' , seasonal.factor = c( 42 ) ...)"
## [1] "CURRENT both OBJECTIVE FUNCTION = 3.18563502551712"
## [1] "BEST method = 'both' PATH MEMBER = c( 42 )"
## [1] "BEST both OBJECTIVE FUNCTION = 3.18563502551712"
## Package: tidyAML
## [1] "CURRNET METHOD: lin"
## [1] "COPY LATEST PARAMETERS DIRECTLY FOR NNS.ARMA() IF ERROR:"
## [1] "NNS.ARMA(... method = 'lin' , seasonal.factor = c( 28 ) ...)"
## [1] "CURRENT lin OBJECTIVE FUNCTION = 3.84631313983007"
## [1] "BEST method = 'lin', seasonal.factor = c( 28 )"
## [1] "BEST lin OBJECTIVE FUNCTION = 3.84631313983007"
## [1] "CURRNET METHOD: nonlin"
## [1] "COPY LATEST PARAMETERS DIRECTLY FOR NNS.ARMA() IF ERROR:"
## [1] "NNS.ARMA(... method = 'nonlin' , seasonal.factor = c( 28 ) ...)"
## [1] "CURRENT nonlin OBJECTIVE FUNCTION = 3.46240626413802"
## [1] "BEST method = 'nonlin' PATH MEMBER = c( 28 )"
## [1] "BEST nonlin OBJECTIVE FUNCTION = 3.46240626413802"
## [1] "CURRNET METHOD: both"
## [1] "COPY LATEST PARAMETERS DIRECTLY FOR NNS.ARMA() IF ERROR:"
## [1] "NNS.ARMA(... method = 'both' , seasonal.factor = c( 28 ) ...)"
## [1] "CURRENT both OBJECTIVE FUNCTION = 3.21198912045445"
## [1] "BEST method = 'both' PATH MEMBER = c( 28 )"
## [1] "BEST both OBJECTIVE FUNCTION = 3.21198912045445"
## Package: TidyDensity
## [1] "CURRNET METHOD: lin"
## [1] "COPY LATEST PARAMETERS DIRECTLY FOR NNS.ARMA() IF ERROR:"
## [1] "NNS.ARMA(... method = 'lin' , seasonal.factor = c( 63 ) ...)"
## [1] "CURRENT lin OBJECTIVE FUNCTION = 3.67028448210995"
## [1] "NNS.ARMA(... method = 'lin' , seasonal.factor = c( 63, 35 ) ...)"
## [1] "CURRENT lin OBJECTIVE FUNCTION = 3.52225248312259"
## [1] "BEST method = 'lin', seasonal.factor = c( 63, 35 )"
## [1] "BEST lin OBJECTIVE FUNCTION = 3.52225248312259"
## [1] "CURRNET METHOD: nonlin"
## [1] "COPY LATEST PARAMETERS DIRECTLY FOR NNS.ARMA() IF ERROR:"
## [1] "NNS.ARMA(... method = 'nonlin' , seasonal.factor = c( 63, 35 ) ...)"
## [1] "CURRENT nonlin OBJECTIVE FUNCTION = 4.3142743227548"
## [1] "BEST method = 'nonlin' PATH MEMBER = c( 63, 35 )"
## [1] "BEST nonlin OBJECTIVE FUNCTION = 4.3142743227548"
## [1] "CURRNET METHOD: both"
## [1] "COPY LATEST PARAMETERS DIRECTLY FOR NNS.ARMA() IF ERROR:"
## [1] "NNS.ARMA(... method = 'both' , seasonal.factor = c( 63, 35 ) ...)"
## [1] "CURRENT both OBJECTIVE FUNCTION = 3.74947524612693"
## [1] "BEST method = 'both' PATH MEMBER = c( 63, 35 )"
## [1] "BEST both OBJECTIVE FUNCTION = 3.74947524612693"
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Pre-Processing
Now we are going to do some basic pre-processing.
data_padded_tbl <- base_data %>%
pad_by_time(
.date_var = date,
.pad_value = 0
)
# Get log interval and standardization parameters
log_params <- liv(data_padded_tbl$value, limit_lower = 0, offset = 1, silent = TRUE)
limit_lower <- log_params$limit_lower
limit_upper <- log_params$limit_upper
offset <- log_params$offset
data_liv_tbl <- data_padded_tbl %>%
# Get log interval transform
mutate(value_trans = liv(value, limit_lower = 0, offset = 1, silent = TRUE)$log_scaled)
# Get Standardization Params
std_params <- standard_vec(data_liv_tbl$value_trans, silent = TRUE)
std_mean <- std_params$mean
std_sd <- std_params$sd
data_transformed_tbl <- data_liv_tbl %>%
# get standardization
mutate(value_trans = standard_vec(value_trans, silent = TRUE)$standard_scaled) %>%
select(-value)
Since this is panel data we can follow one of two different modeling strategies. We can search for a global model in the panel data or we can use nested forecasting finding the best model for each of the time series. Since we only have 5 panels, we will use nested forecasting.
To do this we will use the nest_timeseries and
split_nested_timeseries functions to create a nested tibble.
horizon <- 4*7
nested_data_tbl <- data_transformed_tbl %>%
# 1. Extending: We'll predict n days into the future.
extend_timeseries(
.id_var = package,
.date_var = date,
.length_future = horizon
) %>%
# 2. Nesting: We'll group by id, and create a future dataset
# that forecasts n days of extended data and
# an actual dataset that contains n*2 days
nest_timeseries(
.id_var = package,
.length_future = horizon
#.length_actual = horizon*2
) %>%
# 3. Splitting: We'll take the actual data and create splits
# for accuracy and confidence interval estimation of n das (test)
# and the rest is training data
split_nested_timeseries(
.length_test = horizon
)
nested_data_tbl
## # A tibble: 8 × 4
## package .actual_data .future_data .splits
## <fct> <list> <list> <list>
## 1 healthyR.data <tibble [1,606 × 2]> <tibble [28 × 2]> <split [1578|28]>
## 2 healthyR <tibble [1,599 × 2]> <tibble [28 × 2]> <split [1571|28]>
## 3 healthyR.ts <tibble [1,543 × 2]> <tibble [28 × 2]> <split [1515|28]>
## 4 healthyverse <tibble [1,514 × 2]> <tibble [28 × 2]> <split [1486|28]>
## 5 healthyR.ai <tibble [1,338 × 2]> <tibble [28 × 2]> <split [1310|28]>
## 6 TidyDensity <tibble [1,189 × 2]> <tibble [28 × 2]> <split [1161|28]>
## 7 tidyAML <tibble [797 × 2]> <tibble [28 × 2]> <split [769|28]>
## 8 RandomWalker <tibble [219 × 2]> <tibble [28 × 2]> <split [191|28]>
Now it is time to make some recipes and models using the modeltime workflow.
Modeltime Workflow
Recipe Object
recipe_base <- recipe(
value_trans ~ date
, data = extract_nested_test_split(nested_data_tbl)
)
recipe_base
recipe_date <- recipe_base %>%
step_mutate(date = as.numeric(date))
Models
# Models ------------------------------------------------------------------
# Auto ARIMA --------------------------------------------------------------
model_spec_arima_no_boost <- arima_reg() %>%
set_engine(engine = "auto_arima")
wflw_auto_arima <- workflow() %>%
add_recipe(recipe = recipe_base) %>%
add_model(model_spec_arima_no_boost)
# NNETAR ------------------------------------------------------------------
model_spec_nnetar <- nnetar_reg(
mode = "regression"
, seasonal_period = "auto"
) %>%
set_engine("nnetar")
wflw_nnetar <- workflow() %>%
add_recipe(recipe = recipe_base) %>%
add_model(model_spec_nnetar)
# TSLM --------------------------------------------------------------------
model_spec_lm <- linear_reg() %>%
set_engine("lm")
wflw_lm <- workflow() %>%
add_recipe(recipe = recipe_base) %>%
add_model(model_spec_lm)
# MARS --------------------------------------------------------------------
model_spec_mars <- mars(mode = "regression") %>%
set_engine("earth")
wflw_mars <- workflow() %>%
add_recipe(recipe = recipe_base) %>%
add_model(model_spec_mars)
Nested Modeltime Tables
nested_modeltime_tbl <- modeltime_nested_fit(
# Nested Data
nested_data = nested_data_tbl,
control = control_nested_fit(
verbose = TRUE,
allow_par = FALSE
),
# Add workflows
wflw_auto_arima,
wflw_lm,
wflw_mars,
wflw_nnetar
)
nested_modeltime_tbl <- nested_modeltime_tbl[!is.na(nested_modeltime_tbl$package),]
Model Accuracy
nested_modeltime_tbl %>%
extract_nested_test_accuracy() %>%
filter(!is.na(package)) %>%
knitr::kable()
| package | .model_id | .model_desc | .type | mae | mape | mase | smape | rmse | rsq |
|---|---|---|---|---|---|---|---|---|---|
| healthyR.data | 1 | ARIMA | Test | 0.8119675 | 106.09173 | 0.5667269 | 147.2177 | 0.9791020 | 0.0664329 |
| healthyR.data | 2 | LM | Test | 0.7969567 | 130.14058 | 0.5562499 | 134.5863 | 0.9467616 | 0.0108408 |
| healthyR.data | 3 | EARTH | Test | 0.9761578 | 232.03373 | 0.6813264 | 123.3737 | 1.1697437 | 0.0108408 |
| healthyR.data | 4 | NNAR | Test | 0.8016258 | 103.08275 | 0.5595088 | 179.5996 | 0.9793325 | 0.0000001 |
| healthyR | 1 | ARIMA | Test | 0.6729009 | 94.60582 | 0.6789461 | 171.0713 | 0.8569340 | 0.0016883 |
| healthyR | 2 | LM | Test | 0.6792552 | 97.37531 | 0.6853574 | 179.1648 | 0.8463061 | 0.0033899 |
| healthyR | 3 | EARTH | Test | 0.6816730 | 98.11458 | 0.6877970 | 157.5645 | 0.8432065 | 0.0033899 |
| healthyR | 4 | NNAR | Test | 0.6849794 | 97.20539 | 0.6911331 | 160.0868 | 0.8493549 | 0.1266110 |
| healthyR.ts | 1 | ARIMA | Test | 0.9741876 | 133.90065 | 0.6656652 | 154.3857 | 1.1887227 | 0.0060955 |
| healthyR.ts | 2 | LM | Test | 1.0038903 | 174.81766 | 0.6859612 | 136.2433 | 1.2656331 | 0.0060955 |
| healthyR.ts | 3 | EARTH | Test | 1.1345018 | 281.80037 | 0.7752084 | 134.3926 | 1.3378385 | 0.0060955 |
| healthyR.ts | 4 | NNAR | Test | 0.9563377 | 97.74350 | 0.6534683 | 185.6837 | 1.1519654 | 0.1606090 |
| healthyverse | 1 | ARIMA | Test | 0.7399776 | 256.29751 | 0.7571901 | 115.6270 | 0.8765719 | 0.0027832 |
| healthyverse | 2 | LM | Test | 0.7178546 | 309.84251 | 0.7345525 | 104.1931 | 0.8588975 | 0.0334792 |
| healthyverse | 3 | EARTH | Test | 0.7093389 | 194.79995 | 0.7258387 | 114.6431 | 0.9016571 | 0.0334792 |
| healthyverse | 4 | NNAR | Test | 0.7064777 | 175.92040 | 0.7229110 | 116.5875 | 0.9147379 | 0.0007192 |
| healthyR.ai | 1 | ARIMA | Test | 0.7546859 | 122.83029 | 0.6998472 | 179.0059 | 0.9481992 | 0.0357457 |
| healthyR.ai | 2 | LM | Test | 0.7244442 | 133.74037 | 0.6718030 | 154.4962 | 0.9028161 | 0.0539488 |
| healthyR.ai | 3 | EARTH | Test | 0.7276171 | 133.37527 | 0.6747454 | 155.9489 | 0.9064770 | 0.0539488 |
| healthyR.ai | 4 | NNAR | Test | 0.7187991 | 146.68101 | 0.6665680 | 146.3802 | 0.8932845 | 0.0000589 |
| TidyDensity | 1 | ARIMA | Test | 0.6242475 | 209.09678 | 0.7187209 | 115.4391 | 0.7566124 | 0.0433551 |
| TidyDensity | 2 | LM | Test | 0.6582801 | 275.95266 | 0.7579041 | 105.5566 | 0.8243525 | 0.0019528 |
| TidyDensity | 3 | EARTH | Test | 0.6372743 | 201.13137 | 0.7337192 | 116.5923 | 0.7711928 | 0.0019528 |
| TidyDensity | 4 | NNAR | Test | 0.6375964 | 124.71142 | 0.7340901 | 143.3852 | 0.7761000 | 0.0841651 |
| tidyAML | 1 | ARIMA | Test | 0.6015646 | 319.65245 | 0.8554189 | 103.5759 | 0.7160728 | 0.0529910 |
| tidyAML | 2 | LM | Test | 0.6112991 | 353.96448 | 0.8692614 | 99.1309 | 0.7551168 | 0.0301356 |
| tidyAML | 3 | EARTH | Test | 0.5679999 | 208.44076 | 0.8076902 | 110.9059 | 0.7260562 | 0.0301356 |
| tidyAML | 4 | NNAR | Test | 0.5935106 | 289.76740 | 0.8439662 | 104.8794 | 0.7256868 | 0.0169174 |
| RandomWalker | 1 | ARIMA | Test | 1.4068398 | 170.25603 | 0.6310015 | 144.6026 | 1.7112572 | 0.0592257 |
| RandomWalker | 2 | LM | Test | 1.2610725 | 110.75990 | 0.5656214 | 177.7619 | 1.4854812 | 0.0159481 |
| RandomWalker | 3 | EARTH | Test | 1.2576810 | 113.83585 | 0.5641002 | 172.7444 | 1.4879839 | NA |
| RandomWalker | 4 | NNAR | Test | 1.3874888 | 186.99705 | 0.6223221 | 163.8385 | 1.5117690 | 0.0185977 |
Plot Models
nested_modeltime_tbl %>%
extract_nested_test_forecast() %>%
group_by(package) %>%
plot_modeltime_forecast(
.interactive = FALSE,
.conf_interval_show = FALSE,
.facet_scales = "free"
) +
theme_minimal() +
theme(legend.position = "bottom")
Best Model
best_nested_modeltime_tbl <- nested_modeltime_tbl %>%
modeltime_nested_select_best(
metric = "rmse",
minimize = TRUE,
filter_test_forecasts = TRUE
)
best_nested_modeltime_tbl %>%
extract_nested_best_model_report()
## # Nested Modeltime Table
##
## # A tibble: 8 × 10
## package .model_id .model_desc .type mae mape mase smape rmse rsq
## <fct> <int> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 healthyR.da… 2 LM Test 0.797 130. 0.556 135. 0.947 1.08e-2
## 2 healthyR 3 EARTH Test 0.682 98.1 0.688 158. 0.843 3.39e-3
## 3 healthyR.ts 4 NNAR Test 0.956 97.7 0.653 186. 1.15 1.61e-1
## 4 healthyverse 2 LM Test 0.718 310. 0.735 104. 0.859 3.35e-2
## 5 healthyR.ai 4 NNAR Test 0.719 147. 0.667 146. 0.893 5.89e-5
## 6 TidyDensity 1 ARIMA Test 0.624 209. 0.719 115. 0.757 4.34e-2
## 7 tidyAML 1 ARIMA Test 0.602 320. 0.855 104. 0.716 5.30e-2
## 8 RandomWalker 2 LM Test 1.26 111. 0.566 178. 1.49 1.59e-2
best_nested_modeltime_tbl %>%
extract_nested_test_forecast() %>%
#filter(!is.na(.model_id)) %>%
group_by(package) %>%
plot_modeltime_forecast(
.interactive = FALSE,
.conf_interval_alpha = 0.2,
.facet_scales = "free"
) +
theme_minimal() +
theme(legend.position = "bottom")
Refitting and Future Forecast
Now that we have the best models, we can make our future forecasts.
nested_modeltime_refit_tbl <- best_nested_modeltime_tbl %>%
modeltime_nested_refit(
control = control_nested_refit(verbose = TRUE)
)
nested_modeltime_refit_tbl
## # Nested Modeltime Table
##
## # A tibble: 8 × 5
## package .actual_data .future_data .splits .modeltime_tables
## <fct> <list> <list> <list> <list>
## 1 healthyR.data <tibble> <tibble> <split [1578|28]> <mdl_tm_t [1 × 5]>
## 2 healthyR <tibble> <tibble> <split [1571|28]> <mdl_tm_t [1 × 5]>
## 3 healthyR.ts <tibble> <tibble> <split [1515|28]> <mdl_tm_t [1 × 5]>
## 4 healthyverse <tibble> <tibble> <split [1486|28]> <mdl_tm_t [1 × 5]>
## 5 healthyR.ai <tibble> <tibble> <split [1310|28]> <mdl_tm_t [1 × 5]>
## 6 TidyDensity <tibble> <tibble> <split [1161|28]> <mdl_tm_t [1 × 5]>
## 7 tidyAML <tibble> <tibble> <split [769|28]> <mdl_tm_t [1 × 5]>
## 8 RandomWalker <tibble> <tibble> <split [191|28]> <mdl_tm_t [1 × 5]>
nested_modeltime_refit_tbl %>%
extract_nested_future_forecast() %>%
mutate(across(.value:.conf_hi, .fns = ~ standard_inv_vec(
x = .,
mean = std_mean,
sd = std_sd
)$standard_inverse_value)) %>%
mutate(across(.value:.conf_hi, .fns = ~ liiv(
x = .,
limit_lower = limit_lower,
limit_upper = limit_upper,
offset = offset
)$rescaled_v)) %>%
group_by(package) %>%
plot_modeltime_forecast(
.interactive = FALSE,
.conf_interval_alpha = 0.2,
.facet_scales = "free"
) +
theme_minimal() +
theme(legend.position = "bottom")
