library(fabletools)

Writing a time series model using fabletools provides your model with many additional features without extra effort. Features that aren’t model specific are handled by fabletools, allowing you to spend more time writing methods for your model. Some functionality handled by fabletools includes:

  • Seamless integration with data manipulation and visualisation tools from the tidyverse.
  • Consistent formula interface with other tidy time series models.
  • Transformations with automatic back-transformation of response variables.
  • Batch modelling of many time series and models with parallel support.
  • Accuracy evaluation tools (in-sample, out-of-sample, and cross validation).
  • Visualisation functions for decompositions, models, and forecasts.
  • Support for ensemble and combination modelling (such as decomposition forecasting).
  • Hierarchical, grouped, and temporal reconciliation of forecasts.

The fabletools package promotes consistent interfaces and output structures that allow various time series models to work well together. This vignette will guide you through creating a fabletools model, and provide a glimpse into the steps used to convert user data to modelling inputs, and modelling outputs to user data.

As an example, we’ll create a fabletools model that uses seasonal averages: SMEAN(). It can be thought of as a seasonal version of fable::MEAN(), which instead of averaging the entire series, it averages values from each season.

The model interface

Much like cross-sectional models (such as lm()), tidy time-series models use a formula based interface. Of course not all arguments need to be specified from within the formula (much like na.action in lm()). The model formula is a familiar and user friendly interface for specifying key model concepts (like pdq() in ARIMA()), and data-varying inputs (such as holidays and exogenous regressors). Model specific formula functions (like pdq()) are known as specials (much like specials from stats::terms.formula()).

Before writing code, it is a good idea to think about what interface best suits your model. This is often model specific, however you may find it useful to look at existing interfaces to see how yours could be written consistently. A good example of this is with seasonality: fourier terms are specified with the fourier(period, K) special, and seasonal dummy variables use season(period).

A potential interface for the SMEAN() model could be:

SMEAN(y ~ season(period))

Minimum implementation of a model

At minimum, a model consists of a model function (something that returns a model definition), a set of specials, and a training function.

The model function

Model functions typically consist of two function calls. A model class (defining the training method, the specials, and data checks) with new_model_class(), and new_model_definition to return the model definition:

#' Seasonal mean models
#' 
#' Add the rest of your documentation here.
#' Typically this includes a "Specials" section
#' 
#' @export
SMEAN <- function(formula, ...) {
  # Create a model class which combines the training method, specials, and data checks
  model_smean <- new_model_class("smean",
    # The training method (more on this later)
    train = train_smean,
    # The formula specials (the next section)
    specials = specials_smean,
    # Any checks of the unprocessed data, like gaps, ordered, regular, etc.
    check = function(.data) { 
      if (!tsibble::is_regular(.data)) stop("Data must be regular") 
    }
  )
  
  # Return a model definition which stores the user's model specification
  new_model_definition(model_smean, {{formula}}, ...)
}

Anything passed to ... of new_model_definition() will be passed onward to the model training function. Note that the formula needs to be embraced with {{formula}} in order to allow for non-formula inputs like SMEAN(y).

The specials

The specials for a model are created using new_specials(). The functions specified here will be used to compute specials each time the model is provided with new data (model training, forecasting, refitting, etc.). The results of these functions will be passed to the subsequent method via the specials argument (more on this later).

To enable automatic model specification (with SMEAN(y)), the .required_specials argument will ensure that the special is called at least once. By setting season() as a required special, SMEAN(y) will be parsed as SMEAN(y ~ season()). As no arguments will be provided for omitted required specials, make sure they have good defaults. The fabletools::get_frequencies() function is a useful helper for handling seasonal periods, as automatically chooses appropriate seasonalities when period = NULL, and is able to handle inputs like period = "week".

Anything not handled by defined specials will be treated as exogenous regressors and passed to the xreg() special. That is to say SMEAN(y ~ season("year") + x) will be parsed as SMEAN(y ~ season("year") + xreg(x)). The xreg() special should be defined by all models, even if your model doesn’t support it.

specials_smean <- new_specials(
  season = function(period = NULL) {
    # Your input handling code here.
    get_frequencies(period, self$data, .auto = "smallest")
  },
  xreg = function(...) {
    # This model doesn't support exogenous regressors, time to error.
    stop("Exogenous regressors aren't supported by `SMEAN()`")
  },
  # This model requires `season()`
  # Adding this allows `SMEAN(y)` to automatically include the `season()` special
  .required_specials = "season"
)

The specials are the only thing needed for the formula to work, as the fabletools handles the transformations and response variables specified in the formula’s left side.

The training function

This function is used to apply the model definition created by the model function (SMEAN()) to users data when they use model(data, SMEAN()).

The .data argument is a single series tsibble (no keys), representing the parsed left side of the formula. The index of .data is the time of the measurement, and the measured variables are the transformed response variable(s).

The specials argument is a list of results from parsing the specials used in the right side of the formula. The result from the season() special in SMEAN(y ~ season("year")) would be accessible from specials$season[[1]]. As specials can be used more than once, the nth usage of special xyz() can be accessed with specials$xyz[[n]].

As mentioned earlier, ... will contain additional parameters passed ... of new_model_definition().

The function should return an S3 object that contains everything you need for your future methods (such as forecasting, getting fitted values, refitting, etc.).

train_smean <- function(.data, specials, ...){
  # Extract a vector of response data
  mv <- tsibble::measured_vars(.data)
  if(length(mv) > 1) stop("SMEAN() is a univariate model.")
  y <- .data[[mv]]
  
  # Pull out inputs from the specials
  if(length(specials$season) > 1) stop("The `season()` special of `SMEAN()` should only be used once.")
  m <- specials$season[[1]]
  
  # Compute the seasonal averages
  season_id <- seq(0, length(y) - 1) %% m
  season_y <- split(y, season_id)
  season_avg <- vapply(season_y, FUN = mean, FUN.VALUE = numeric(1L), 
                       USE.NAMES = FALSE)
  
  # Compute fitted values and residuals
  fit <- season_avg[season_id+1]
  e <- y - fit
  
  # Create S3 model object
  # It should be small, but contain everything needed for methods below
  structure(
    list(
      coef = season_avg,
      n = length(y),
      y_name = mv,
      fitted = fit,
      residuals = e,
      sigma2 = var(e, na.rm = TRUE)
    ),
    class = "model_smean"
  )
}

Great, that’s the bare minimum for a model complete with interface and training method. Let’s try it out.

fit <- tsibbledata::aus_production %>%
  model(SMEAN(Beer))
fit
#> # A mable: 1 x 1
#>   `SMEAN(Beer)`
#>         <model>
#> 1    <modl_smn>

It doesn’t look like much, but it has used the above specials and training method to compute the seasonal average and store it in the object. However we can’t see any details about the model yet. To make the model useful, we’ll need to define some methods.

Methods for models

Method Value Description
model_sum() character(1L) A short summary of the model to display in the mable
report() console output A detailed summary of the model, similar to summary()
equation() character(1L) The mathematical equation for the fitted model
forecast() distribution Produce forecasts from the model
stream() updated model Extend the fit of the model with additional data
generate() tsibble Generate potential reponse values at certain times from the model
interpolate() tsibble Interpolate missing values using the model
refit() refitted model Apply the model to a new dataset
tidy() tibble of coefficients Extract coefficients from the model
glance() tibble of statistics Extract summary statistics from the model
augment() tibble of data Augment a dataset with information from the model
components() dable of components Extract decomposed elements from the model
fitted() numeric Extract fitted values from the model
residuals() numeric Extract residuals from the model
#' @importFrom fabletools model_sum
#' @export
model_sum.model_smean <- function(x){
  sprintf("SMEAN[%i]", length(x$coef))
}

fit
#> # A mable: 1 x 1
#>   `SMEAN(Beer)`
#>         <model>
#> 1    <SMEAN[4]>
#' @importFrom fabletools report
#' @export
report.model_smean <- function(x){
  m <- length(x$coef)
  
  cat("\n")
  cat(paste("Seasonal period:", m))
  cat("\n\n")
  cat("Seasonal averages:\n")
  
  print.default(
    setNames(x$coef, paste0("s", seq_len(m))),
    print.gap = 2
  )
  cat(paste("\nsigma^2:", round(x$sigma2, 4), "\n"))
}

report(fit)
#> Series: Beer 
#> Model: SMEAN[4] 
#> 
#> Seasonal period: 4
#> 
#> Seasonal averages:
#>       s1        s2        s3        s4  
#> 416.8182  372.6182  387.3704  485.4444  
#> 
#> sigma^2: 5494.6686
#' @importFrom fabletools tidy
#' @export
tidy.model_smean <- function(x){
  tibble::tibble(
    term = paste0("season_", seq_along(x$coef)), 
    estimate = x$coef
  )
}

tidy(fit)
#> # A tibble: 4 x 3
#>   .model      term     estimate
#>   <chr>       <chr>       <dbl>
#> 1 SMEAN(Beer) season_1     417.
#> 2 SMEAN(Beer) season_2     373.
#> 3 SMEAN(Beer) season_3     387.
#> 4 SMEAN(Beer) season_4     485.
#' @importFrom fabletools glance
#' @export
glance.model_smean <- function(x){
  tibble::tibble(
    sigma2 = x$sigma2
  )
}

glance(fit)
#> # A tibble: 1 x 2
#>   .model      sigma2
#>   <chr>        <dbl>
#> 1 SMEAN(Beer)  5495.
#' @importFrom fabletools forecast
#' @export
forecast.model_smean <- function(object, new_data, ...){
  # Extract required parameters
  h <- NROW(new_data)
  n <- object$n
  m <- length(object$coef)
  coef <- object$coef
  
  # Compute forecast variance
  season_id <- seq(0, n - 1) %% m
  season_e <- split(object$residuals, season_id)
  season_sd <- vapply(season_e, FUN = sd, FUN.VALUE = numeric(1L), 
                       USE.NAMES = FALSE, na.rm = TRUE)
  
  # Create forecast distributions
  fc_id <- (seq(0, h-1) + n %% m) %% m + 1
  mu <- coef[fc_id]
  sigma <- season_sd[fc_id]
  distributional::dist_normal(mu, sigma)
}

forecast(fit)
#> # A fable: 8 x 4 [1Q]
#> # Key:     .model [1]
#>   .model      Quarter         Beer .mean
#>   <chr>         <qtr>       <dist> <dbl>
#> 1 SMEAN(Beer) 2010 Q3 N(387, 4808)  387.
#> 2 SMEAN(Beer) 2010 Q4 N(485, 7057)  485.
#> 3 SMEAN(Beer) 2011 Q1 N(417, 5352)  417.
#> 4 SMEAN(Beer) 2011 Q2 N(373, 5083)  373.
#> 5 SMEAN(Beer) 2011 Q3 N(387, 4808)  387.
#> 6 SMEAN(Beer) 2011 Q4 N(485, 7057)  485.
#> 7 SMEAN(Beer) 2012 Q1 N(417, 5352)  417.
#> 8 SMEAN(Beer) 2012 Q2 N(373, 5083)  373.
#' @importFrom fabletools stream
#' @export
stream.model_smean <- function(object, new_data, specials, ...){
  # Extract a vector of response data
  mv <- tsibble::measured_vars(new_data)
  y <- new_data[[mv]]
  
  # Compute the new seasonal averages
  m <- length(object$coef)
  season_id <- (seq(0, length(y) - 1) + object$n %% m) %% m
  season_y <- split(y, season_id)
  season_avg <- vapply(season_y, FUN = mean, FUN.VALUE = numeric(1L), 
                       USE.NAMES = FALSE)
  weight_new <- vapply(season_y, FUN = length, FUN.VALUE = integer(1L),
                       USE.NAMES = FALSE)
  
  # Update coefficients to include new estimates
  weight_orig <- rep(object$n %/% m, m) + c(rep(1, object$n %% m), rep(0, m - object$n %% m))
  new_coef <- (object$coef * weight_orig + season_avg * weight_new) / (weight_orig + weight_new)
  coef_change <- new_coef - object$coef
  
  # Update model
  new_fits <- new_coef[season_id+1]
  new_e <- y - new_fits
  object$coef <- new_coef
  object$fitted <- c(object$fitted + rep_len(coef_change, object$n), new_fits)
  object$residuals <- c(object$residuals - rep_len(coef_change, object$n), new_e)
  object$n <- object$n + length(y)
  object$sigma2 <- var(object$residuals, na.rm = TRUE)
  
  # Return updated model object
  object
}

us_acc_deaths <- as_tsibble(USAccDeaths)
fit_stream <- us_acc_deaths %>% 
  dplyr::slice(1:60) %>% 
  model(SMEAN(value))
report(fit_stream)
#> Series: value 
#> Model: SMEAN[12] 
#> 
#> Seasonal period: 12
#> 
#> Seasonal averages:
#>      s1       s2       s3       s4       s5       s6       s7       s8  
#>  8085.6   7362.2   8116.6   8292.0   9126.2   9627.6  10446.6   9733.6  
#>      s9      s10      s11      s12  
#>  8618.4   8974.2   8434.0   8616.8  
#> 
#> sigma^2: 251827.8712

# Update the model with new data
us_acc_deaths_new <- us_acc_deaths %>% dplyr::slice(61:72)
fit_stream <- fit_stream %>% 
  stream(us_acc_deaths_new)
report(fit_stream)
#> Series: value 
#> Model: SMEAN[12] 
#> 
#> Seasonal period: 12
#> 
#> Seasonal averages:
#>        s1         s2         s3         s4         s5         s6         s7  
#>  8044.000   7283.833   8062.333   8275.333   9124.333   9595.333  10452.833  
#>        s8         s9        s10        s11        s12  
#>  9749.167   8700.333   8990.167   8467.167   8720.667  
#> 
#> sigma^2: 222480.9038

# Check that it matches a model of the full data
us_acc_deaths %>% 
  model(SMEAN(value)) %>% 
  report()
#> Series: value 
#> Model: SMEAN[12] 
#> 
#> Seasonal period: 12
#> 
#> Seasonal averages:
#>        s1         s2         s3         s4         s5         s6         s7  
#>  8044.000   7283.833   8062.333   8275.333   9124.333   9595.333  10452.833  
#>        s8         s9        s10        s11        s12  
#>  9749.167   8700.333   8990.167   8467.167   8720.667  
#> 
#> sigma^2: 222480.9038
#' @importFrom fabletools fitted
#' @export
fitted.model_smean <- function(object, ...){
  object$fitted
}

fitted(fit)
#> # A tsibble: 218 x 3 [1Q]
#> # Key:       .model [1]
#>    .model      Quarter .fitted
#>    <chr>         <qtr>   <dbl>
#>  1 SMEAN(Beer) 1956 Q1    417.
#>  2 SMEAN(Beer) 1956 Q2    373.
#>  3 SMEAN(Beer) 1956 Q3    387.
#>  4 SMEAN(Beer) 1956 Q4    485.
#>  5 SMEAN(Beer) 1957 Q1    417.
#>  6 SMEAN(Beer) 1957 Q2    373.
#>  7 SMEAN(Beer) 1957 Q3    387.
#>  8 SMEAN(Beer) 1957 Q4    485.
#>  9 SMEAN(Beer) 1958 Q1    417.
#> 10 SMEAN(Beer) 1958 Q2    373.
#> # … with 208 more rows
#' @importFrom fabletools residuals
#' @export
residuals.model_smean <- function(object, ...){
  object$residuals
}

residuals(fit)
#> # A tsibble: 218 x 3 [1Q]
#> # Key:       .model [1]
#>    .model      Quarter .resid
#>    <chr>         <qtr>  <dbl>
#>  1 SMEAN(Beer) 1956 Q1  -133.
#>  2 SMEAN(Beer) 1956 Q2  -160.
#>  3 SMEAN(Beer) 1956 Q3  -160.
#>  4 SMEAN(Beer) 1956 Q4  -177.
#>  5 SMEAN(Beer) 1957 Q1  -155.
#>  6 SMEAN(Beer) 1957 Q2  -145.
#>  7 SMEAN(Beer) 1957 Q3  -151.
#>  8 SMEAN(Beer) 1957 Q4  -165.
#>  9 SMEAN(Beer) 1958 Q1  -145.
#> 10 SMEAN(Beer) 1958 Q2  -140.
#> # … with 208 more rows
#' @importFrom fabletools components
#' @export
components.model_smean <- function(object, ...){
  # Create a tsibble of the components
  dcmp <- tibble::tibble(
    !!object$y_name := fitted(object) + residuals(object),
    season = fitted(object),
    remainder = residuals(object)
  )
  
  # Describe how the components combine into other columns
  aliases <- tibble::lst(!!object$y_name := quote(season + remainder))
  
  # Define the behaviour of seasonal components
  # This is used for automatic modelling of seasonal components in `decomposition_model()`
  # It may also be used for plotting in the future.
  seasonalities <- list(season = list(period = length(object$coef)))
  
  # Return a dable
  as_dable(
    dcmp,
    resp = !!sym(object$y_name), method = model_sum(object),
    seasons = seasonalities, aliases = aliases
  )
}

components(fit) # Need to store index somewhere. This workflow should improve.