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The purpose of forecastML is to provide a series of functions and visualizations that simplify the process of multi-step-ahead forecasting with standard machine learning algorithms. It’s a wrapper package aimed at providing maximum flexibility in model-building–choose any machine learning algorithm from any R or Python package–while helping the user quickly assess the (a) accuracy, (b) stability, and (c) generalizability of grouped (i.e., multiple related time series) and ungrouped forecasts produced from potentially high-dimensional modeling datasets.

This package is inspired by Bergmeir, Hyndman, and Koo’s 2018 paper A note on the validity of cross-validation for evaluating autoregressive time series prediction. which supports–under certain conditions–forecasting with high-dimensional ML models without having to use methods that are time series specific.

The following quote from Bergmeir et al.’s article nicely sums up the aim of this package:

“When purely (non-linear, nonparametric) autoregressive methods are applied to forecasting problems, as is often the case (e.g., when using Machine Learning methods), the aforementioned problems of CV are largely irrelevant, and CV can and should be used without modification, as in the independent case.”

User-contributed notebooks welcome!

Lightning Example

library(forecastML)
library(glmnet)

data("data_seatbelts", package = "forecastML")

data_train <- forecastML::create_lagged_df(data_seatbelts, type = "train", method = "direct",
                                           outcome_col = 1, lookback = 1:15, horizon = 1:12)

windows <- forecastML::create_windows(data_train, window_length = 0)

model_fun <- function(data) {
  x <- as.matrix(data[, -1, drop = FALSE])
  y <- as.matrix(data[, 1, drop = FALSE])
  model <- glmnet::cv.glmnet(x, y)
}

model_results <- forecastML::train_model(data_train, windows, model_name = "LASSO", model_function = model_fun)

prediction_fun <- function(model, data_features) {
  data_pred <- data.frame("y_pred" = predict(model, as.matrix(data_features)),
                          "y_pred_lower" = predict(model, as.matrix(data_features)) - 30,
                          "y_pred_upper" = predict(model, as.matrix(data_features)) + 30)
}

data_forecast <- forecastML::create_lagged_df(data_seatbelts, type = "forecast", method = "direct",
                                              outcome_col = 1, lookback = 1:15, horizon = 1:12)

data_forecasts <- predict(model_results, prediction_function = list(prediction_fun), data = data_forecast)

data_forecasts <- forecastML::combine_forecasts(data_forecasts)

plot(data_forecasts, data_actual = data_seatbelts[-(1:100), ], actual_indices = (1:nrow(data_seatbelts))[-(1:100)])

README Contents

Install

install.packages("forecastML")
library(forecastML)
remotes::install_github("nredell/forecastML")
library(forecastML)

Approach to Forecasting

Direct forecasting

The direct forecasting approach used in forecastML involves the following steps:

1. Build a series of horizon-specific short-, medium-, and long-term forecast models.

2. Assess model generalization performance across a variety of heldout datasets through time.

3. Select those models that consistently performed the best at each forecast horizon and combine them to produce a single ensemble forecast.

Multi-output forecasting

The multi-output forecasting approach used in forecastML involves the following steps:

1. Build a single multi-output model that simultaneously forecasts over both short- and long-term forecast horizons.

2. Assess model generalization performance across a variety of heldout datasets through time.

3. Select the hyperparamters that minimize forecast error over all the relevant forecast horizons and re-train.

Vignettes

The main functions covered in each vignette are shown below as function().

Cheat Sheets

  1. fill_gaps: Optional if no temporal gaps/missing rows in data collection. Fill gaps in data collection and prepare a dataset of evenly-spaced time series for modeling with lagged features. Returns a ‘data.frame’ with missing rows added in so that you can either (a) impute, remove, or ignore NAs prior to the forecastML pipeline or (b) impute, remove, or ignore them in the user-defined modeling function–depending on the NA handling capabilities of the user-specified model.

  2. create_lagged_df: Create model training and forecasting datasets with lagged, grouped, dynamic, and static features.

  3. create_windows: Create time-contiguous validation datasets for model evaluation.

  4. train_model: Train the user-defined model across forecast horizons and validation datasets.

  5. return_error: Compute forecast error across forecast horizons and validation datasets.

  6. return_hyper: Return user-defined model hyperparameters across validation datasets.

  7. combine_forecasts: Combine multiple horizon-specific forecast models to produce one forecast.


FAQ

Examples - Numeric Outcomes with R and Python

Direct forecast in R

Below is an example of how to create 12 horizon-specific ML models to forecast the number of DriversKilled 12 time periods into the future using the Seatbelts dataset. Notice in the last plot that there are multiple forecasts; these are from the slightly different LASSO models trained in the nested cross-validation. An example of selecting optimal hyperparameters and retraining to create a single forecast model (i.e., create_windows(..., window_length = 0)) can be found in the overview vignette.

library(glmnet)
library(forecastML)

# Sampled Seatbelts data from the R package datasets.
data("data_seatbelts", package = "forecastML")

# Example - Training data for 12 horizon-specific models w/ common lags per feature. The data do 
# not have any missing rows or temporal gaps in data collection; if there were gaps, 
# we would need to use fill_gaps() first.
horizons <- 1:12  # 12 models that forecast 1, 1:2, 1:3, ..., and 1:12 time steps ahead.
lookback <- 1:15  # A lookback of 1 to 15 dataset rows (1:15 * 'date frequency' if dates are given).

#------------------------------------------------------------------------------
# Create a dataset of lagged features for modeling.
data_train <- forecastML::create_lagged_df(data_seatbelts, type = "train",
                                           outcome_col = 1, lookback = lookback,
                                           horizon = horizons)

#------------------------------------------------------------------------------
# Create validation datasets for outer-loop nested cross-validation.
windows <- forecastML::create_windows(data_train, window_length = 12)

#------------------------------------------------------------------------------
# User-define model - LASSO
# A user-defined wrapper function for model training that takes the following
# arguments: (1) a horizon-specific data.frame made with create_lagged_df(..., type = "train")
# (e.g., my_lagged_df$horizon_h) and, optionally, (2) any number of additional named arguments
# which can also be passed in '...' in train_model(). The function returns a model object suitable for 
# the user-defined predict function. The returned model may also be a list that holds meta-data such 
# as hyperparameter settings.

model_function <- function(data, my_outcome_col) {  # my_outcome_col = 1 could be defined here.

  x <- data[, -(my_outcome_col), drop = FALSE]
  y <- data[, my_outcome_col, drop = FALSE]
  x <- as.matrix(x, ncol = ncol(x))
  y <- as.matrix(y, ncol = ncol(y))

  model <- glmnet::cv.glmnet(x, y)
  return(model)  # This model is the first argument in the user-defined predict() function below.
}

#------------------------------------------------------------------------------
# Train a model across forecast horizons and validation datasets.
# my_outcome_col = 1 is passed in ... but could have been defined in the user-defined model function.
model_results <- forecastML::train_model(data_train,
                                         windows = windows,
                                         model_name = "LASSO", 
                                         model_function = model_function,
                                         my_outcome_col = 1,  # ...
                                         use_future = FALSE)

#------------------------------------------------------------------------------
# User-defined prediction function - LASSO
# The predict() wrapper function takes 2 positional arguments. First,
# the returned model from the user-defined modeling function (model_function() above).
# Second, a data.frame of model features. If predicting on validation data, expect the input data to be 
# passed in the same format as returned by create_lagged_df(type = 'train') but with the outcome column 
# removed. If forecasting, expect the input data to be in the same format as returned by 
# create_lagged_df(type = 'forecast') but with the 'index' and 'horizon' columns removed. The function 
# can return a 1- or 3-column data.frame with either (a) point
# forecasts or (b) point forecasts plus lower and upper forecast bounds (column order and names do not matter).

prediction_function <- function(model, data_features) {

  x <- as.matrix(data_features, ncol = ncol(data_features))
  data_pred <- data.frame("y_pred" = predict(model, x, s = "lambda.min"),  # 1 column is required.
                          "y_pred_lower" = predict(model, x, s = "lambda.min") - 50,  # optional.
                          "y_pred_upper" = predict(model, x, s = "lambda.min") + 50)  # optional.
  return(data_pred)
}

# Predict on the validation datasets.
data_valid <- predict(model_results, prediction_function = list(prediction_function), data = data_train)

#------------------------------------------------------------------------------
# Plot forecasts for each validation dataset.
plot(data_valid, horizons = c(1, 6, 12))

#------------------------------------------------------------------------------
# Forecast.

# Forward-looking forecast data.frame.
data_forecast <- forecastML::create_lagged_df(data_seatbelts, type = "forecast",
                                              outcome_col = 1, lookback = lookback, horizons = horizons)

# Forecasts.
data_forecasts <- predict(model_results, prediction_function = list(prediction_function), data = data_forecast)

# We'll plot a background dataset of actuals as well.
plot(data_forecasts,
     data_actual = data_seatbelts[-(1:150), ], 
     actual_indices = as.numeric(row.names(data_seatbelts[-(1:150), ])), 
     horizons = c(1, 6, 12), windows = c(5, 10, 15))


Direct forecast in R & Python

Now we’ll look at an example similar to above. The main difference is that our user-defined modeling and prediction functions are now written in Python. Thanks to the reticulate R package, entire ML workflows already written in Python can be imported into forecastML with the simple addition of 2 lines of R code.

library(forecastML)
library(reticulate)  # Move Python objects in and out of R. See the reticulate package for setup info.

reticulate::source_python("modeling_script.py")  # Run a Python file and import objects into R.


data("data_seatbelts", package = "forecastML")

horizons <- c(1, 12)  # 2 models that forecast 1 and 1:12 time steps ahead.

# A lookback across select time steps in the past. Feature lags 1 through 9 will be silently dropped from the 12-step-ahead model.
lookback <- c(1, 3, 6, 9, 12, 15)

date_frequency <- "1 month"  # Time step frequency.

# The date indices, which don't come with the stock dataset, should not be included in the modeling data.frame.
dates <- seq(as.Date("1969-01-01"), as.Date("1984-12-01"), by = date_frequency)

# Create a dataset of features for modeling.
data_train <- forecastML::create_lagged_df(data_seatbelts, type = "train", outcome_col = 1,
                                           lookback = lookback, horizon = horizons,
                                           dates = dates, frequency = date_frequency)

# Create 2 custom validation datasets for outer-loop nested cross-validation. The purpose of
# the multiple validation windows is to assess expected forecast accuracy for specific
# time periods while supporting an investigation of the hyperparameter stability for
# models trained on different time periods. Validation windows can overlap.
window_start <- c(as.Date("1983-01-01"), as.Date("1984-01-01"))
window_stop <- c(as.Date("1983-12-01"), as.Date("1984-12-01"))

windows <- forecastML::create_windows(data_train, window_start = window_start, window_stop = window_stop)


modeling_script.py


import pandas as pd
from sklearn import linear_model
from sklearn.preprocessing import StandardScaler

# User-defined model.
# A user-defined wrapper function for model training that takes the following
# arguments: (1) a horizon-specific pandas DataFrame made with create_lagged_df(..., type = "train")
# (e.g., my_lagged_df$horizon_h)
def py_model_function(data):
  
  X = data.iloc[:, 1:]
  y = data.iloc[:, 0]
  
  scaler = StandardScaler()
  X = scaler.fit_transform(X)
  
  model_lasso = linear_model.Lasso(alpha = 0.1)
  
  model_lasso.fit(X = X, y = y)
  
  return({'model': model_lasso, 'scaler': scaler})

# User-defined prediction function.
# The predict() wrapper function takes 2 positional arguments. First,
# the returned model from the user-defined modeling function (py_model_function() above).
# Second, a pandas DataFrame of model features. For numeric outcomes, the function 
# can return a 1- or 3-column pandas DataFrame with either (a) point
# forecasts or (b) point forecasts plus lower and upper forecast bounds (column order and names do not matter).
def py_prediction_function(model_list, data_x):
  
  data_x = model_list['scaler'].transform(data_x)
  
  data_pred = pd.DataFrame({'y_pred': model_list['model'].predict(data_x)})
  
  return(data_pred)


# Train a model across forecast horizons and validation datasets.
model_results <- forecastML::train_model(data_train,
                                         windows = windows,
                                         model_name = "LASSO",
                                         model_function = py_model_function,
                                         use_future = FALSE)

# Predict on the validation datasets.
data_valid <- predict(model_results, prediction_function = list(py_prediction_function), data = data_train)

# Plot forecasts for each validation dataset.
plot(data_valid, horizons = c(1, 12))


# Forward-looking forecast data.frame.
data_forecast <- forecastML::create_lagged_df(data_seatbelts, type = "forecast", outcome_col = 1,
                                              lookback = lookback, horizon = horizons,
                                              dates = dates, frequency = date_frequency)

# Forecasts.
data_forecasts <- predict(model_results, prediction_function = list(py_prediction_function),
                          data = data_forecast)

# We'll plot a background dataset of actuals as well.
plot(data_forecasts, data_actual = data_seatbelts[-(1:150), ], 
     actual_indices = dates[-(1:150)], horizons = c(1, 12))


Multi-output forecast in R

library(forecastML)
library(keras)  # Using the TensorFlow 2.0 backend.

data("data_seatbelts", package = "forecastML")

data_seatbelts[] <- lapply(data_seatbelts, function(x) {
  (x - mean(x, na.rm = TRUE)) / sd(x, na.rm = TRUE)
})

date_frequency <- "1 month"
dates <- seq(as.Date("1969-01-01"), as.Date("1984-12-01"), by = date_frequency)

data_train <- forecastML::create_lagged_df(data_seatbelts, type = "train", method = "multi_output",
                                           outcome_col = 1, lookback = 1:15, horizons = 1:12,
                                           dates = dates, frequency = date_frequency,
                                           dynamic_features = "law")

# 'window_length = 0' creates 1 historical training dataset with no external validation datasets. 
# Set it to, say, 24 to see the model and forecast stability when trained across different slices 
# of historical data.
windows <- forecastML::create_windows(data_train, window_length = 0)

#------------------------------------------------------------------------------
# 'data_y' consists of 1 column for each forecast horizon--here, 12.
model_fun <- function(data, horizons) {  # 'horizons' is passed in train_model().

  data_x <- apply(as.matrix(data[, -(1:length(horizons))]), 2, function(x){ifelse(is.na(x), 0, x)})
  data_y <- apply(as.matrix(data[, 1:length(horizons)]), 2, function(x){ifelse(is.na(x), 0, x)})

  layers_x_input <- keras::layer_input(shape = ncol(data_x))

  layers_x_output <- layers_x_input %>%
    keras::layer_dense(ncol(data_x), activation = "relu") %>%
    keras::layer_dense(ncol(data_x), activation = "relu") %>%
    keras::layer_dense(length(horizons))

  model <- keras::keras_model(inputs = layers_x_input, outputs = layers_x_output) %>%
    keras::compile(optimizer = 'adam', loss = 'mean_absolute_error')

  early_stopping <- callback_early_stopping(monitor = 'val_loss', patience = 2)

  tensorflow::tf$random$set_seed(224)

  model_results <- model %>%
    keras::fit(x = list(as.matrix(data_x)), y = list(as.matrix(data_y)),
               validation_split = 0.2, callbacks = c(early_stopping), verbose = FALSE)

  return(list("model" = model, "model_results" = model_results))
}
#------------------------------------------------------------------------------
# The predict() wrapper function will return a data.frame with a number of columns 
# equaling the number of forecast horizons.
prediction_fun <- function(model, data_features) {

  data_features[] <- lapply(data_features, function(x){ifelse(is.na(x), 0, x)})
  data_features <- list(as.matrix(data_features, ncol = ncol(data_features)))

  data_pred <- data.frame(predict(model$model, data_features))
  names(data_pred) <- paste0("y_pred_", 1:ncol(data_pred))

  return(data_pred)
}
#------------------------------------------------------------------------------

model_results <- forecastML::train_model(data_train, windows, model_name = "Multi-Output NN",
                                         model_function = model_fun,
                                         horizons = 1:12)

data_valid <- predict(model_results, prediction_function = list(prediction_fun), data = data_train)

# We'll plot select forecast horizons to reduce visual clutter.
plot(data_valid, facet = ~ model, horizons = c(1, 3, 6, 12))

data_forecast <- forecastML::create_lagged_df(data_seatbelts, type = "forecast", method = "multi_output",
                                              outcome_col = 1, lookback = 1:15, horizons = 1:12,
                                              dates = dates, frequency = date_frequency,
                                              dynamic_features = "law")

data_forecasts <- predict(model_results, prediction_function = list(prediction_fun), data = data_forecast)

plot(data_forecasts, facet = NULL, data_actual = data_seatbelts[-(1:100), ], actual_indices = dates[-(1:100)])

Examples - Factor Outcomes with R and Python

R

data("data_seatbelts", package = "forecastML")

# Create an artifical factor outcome for illustration' sake.
data_seatbelts$DriversKilled <- cut(data_seatbelts$DriversKilled, 3)

horizons <- c(1, 12)  # 2 models that forecast 1 and 1:12 time steps ahead.

# A lookback across select time steps in the past. Feature lag 1 will be silently dropped from the 12-step-ahead model.
lookback <- c(1, 12, 18)

date_frequency <- "1 month"  # Time step frequency.

# The date indices, which don't come with the stock dataset, should not be included in the modeling data.frame.
dates <- seq(as.Date("1969-01-01"), as.Date("1984-12-01"), by = date_frequency)

# Create a dataset of features for modeling.
data_train <- forecastML::create_lagged_df(data_seatbelts, type = "train", outcome_col = 1,
                                           lookback = lookback, horizon = horizons,
                                           dates = dates, frequency = date_frequency)

# We won't use nested cross-validation; rather, we'll train a model over the entire training dataset.
windows <- forecastML::create_windows(data_train, window_length = 0)

# This is the model-training dataset.
plot(windows, data_train)

model_function <- function(data, my_outcome_col) {  # my_outcome_col = 1 could be defined here.
  
  outcome_names <- names(data)[1]
  model_formula <- formula(paste0(outcome_names,  "~ ."))
  
  set.seed(224)
  model <- randomForest::randomForest(formula = model_formula, data = data, ntree = 3)
  return(model)  # This model is the first argument in the user-defined predict() function below.
}

#------------------------------------------------------------------------------
# Train a model across forecast horizons and validation datasets.
# my_outcome_col = 1 is passed in ... but could have been defined in the user-defined model function.
model_results <- forecastML::train_model(data_train,
                                         windows = windows,
                                         model_name = "RF", 
                                         model_function = model_function,
                                         my_outcome_col = 1,  # ...
                                         use_future = FALSE)

#------------------------------------------------------------------------------
# User-defined prediction function.
#
# The predict() wrapper function takes 2 positional arguments. First,
# the returned model from the user-defined modeling function (model_function() above).
# Second, a data.frame of model features. If predicting on validation data, expect the input data to be 
# passed in the same format as returned by create_lagged_df(type = 'train') but with the outcome column 
# removed. If forecasting, expect the input data to be in the same format as returned by 
# create_lagged_df(type = 'forecast') but with the 'index' and 'horizon' columns removed.
# 
# For factor outcomes, the function can return either (a) a 1-column data.frame with factor level 
# predictions or (b) an L-column data.frame of predicted class probabilities where 'L' equals the 
# number of levels in the outcome; the order of the return()'d columns should match the order of the 
# outcome factor levels from left to right which is the default behavior of most predict() functions.

# Predict/forecast a single factor level.
prediction_function_level <- function(model, data_features) {
  
  data_pred <- data.frame("y_pred" = predict(model, data_features, type = "response"))
  
  return(data_pred)
}

# Predict/forecast outcome class probabilities.
prediction_function_prob <- function(model, data_features) {
  
  data_pred <- data.frame("y_pred" = predict(model, data_features, type = "prob"))
  
  return(data_pred)
}

# Predict on the validation datasets.
data_valid_level <- predict(model_results, 
                            prediction_function = list(prediction_function_level), 
                            data = data_train)
data_valid_prob <- predict(model_results, 
                           prediction_function = list(prediction_function_prob), 
                           data = data_train)
plot(data_valid_level, horizons = c(1, 12))

plot(data_valid_prob, horizons = c(1, 12))

# Forward-looking forecast data.frame.
data_forecast <- forecastML::create_lagged_df(data_seatbelts, type = "forecast",
                                              outcome_col = 1, lookback = lookback, horizons = horizons)

# Forecasts.
data_forecasts_level <- predict(model_results,
                                prediction_function = list(prediction_function_level),
                                data = data_forecast)

data_forecasts_prob <- predict(model_results,
                                prediction_function = list(prediction_function_prob),
                                data = data_forecast)
plot(data_forecasts_level)

plot(data_forecasts_prob)