In business-science/sweep: Tidy Tools for Forecasting

knitr::opts_chunk$set(
    # message = FALSE,
    # warning = FALSE,
    fig.width = 8, 
    fig.height = 4.5,
    fig.align = 'center',
    out.width='95%', 
    dpi = 200
)

# devtools::load_all() # Travis CI fails on load_all()

Extending broom to time series forecasting

The sweep package extends the broom tools (tidy, glance, and augment) for performing forecasts and time series analysis in the "tidyverse". The package is geared towards the workflow required to perform forecasts using Rob Hyndman's forecast package, and contains the following elements:

1. model tidiers: sw_tidy, sw_glance, sw_augment, sw_tidy_decomp functions extend tidy, glance, and augment from the broom package specifically for models (ets(), Arima(), bats(), etc) used for forecasting.

2. forecast tidier: sw_sweep converts a forecast object to a tibble that can be easily manipulated in the "tidyverse".

To illustrate, let's take a basic forecasting workflow starting from data collected in a tibble format and then performing a forecast to achieve the end result in tibble format.

Prerequisites

Before we get started, load the following packages.

library(ggplot2)
library(tidyquant)
library(timetk)
library(sweep)
library(forecast)

Forecasting Sales of Beer, Wine, and Distilled Alcohol Beverages

We'll use the tidyquant package to get the US alcohol sales, which comes from the FRED data base (the origin is the US Bureau of the Census, one of the 80+ data sources FRED connects to). The FRED code is "S4248SM144NCEN" and the data set can be found here.

alcohol_sales_tbl <- tq_get("S4248SM144NCEN", 
                            get  = "economic.data", 
                            from = "2007-01-01",
                            to   = "2016-12-31")
alcohol_sales_tbl

We can quickly visualize using the ggplot2 package. We can see that there appears to be some seasonality and an upward trend.

alcohol_sales_tbl %>%
    ggplot(aes(x = date, y = price)) +
    geom_line(linewidth = 1, color = palette_light()[[1]]) +
    geom_smooth(method = "loess") +
    labs(title = "US Alcohol Sales: Monthly", x = "", y = "Millions") +
    scale_y_continuous(labels = scales::dollar) +
    scale_x_date(date_breaks = "1 year", date_labels = "%Y") +
    theme_tq()

Forecasting Workflow

The forecasting workflow involves a few basic steps:

1. Step 1: Coerce to a ts object class.
2. Step 2: Apply a model (or set of models)
3. Step 3: Forecast the models (similar to predict)
4. Step 4: Use sw_sweep() to tidy the forecast.

Note that we purposely omit other steps such as testing the series for stationarity (Box.test(type = "Ljung")) and analysis of autocorrelations (Acf, Pacf) for brevity purposes. We recommend the analyst to follow the forecasting workflow in "Forecasting: principles and practice"

Step 1: Coerce to a ts object class

The forecast package uses the ts data structure, which is quite a bit different than tibbles that we are currently using. Fortunately, it's easy to get to the correct structure with tk_ts() from the timetk package. The start and freq variables are required for the regularized time series (ts) class, and these specify how to treat the time series. For monthly, the frequency should be specified as 12. This results in a nice calendar view. The silent = TRUE tells the tk_ts() function to skip the warning notifying us that the "date" column is being dropped. Non-numeric columns must be dropped for ts class, which is matrix based and a homogeneous data class.

alcohol_sales_ts <- tk_ts(alcohol_sales_tbl, start = 2007, freq = 12, silent = TRUE)
alcohol_sales_ts

A significant benefit is that the resulting ts object maintains a "timetk index", which will help with forecasting dates later. We can verify this using has_timetk_idx() from the timetk package.

has_timetk_idx(alcohol_sales_ts)

Now that a time series has been coerced, let's proceed with modeling.

Step 2: Modeling a time series

The modeling workflow takes a time series object and applies a model. Nothing new here: we'll simply use the ets() function from the forecast package to get an Exponential Smoothing ETS (Error, Trend, Seasonal) model.

fit_ets <- alcohol_sales_ts %>%
    ets()

Where sweep can help is in the evaluation of a model. Expanding on the broom package there are four functions:

• sw_tidy(): Returns a tibble of model parameters
• sw_glance(): Returns the model accuracy measurements
• sw_augment(): Returns the fitted and residuals of the model
• sw_tidy_decomp(): Returns a tidy decomposition from a model

The guide below shows which model object compatibility with sweep tidier functions.

tibble::tribble(
    ~Object,       ~`sw_tidy()`, ~`sw_glance()`, ~`sw_augment()`, ~`sw_tidy_decomp()`, ~`sw_sweep()`,
    "ar",          "",  "",  "", "",   "",
    "arima",       "X", "X", "X", "",  "",
    "Arima",       "X", "X", "X", "",  "",
    "ets",         "X", "X", "X", "X", "",
    "baggedETS",   "",  "",  "",  "",  "",
    "bats",        "X", "X", "X", "X", "",
    "tbats",       "X", "X", "X", "X", "",
    "nnetar",      "X", "X", "X", "",  "",
    "stl",         "",  "",  "",  "X", "",
    "HoltWinters", "X", "X", "X", "X", "",
    "StructTS",      "X", "X", "X", "X", "",
    "tslm",        "X", "X", "X", "",  "",
    "decompose",   "",  "",  "",  "X", "",
    "adf.test",    "X", "X", "",  "",  "",
    "Box.test",    "X", "X", "",  "",  "",
    "kpss.test",   "X", "X", "",  "",  "",
    "forecast",    "",  "",  "",  "",  "X"
) %>%
    knitr::kable(caption = "Function Compatibility",
                 align = c("l", "c", "c", "c", "c", "c"))

Going through the tidiers, we can get useful model information.

sw_tidy

sw_tidy() returns the model parameters.

sw_tidy(fit_ets)

sw_glance

sw_glance() returns the model quality parameters.

sw_glance(fit_ets)

sw_augment

sw_augment() returns the actual, fitted and residual values.

augment_fit_ets <- sw_augment(fit_ets)
augment_fit_ets

We can review the residuals to determine if their are any underlying patterns left. Note that the index is class yearmon, which is a regularized date format.

augment_fit_ets %>%
    ggplot(aes(x = index, y = .resid)) +
    geom_hline(yintercept = 0, color = "grey40") +
    geom_point(color = palette_light()[[1]], alpha = 0.5) +
    geom_smooth(method = "loess") +
    scale_x_yearmon(n = 10) +
    labs(title = "US Alcohol Sales: ETS Residuals", x = "") + 
    theme_tq()

sw_tidy_decomp

sw_tidy_decomp() returns the decomposition of the ETS model.

decomp_fit_ets <- sw_tidy_decomp(fit_ets)
decomp_fit_ets 

We can review the decomposition using ggplot2 as well. The data will need to be manipulated slightly for the facet visualization. The gather() function from the tidyr package is used to reshape the data into a long format data frame with column names "key" and "value" indicating all columns except for index are to be reshaped. The "key" column is then mutated using mutate() to a factor which preserves the order of the keys so "observed" comes first when plotting.

decomp_fit_ets %>%
    tidyr::gather(key = key, value = value, -index) %>%
    dplyr::mutate(key = as.factor(key)) %>%
    ggplot(aes(x = index, y = value, group = key)) +
    geom_line(color = palette_light()[[2]]) +
    geom_ma(ma_fun = SMA, n = 12, size = 1) +
    facet_wrap(~ key, scales = "free_y") +
    scale_x_yearmon(n = 10) +
    labs(title = "US Alcohol Sales: ETS Decomposition", x = "") + 
    theme_tq() +
    theme(axis.text.x = element_text(angle = 45, hjust = 1))

Under normal circumstances it would make sense to refine the model at this point. However, in the interest of showing capabilities (rather than how to forecast) we move onto forecasting the model. For more information on how to forecast, please refer to the online book "Forecasting: principles and practices".

Step 3: Forecasting the model

Next we forecast the ETS model using the forecast() function. The returned forecast object isn't in a "tidy" format (i.e. data frame). This is where the sw_sweep() function helps.

fcast_ets <- fit_ets %>%
    forecast(h = 12) 

Step 4: Tidy the forecast object

We'll use the sw_sweep() function to coerce a forecast into a "tidy" data frame. The sw_sweep() function then coerces the forecast object into a tibble that can be sent to ggplot for visualization. Let's inspect the result.

sw_sweep(fcast_ets, fitted = TRUE)

The tibble returned contains "index", "key" and "value" (or in this case "price") columns in a long or "tidy" format that is ideal for visualization with ggplot2. The "index" is in a regularized format (in this case yearmon) because the forecast package uses ts objects. We'll see how we can get back to the original irregularized format (in this case date) later. The "key" and "price" columns contains three groups of key-value pairs:

1. actual: the actual values from the original data
2. fitted: the model values returned from the ets() function (excluded by default)
3. forecast: the predicted values from the forecast() function

The sw_sweep() function contains an argument fitted = FALSE by default meaning that the model "fitted" values are not returned. We can toggle this on if desired. The remaining columns are the forecast confidence intervals (typically 80 and 95, but this can be changed with forecast(level = c(80, 95))). These columns are setup in a wide format to enable using the geom_ribbon().

Let's visualize the forecast with ggplot2. We'll use a combination of geom_line() and geom_ribbon(). The fitted values are toggled off by default to reduce the complexity of the plot, but these can be added if desired. Note that because we are using a regular time index of the yearmon class, we need to add scale_x_yearmon().

sw_sweep(fcast_ets) %>%
    ggplot(aes(x = index, y = price, color = key)) +
    geom_ribbon(aes(ymin = lo.95, ymax = hi.95), 
                fill = "#D5DBFF", color = NA, linewidth = 0) +
    geom_ribbon(aes(ymin = lo.80, ymax = hi.80, fill = key), 
                fill = "#596DD5", color = NA, linewidth = 0, alpha = 0.8) +
    geom_line(linewidth = 1) +
    labs(title = "US Alcohol Sales, ETS Model Forecast", x = "", y = "Millions",
         subtitle = "Regular Time Index") +
    scale_y_continuous(labels = scales::label_dollar()) +
    scale_x_yearmon(n = 12, format = "%Y") +
    scale_color_tq() +
    scale_fill_tq() +
    theme_tq() 

Because the ts object was created with the tk_ts() function, it contained a timetk index that was carried with it throughout the forecasting workflow. As a result, we can use the timetk_idx argument, which maps the original irregular index (dates) and a generated future index to the regularized time series (yearmon). This results in the ability to return an index of date and datetime, which is not currently possible with the forecast objects. Notice that the index is returned as date class.

sw_sweep(fcast_ets, timetk_idx = TRUE) %>%
    head()

sw_sweep(fcast_ets, timetk_idx = TRUE) %>%
    tail()

We can build the same plot with dates in the x-axis now.

sw_sweep(fcast_ets, timetk_idx = TRUE) %>%
    ggplot(aes(x = index, y = price, color = key)) +
    geom_ribbon(aes(ymin = lo.95, ymax = hi.95), 
                fill = "#D5DBFF", color = NA, linewidth = 0) +
    geom_ribbon(aes(ymin = lo.80, ymax = hi.80, fill = key), 
                fill = "#596DD5", color = NA, linewidth = 0, alpha = 0.8) +
    geom_line(linewidth = 1) +
    labs(title = "US Alcohol Sales, ETS Model Forecast", x = "", y = "Millions", 
         subtitle = "Irregular Time Index") +
    scale_y_continuous(labels = scales::dollar) +
    scale_x_date(date_breaks = "1 year", date_labels = "%Y") +
    scale_color_tq() +
    scale_fill_tq() +
    theme_tq() 

In this example, there is not much benefit to returning an irregular time series. However, when working with frequencies below monthly, the ability to return irregular index values becomes more apparent.

Recap

This was an overview of how various functions within the sweep package can be used to assist in forecast analysis. In the next vignette, we discuss some more powerful concepts including forecasting at scale with grouped time series analysis.

business-science/sweep documentation built on Feb. 2, 2024, 2:49 a.m.