Introduction to sweep

Matt Dancho

2018-03-03

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

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
## # A tibble: 120 x 2
##    date       price
##    <date>     <int>
##  1 2007-01-01  6627
##  2 2007-02-01  6743
##  3 2007-03-01  8195
##  4 2007-04-01  7828
##  5 2007-05-01  9570
##  6 2007-06-01  9484
##  7 2007-07-01  8608
##  8 2007-08-01  9543
##  9 2007-09-01  8123
## 10 2007-10-01  9649
## # ... with 110 more rows

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(size = 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
##        Jan   Feb   Mar   Apr   May   Jun   Jul   Aug   Sep   Oct   Nov
## 2007  6627  6743  8195  7828  9570  9484  8608  9543  8123  9649  9390
## 2008  7093  7483  8365  8895  9794  9977  9553  9375  9225  9948  8758
## 2009  7266  7578  8688  9162  9369 10167  9507  8923  9272  9075  8949
## 2010  6558  7481  9475  9424  9351 10552  9077  9273  9420  9413  9866
## 2011  6901  8014  9833  9281  9967 11344  9106 10468 10085  9612 10328
## 2012  7486  8641  9709  9423 11342 11274  9845 11163  9532 10754 10953
## 2013  8395  8888 10109 10493 12217 11385 11186 11462 10494 11541 11139
## 2014  8559  9061 10058 10979 11794 11906 10966 10981 10827 11815 10466
## 2015  8398  9061 10720 11105 11505 12903 11866 11223 12023 11986 11510
## 2016  8540 10158 11879 11155 11916 13291 10540 12212 11786 11424 12482
##        Dec
## 2007 10065
## 2008 10839
## 2009 10843
## 2010 11455
## 2011 11483
## 2012 11922
## 2013 12709
## 2014 13303
## 2015 14190
## 2016 13832

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)
## [1] TRUE

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:

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

Function Compatibility
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

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

sw_tidy

sw_tidy() returns the model parameters.

sw_tidy(fit_ets)
## # A tibble: 16 x 2
##    term     estimate
##    <chr>       <dbl>
##  1 alpha    0.176   
##  2 beta     0.000386
##  3 gamma    0.000501
##  4 l     8389       
##  5 b       38.9     
##  6 s0       1.18    
##  7 s1       1.02    
##  8 s2       1.03    
##  9 s3       0.991   
## 10 s4       1.04    
## 11 s5       1.00    
## 12 s6       1.11    
## 13 s7       1.07    
## 14 s8       0.977   
## 15 s9       0.982   
## 16 s10      0.835

sw_glance

sw_glance() returns the model quality parameters.

sw_glance(fit_ets)
## # A tibble: 1 x 12
##   model.desc  sigma logLik   AIC   BIC    ME  RMSE   MAE    MPE  MAPE
##   <chr>       <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>  <dbl> <dbl>
## 1 ETS(M,A,M) 0.0455  -1012  2059  2106 -53.6   430   363 -0.695  3.65
## # ... with 2 more variables: MASE <dbl>, ACF1 <dbl>

sw_augment

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

augment_fit_ets <- sw_augment(fit_ets)
augment_fit_ets
## # A tibble: 120 x 4
##    index         .actual .fitted     .resid
##    <S3: yearmon>   <dbl>   <dbl>      <dbl>
##  1 Jan 2007         6627    6411  0.0337   
##  2 Feb 2007         6743    7115 -0.0523   
##  3 Mar 2007         8195    8322 -0.0153   
##  4 Apr 2007         7828    8298 -0.0566   
##  5 May 2007         9570    9044  0.0582   
##  6 Jun 2007         9484    9544 -0.00628  
##  7 Jul 2007         8608    8607  0.0000959
##  8 Aug 2007         9543    8992  0.0613   
##  9 Sep 2007         8123    8693 -0.0656   
## 10 Oct 2007         9649    8978  0.0748   
## # ... with 110 more rows

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 
## # A tibble: 121 x 5
##    index         observed level slope season
##    <S3: yearmon>    <dbl> <dbl> <dbl>  <dbl>
##  1 Dec 2006            NA  8389  38.9  1.18 
##  2 Jan 2007          6627  8478  39.0  0.761
##  3 Feb 2007          6743  8439  38.8  0.835
##  4 Mar 2007          8195  8455  38.8  0.982
##  5 Apr 2007          7828  8409  38.6  0.977
##  6 May 2007          9570  8534  38.8  1.07 
##  7 Jun 2007          9484  8563  38.7  1.11 
##  8 Jul 2007          8608  8602  38.7  1.00 
##  9 Aug 2007          9543  8734  38.9  1.04 
## 10 Sep 2007          8123  8672  38.7  0.991
## # ... with 111 more rows

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 %>%
    gather(key = key, value = value, -index) %>%
    mutate(key = forcats::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))
## Warning: Removed 1 rows containing missing values (geom_path).

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)
## # A tibble: 252 x 7
##    index         key    price lo.80 lo.95 hi.80 hi.95
##    <S3: yearmon> <chr>  <dbl> <dbl> <dbl> <dbl> <dbl>
##  1 Jan 2007      actual  6627    NA    NA    NA    NA
##  2 Feb 2007      actual  6743    NA    NA    NA    NA
##  3 Mar 2007      actual  8195    NA    NA    NA    NA
##  4 Apr 2007      actual  7828    NA    NA    NA    NA
##  5 May 2007      actual  9570    NA    NA    NA    NA
##  6 Jun 2007      actual  9484    NA    NA    NA    NA
##  7 Jul 2007      actual  8608    NA    NA    NA    NA
##  8 Aug 2007      actual  9543    NA    NA    NA    NA
##  9 Sep 2007      actual  8123    NA    NA    NA    NA
## 10 Oct 2007      actual  9649    NA    NA    NA    NA
## # ... with 242 more rows

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, size = 0) +
    geom_ribbon(aes(ymin = lo.80, ymax = hi.80, fill = key), 
                fill = "#596DD5", color = NA, size = 0, alpha = 0.8) +
    geom_line(size = 1) +
    labs(title = "US Alcohol Sales, ETS Model Forecast", x = "", y = "Millions",
         subtitle = "Regular Time Index") +
    scale_y_continuous(labels = scales::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()
## # A tibble: 6 x 7
##   index      key    price lo.80 lo.95 hi.80 hi.95
##   <date>     <chr>  <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2007-01-01 actual  6627    NA    NA    NA    NA
## 2 2007-02-01 actual  6743    NA    NA    NA    NA
## 3 2007-03-01 actual  8195    NA    NA    NA    NA
## 4 2007-04-01 actual  7828    NA    NA    NA    NA
## 5 2007-05-01 actual  9570    NA    NA    NA    NA
## 6 2007-06-01 actual  9484    NA    NA    NA    NA
sw_sweep(fcast_ets, timetk_idx = TRUE) %>%
    tail()
## # A tibble: 6 x 7
##   index      key      price lo.80 lo.95 hi.80 hi.95
##   <date>     <chr>    <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 2017-07-01 forecast 12056 11291 10887 12820 13225
## 2 2017-08-01 forecast 12576 11768 11341 13384 13811
## 3 2017-09-01 forecast 12012 11231 10817 12793 13206
## 4 2017-10-01 forecast 12531 11706 11270 13356 13793
## 5 2017-11-01 forecast 12407 11581 11144 13234 13671
## 6 2017-12-01 forecast 14451 13477 12962 15424 15940

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, size = 0) +
    geom_ribbon(aes(ymin = lo.80, ymax = hi.80, fill = key), 
                fill = "#596DD5", color = NA, size = 0, alpha = 0.8) +
    geom_line(size = 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.