Tidymodels Approach to Time Series Forecasting: modeltime methods

class: center, middle, inverse, title-slide

.title[
# Tidymodels Approach to Time Series Forecasting: modeltime methods
]
.author[
### Dr. Kam Tin Seong Assoc. Professor of Information Systems
]
.institute[
### School of Computing and Information Systems, Singapore Management University
]
.date[
### 2022-7-16 (updated: 2022-07-27)
]

---

# Content

.large[
In this topic, we are going to explore the tidymodels approach in time series forecasting.

- import and wrangling time-series data by using appropriate tidyverse methods,
- visualise and analyse time-series data,
- calibrate time-series forecasting models by using exponential smoothing and ARIMA techniques, and
- compare and evaluate the performance of forecasting models.
]

---
## Setting Up R Environment

.pull-left[
For the purpose of this hands-on exercise, the following R packages will be used.

```r
pacman::p_load(tidyverse, tidymodels, 
               timetk, modeltime)
```

+ [**tidyverse**](https://lubridate.tidyverse.org/) provides a collection of commonly used functions for importing, wrangling and visualising data.  In this hands-on exercise the main packages used are readr, dplyr, tidyr and ggplot2.  
]

.pull-right[
+ [**modeltime**](https://business-science.github.io/modeltime/index.html) a new time series forecasting package designed to speed up model evaluation, selection, and forecasting. modeltime does this by integrating the [**tidymodels**](https://www.tidymodels.org/) machine learning ecosystem of packages into a streamlined workflow for tidyverse
forecasting. 
]

---
## Introducing modeltime workflow

.center[
![:scale 80%](img/image17.jpg)
]

.small[
Source: [Getting Started with Modeltime](https://business-science.github.io/modeltime/articles/getting-started-with-modeltime.html)
]

---
## The data

.pull-left[
In this sharing, [**Store Sales - Time Series Forecasting: Use machine learning to predict grocery sales**](https://www.kaggle.com/competitions/store-sales-time-series-forecasting/overview) from Kaggle competition will be used.  For the purpose of this sharing, the main data set used is *train.csv*.  It consists of six columns.  They are:

+ *id* contains unique id for each records.
+ *date* gives the sales dates.
+ *store_nbr* identifies the store at which the products are sold.
+ *family* identifies the type of product sold.
+ *sales* gives the total sales for a product family at a particular store at a given date. Fractional values are possible since products can be sold in fractional units (1.5 kg of cheese, for instance, as opposed to 1 bag of chips).
+ *onpromotion* gives the total number of items in a product family that were being promoted at a store at a given date.
]

--
.pull-right[
For the purpose of this sharing, I will focus of grocery sales instead of all products.  Code chunk below is used to extract grocery sales from *train.csv* and saved the output into an rds file format for subsequent used.

```r
store_sales <- read_csv(
 "data/store_sales/train.csv") %>%
 filter(family == "GROCERY I") %>%
 write_rds("data/store_sales/grocery.rds")
```
]

---
## Time Series Forecasting Process

.pull-left[
.large[
+ Collect data and split into training and test sets
+ Create & Fit Multiple Models
+ Add fitted models to a Model Table
+ Calibrate the models to a testing set.
+ Perform Testing Set Forecast & Accuracy Evaluation
+ Refit the models to Full Dataset & Forecast Forward
]]

---
### Step 1: Data Import and Sampling

.pull-left[

In the code chunk below, `read_rds()` of **readr** package is used to import both data sets into R environment.

```r
grocery <- read_rds(
 "data/store_sales/grocery.rds") %>%
 mutate(across(c(1, 3, 4), 
 as.factor)) %>%
 group_by(family, date) %>%
 summarise(sum_sales = sum(sales)) %>%
 ungroup()
```
]

.pull-right[
Optionally, you can also import the rest of the data sets provided at Kaggle by usign the code chunk below.

```r
holidays_events <- read_csv(
 "data/store_sales/holidays_events.csv")
oil <- read_csv(
 "data/store_sales/oil.csv")
stores <- read_csv(
 "data/store_sales/stores.csv")
transactions <- read_csv(
 "data/store_sales/transactions.csv")
```
]

---
### Step 1: Data Import and Sampling

.pull-left[
*grocery* tibble data frame consists of 1684 days of daily sales data starts from 1st January 2013.  We will split the data set into training and hold-out data sets by using [`initial_time_split()`](https://rsample.tidymodels.org/reference/initial_split.html) of [**rsample**](https://rsample.tidymodels.org/) package, a member of the tidymodels family.

```r
splits <- grocery %>%
 initial_time_split(prop = 0.955)
```
]

--
.pull-right[
For checking purposes, the code chunk below can be used save the split sample data sets into *training* and *holdout* tibble data tables respectively.

```r
training <- training(splits)
holdout <- testing(splits)
```
]

---
### Step 2: Create & Fit Multiple Models

.pull-left[
In this step, we will build and fit four models using the code chunks below:

**Model 1: Exponential Smoothing (Modeltime)**

An Error-Trend-Season (ETS) model by using `exp_smoothing()`.

```r
model_fit_ets <- exp_smoothing() %>%
 set_engine(engine = "ets") %>%
 fit(sum_sales ~ `date`, 
 data = training(splits))
```

**Model 2: Auto ARIMA (Modeltime)**

An auto ARIMA model by using `arima_reg()`.

```r
model_fit_arima <- arima_reg() %>%
 set_engine(engine = "auto_arima") %>%
 fit(sum_sales ~ `date`, 
 data = training(splits))
```
]

.pull-right[

**Model 3: Boosted Auto ARIMA (Modeltime)**

An Boosted auto ARIMA model by using `arima_boost()`.

```r
model_fit_arima_boosted <- arima_boost(
 min_n = 2,
 learn_rate = 0.015) %>%
 set_engine(
 engine = "auto_arima_xgboost") %>%
 fit(sum_sales ~ `date`, 
 data = training(splits))
```

**Model 4: prophet (Modeltime)**

A prophet model using `prophet_reg()`.

```r
model_fit_prophet <- prophet_reg() %>%
 set_engine(engine = "prophet") %>%
 fit(sum_sales ~ `date`, 
 data = training(splits))
```
]

---
### Step 3: Add fitted models to a Model Table

Next, modeltime_table() of modeltime package is used to add each of the models to a Modeltime Table.

```r
models_tbl <- modeltime_table(
 model_fit_ets,
 model_fit_arima,
 model_fit_arima_boosted,
 model_fit_prophet)

models_tbl
```

```
## # Modeltime Table
## # A tibble: 4 × 3
## .model_id .model .model_desc 
## <int> <list> <chr> 
## 1 1 <fit[+]> ETS(M,N,M) 
## 2 2 <fit[+]> ARIMA(3,0,0)(1,1,2)[7]
## 3 3 <fit[+]> ARIMA(1,0,3)(2,1,2)[7]
## 4 4 <fit[+]> PROPHET
```

---
### Step 4 - Calibrate the model to a testing set

In the code chunk below, [`modeltime_caibrate()`](https://business-science.github.io/modeltime/reference/modeltime_calibrate.html) is used to add a new column called *.calibrate_data* into the newly *created models_tbl* tibble data table.

```r
calibration_tbl <- models_tbl %>%
 modeltime_calibrate(new_data = testing(splits))

calibration_tbl
```

```
## # Modeltime Table
## # A tibble: 4 × 5
## .model_id .model .model_desc .type .calibration_data
## <int> <list> <chr> <chr> <list> 
## 1 1 <fit[+]> ETS(M,N,M) Test <tibble [76 × 4]>
## 2 2 <fit[+]> ARIMA(3,0,0)(1,1,2)[7] Test <tibble [76 × 4]>
## 3 3 <fit[+]> ARIMA(1,0,3)(2,1,2)[7] Test <tibble [76 × 4]>
## 4 4 <fit[+]> PROPHET Test <tibble [76 × 4]>
```

Note that Calibration Data is simply forecasting predictions and residuals that are calculated from the hold-out data (also know as test data in machine learning)

---
### Step 5: Model Accuracy Assessment

In general, there are two ways to assess accuracy of the models.  They are by means of accuracy metrics or visualisation.

In the code chunk below, [`modeltime_accuracy()`](https://business-science.github.io/modeltime/reference/modeltime_accuracy.html) of modeltime package is used compute the accuracy metrics.  Then, [`table_modeltime_accuracy()`](https://business-science.github.io/modeltime/reference/table_modeltime_accuracy.html) is used to present the accuracy metrics in tabular form.

```r
calibration_tbl %>%
  modeltime_accuracy %>%
  table_modeltime_accuracy(
    .interactive = FALSE)
```

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<table class="gt_table">
 <thead class="gt_header">
 <tr>
 <th colspan="9" class="gt_heading gt_title gt_font_normal gt_bottom_border" style>Accuracy Table</th>
 </tr>
 
 </thead>
 <thead class="gt_col_headings">
 <tr>
 <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">.model_id</th>
 <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1">.model_desc</th>
 <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1">.type</th>
 <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">mae</th>
 <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">mape</th>
 <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">mase</th>
 <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">smape</th>
 <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">rmse</th>
 <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">rsq</th>
 </tr>
 </thead>
 <tbody class="gt_table_body">
 <tr><td class="gt_row gt_right">1</td>
<td class="gt_row gt_left">ETS(M,N,M)</td>
<td class="gt_row gt_left">Test</td>
<td class="gt_row gt_right">25250.52</td>
<td class="gt_row gt_right">9.86</td>
<td class="gt_row gt_right">0.65</td>
<td class="gt_row gt_right">9.61</td>
<td class="gt_row gt_right">31554.80</td>
<td class="gt_row gt_right">0.64</td></tr>
 <tr><td class="gt_row gt_right">2</td>
<td class="gt_row gt_left">ARIMA(3,0,0)(1,1,2)[7]</td>
<td class="gt_row gt_left">Test</td>
<td class="gt_row gt_right">23087.67</td>
<td class="gt_row gt_right">8.90</td>
<td class="gt_row gt_right">0.59</td>
<td class="gt_row gt_right">8.79</td>
<td class="gt_row gt_right">29863.72</td>
<td class="gt_row gt_right">0.66</td></tr>
 <tr><td class="gt_row gt_right">3</td>
<td class="gt_row gt_left">ARIMA(1,0,3)(2,1,2)[7]</td>
<td class="gt_row gt_left">Test</td>
<td class="gt_row gt_right">23049.21</td>
<td class="gt_row gt_right">8.89</td>
<td class="gt_row gt_right">0.59</td>
<td class="gt_row gt_right">8.78</td>
<td class="gt_row gt_right">29829.18</td>
<td class="gt_row gt_right">0.66</td></tr>
 <tr><td class="gt_row gt_right">4</td>
<td class="gt_row gt_left">PROPHET</td>
<td class="gt_row gt_left">Test</td>
<td class="gt_row gt_right">22386.78</td>
<td class="gt_row gt_right">8.56</td>
<td class="gt_row gt_right">0.58</td>
<td class="gt_row gt_right">8.61</td>
<td class="gt_row gt_right">30521.01</td>
<td class="gt_row gt_right">0.66</td></tr>
 </tbody>
 
 
</table>
</div>

---
### Step 5: Model Accuracy Assessment

.pull-left[
Visualizing the Test Error is easy to do using the interactive plotly visualization (just toggle the visibility of the models using the Legend).

```r
calibration_tbl %>%
  modeltime_forecast(
    new_data = testing(splits),
    actual_data = grocery) %>%
  plot_modeltime_forecast(
    .legend_max_width = 25, 
    .interactive = TRUE,
    .plotly_slider = TRUE)
```
]

.pull-right[
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---
### Step 6 - Refit to Full Dataset & Forecast Forward

The final step is to refit the models to the full dataset using [`modeltime_refit()`](https://business-science.github.io/modeltime/reference/modeltime_refit.html) and forecast them forward.

.pull-left[
The code chunk below uses modeltime_refit() to refit the forecasting models with the full data.

```r
refit_tbl <- calibration_tbl %>%
 modeltime_refit(data = grocery)
```
]

--
.pull-right[
Then, `modeltime_forecast()` is used to forecast to a selected future time period, in this example 6 weeks.

```r
forecast_tbl <- refit_tbl %>%
 modeltime_forecast(
 h = "6 weeks",
 actual_data = grocery,
 keep_data = TRUE) 
```
]

Notice that this newly derived *forecast_tbl* consists of 1852 rows (1684 rows for the original grocery sales data plus 7 days x 6 weeks x 4 models forecasted data)

---
### Step 6 - Refit to Full Dataset & Forecast Forward

```r
forecast_tbl %>%
  plot_modeltime_forecast(
    .legend_max_width = 25, 
    .interactive = TRUE,
    .plotly_slider = TRUE)
```

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---
### Step 6 - Refit to Full Dataset & Forecast Forward

Let us also examine the model accuracy metrics after refitting the full data set.

```r
refit_tbl %>%
  modeltime_accuracy() %>%
  table_modeltime_accuracy(
    .interactive = FALSE)
```

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<table class="gt_table">
 <thead class="gt_header">
 <tr>
 <th colspan="9" class="gt_heading gt_title gt_font_normal gt_bottom_border" style>Accuracy Table</th>
 </tr>
 
 </thead>
 <thead class="gt_col_headings">
 <tr>
 <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">.model_id</th>
 <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1">.model_desc</th>
 <th class="gt_col_heading gt_columns_bottom_border gt_left" rowspan="1" colspan="1">.type</th>
 <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">mae</th>
 <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">mape</th>
 <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">mase</th>
 <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">smape</th>
 <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">rmse</th>
 <th class="gt_col_heading gt_columns_bottom_border gt_right" rowspan="1" colspan="1">rsq</th>
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 <tbody class="gt_table_body">
 <tr><td class="gt_row gt_right">1</td>
<td class="gt_row gt_left">ETS(M,N,M)</td>
<td class="gt_row gt_left">Test</td>
<td class="gt_row gt_right">25250.52</td>
<td class="gt_row gt_right">9.86</td>
<td class="gt_row gt_right">0.65</td>
<td class="gt_row gt_right">9.61</td>
<td class="gt_row gt_right">31554.80</td>
<td class="gt_row gt_right">0.64</td></tr>
 <tr><td class="gt_row gt_right">2</td>
<td class="gt_row gt_left">ARIMA(3,0,0)(1,1,2)[7]</td>
<td class="gt_row gt_left">Test</td>
<td class="gt_row gt_right">23087.67</td>
<td class="gt_row gt_right">8.90</td>
<td class="gt_row gt_right">0.59</td>
<td class="gt_row gt_right">8.79</td>
<td class="gt_row gt_right">29863.72</td>
<td class="gt_row gt_right">0.66</td></tr>
 <tr><td class="gt_row gt_right">3</td>
<td class="gt_row gt_left">UPDATE: ARIMA(4,0,4)(1,1,2)[7] WITH DRIFT</td>
<td class="gt_row gt_left">Test</td>
<td class="gt_row gt_right">23049.21</td>
<td class="gt_row gt_right">8.89</td>
<td class="gt_row gt_right">0.59</td>
<td class="gt_row gt_right">8.78</td>
<td class="gt_row gt_right">29829.18</td>
<td class="gt_row gt_right">0.66</td></tr>
 <tr><td class="gt_row gt_right">4</td>
<td class="gt_row gt_left">PROPHET</td>
<td class="gt_row gt_left">Test</td>
<td class="gt_row gt_right">22386.78</td>
<td class="gt_row gt_right">8.56</td>
<td class="gt_row gt_right">0.58</td>
<td class="gt_row gt_right">8.61</td>
<td class="gt_row gt_right">30521.01</td>
<td class="gt_row gt_right">0.66</td></tr>
 </tbody>
 
 
</table>
</div>