> ## Documentation Index
> Fetch the complete documentation index at: https://nixtlaverse.nixtla.io/llms.txt
> Use this file to discover all available pages before exploring further.

# Forecasting at Scale using ETS and ray (M5)

> Forecast the M5 dataset

In this notebook we show how to use `StatsForecast` and `ray` to
forecast thounsands of time series in less than 6 minutes (M5 dataset).
Also, we show that `StatsForecast` has better performance in time and
accuracy compared to [`Prophet` running on a Spark
cluster](./prophet_spark_m5.html) using DataBricks.

In this example, we used a ray cluster (AWS) of 11 instances of type
m5.2xlarge (8 cores, 32 GB RAM).

## Installing StatsForecast Library

```python theme={null}
%%capture
!pip install "statsforecast[ray]" neuralforecast s3fs pyarrow
```

```python theme={null}
%%capture
from time import time

import pandas as pd
from neuralforecast.data.datasets.m5 import M5, M5Evaluation
from statsforecast import StatsForecast
from statsforecast.models import ETS
```

## Download data

The example uses the [M5
dataset](https://github.com/Mcompetitions/M5-methods/blob/master/M5-Competitors-Guide.pdf).
It consists of `30,490` bottom time series.

```python theme={null}
Y_df = pd.read_parquet('s3://m5-benchmarks/data/train/target.parquet')
Y_df = Y_df.rename(columns={
    'item_id': 'unique_id', 
    'timestamp': 'ds', 
    'demand': 'y'
})
Y_df['ds'] = pd.to_datetime(Y_df['ds'])
```

```python theme={null}
Y_df.head()
```

|   | unique\_id           | ds         | y   |
| - | -------------------- | ---------- | --- |
| 0 | FOODS\_1\_001\_CA\_1 | 2011-01-29 | 3.0 |
| 1 | FOODS\_1\_001\_CA\_1 | 2011-01-30 | 0.0 |
| 2 | FOODS\_1\_001\_CA\_1 | 2011-01-31 | 0.0 |
| 3 | FOODS\_1\_001\_CA\_1 | 2011-02-01 | 1.0 |
| 4 | FOODS\_1\_001\_CA\_1 | 2011-02-02 | 4.0 |

Since the M5 dataset contains intermittent time series, we add a
constant to avoid problems during the training phase. Later, we will
substract the constant from the forecasts.

```python theme={null}
constant = 10
Y_df['y'] += constant
```

## Train the model

`StatsForecast` receives a list of models to fit each time series. Since
we are dealing with Daily data, it would be benefitial to use 7 as
seasonality. Observe that we need to pass the ray address to the
`ray_address` argument.

```python theme={null}
fcst = StatsForecast(
    df=Y_df, 
    models=[ETS(season_length=7, model='ZNA')], 
    freq='D', 
    #n_jobs=-1
    ray_address='ray://ADDRESS:10001'
)
```

```python theme={null}
init = time()
Y_hat = fcst.forecast(28)
end = time()
print(f'Minutes taken by StatsForecast using: {(end - init) / 60}')
```

```text theme={null}
/home/ubuntu/miniconda/envs/ray/lib/python3.7/site-packages/ray/util/client/worker.py:618: UserWarning: More than 10MB of messages have been created to schedule tasks on the server. This can be slow on Ray Client due to communication overhead over the network. If you're running many fine-grained tasks, consider running them inside a single remote function. See the section on "Too fine-grained tasks" in the Ray Design Patterns document for more details: https://docs.google.com/document/d/167rnnDFIVRhHhK4mznEIemOtj63IOhtIPvSYaPgI4Fg/edit#heading=h.f7ins22n6nyl. If your functions frequently use large objects, consider storing the objects remotely with ray.put. An example of this is shown in the "Closure capture of large / unserializable object" section of the Ray Design Patterns document, available here: https://docs.google.com/document/d/167rnnDFIVRhHhK4mznEIemOtj63IOhtIPvSYaPgI4Fg/edit#heading=h.1afmymq455wu
  UserWarning,
```

```text theme={null}
Minutes taken by StatsForecast using: 5.4817593971888225
```

`StatsForecast` and `ray` took only 5.48 minutes to train `30,490` time
series, compared to 18.23 minutes for Prophet and Spark.

We remove the constant.

```python theme={null}
Y_hat['ETS'] -= constant
```

### Evaluating performance

The M5 competition used the weighted root mean squared scaled error. You
can find details of the metric
[here](https://github.com/Mcompetitions/M5-methods/blob/master/M5-Competitors-Guide.pdf).

```python theme={null}
Y_hat = Y_hat.reset_index().set_index(['unique_id', 'ds']).unstack()
Y_hat = Y_hat.droplevel(0, 1).reset_index()
```

```python theme={null}
*_, S_df = M5.load('./data')
Y_hat = S_df.merge(Y_hat, how='left', on=['unique_id'])
```

```text theme={null}
100%|███████████████████████████████████████████████████████████| 50.2M/50.2M [00:00<00:00, 77.1MiB/s]
```

```python theme={null}
M5Evaluation.evaluate(y_hat=Y_hat, directory='./data')
```

|         | wrmsse   |
| ------- | -------- |
| Total   | 0.677233 |
| Level1  | 0.435558 |
| Level2  | 0.522863 |
| Level3  | 0.582109 |
| Level4  | 0.488484 |
| Level5  | 0.567825 |
| Level6  | 0.587605 |
| Level7  | 0.662774 |
| Level8  | 0.647712 |
| Level9  | 0.732107 |
| Level10 | 1.013124 |
| Level11 | 0.970465 |
| Level12 | 0.916175 |

Also, `StatsForecast` is more accurate than Prophet, since the overall
WMRSSE is `0.68`, against `0.77` obtained by prophet.