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final 1.1.5 docs updates

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docs/_docs/additional_topics.md
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@ -6,10 +6,16 @@ permalink: /docs/additional_topics.html
subsections:
- title: Saving models
id: saving-models
- title: Flat trend and custom trends
id: flat-trend-and-custom-trends
- title: Flat trend
id: flat-trend
- title: Custom trends
id: custom-trends
- title: Updating fitted models
id: updating-fitted-models
- title: 'minmax' scaling (new in 1.1.5)
id: 'minmax'-scaling-(new-in-1.1.5)
- title: Inspecting transformed data (new in 1.1.5)
id: inspecting-transformed-data-(new-in-1.1.5)
- title: External references
id: external-references
---
@ -47,13 +53,13 @@ with open('serialized_model.json', 'r') as fin:
The json file will be portable across systems, and deserialization is backwards compatible with older versions of prophet.
<a id="flat-trend-and-custom-trends"> </a>
<a id="flat-trend"> </a>
### Flat trend and custom trends
### Flat trend
For time series that exhibit strong seasonality patterns rather than trend changes, or when we want to rely on the pattern of exogenous regressors (e.g. for causal inference with time series), it may be useful to force the trend growth rate to be flat. This can be achieved simply by passing `growth=flat` when creating the model:
For time series that exhibit strong seasonality patterns rather than trend changes, or when we want to rely on the pattern of exogenous regressors (e.g. for causal inference with time series), it may be useful to force the trend growth rate to be flat. This can be achieved simply by passing `growth='flat'` when creating the model:
```R
@ -64,7 +70,103 @@ m <- prophet(df, growth='flat')
# Python
m = Prophet(growth='flat')
```
Note that if this is used on a time series that doesn't have a constant trend, any trend will be fit with the noise term and so there will be high predictive uncertainty in the forecast.
Below is a comparison of counterfactual forecasting under two methods: using linear growth for a single time series, versus flat growth with an exogenous regressor.
```python
# Python
import pandas as pd
from prophet import Prophet
import matplotlib.pyplot as plt
import warnings
warnings.simplefilter(action='ignore', category=FutureWarning)
regressor = "location_4"
target = "location_41"
cutoff = pd.to_datetime("2023-04-17 00:00:00")
df = (
pd.read_csv("../examples/example_pedestrians_multivariate.csv", parse_dates=["ds"])
.rename(columns={target: "y"})
)
train = df.loc[df["ds"] < cutoff]
test = df.loc[df["ds"] >= cutoff]
```
```python
# Python
def fit_model(growth):
m = Prophet(growth=growth, seasonality_mode="multiplicative", daily_seasonality=15)
m.add_regressor("location_4", mode="multiplicative")
m.fit(train)
preds = pd.merge(
test,
m.predict(test),
on="ds",
how="inner"
)
mape = ((preds["yhat"] - preds["y"]).abs() / preds_linear["y"]).mean()
return m, preds, mape
```
```python
# Python
m_linear, preds_linear, mape_linear = fit_model("linear")
```
01:19:58 - cmdstanpy - INFO - Chain [1] start processing
01:19:58 - cmdstanpy - INFO - Chain [1] done processing
```python
# Python
m_flat, preds_flat, mape_flat = fit_model("flat")
```
01:19:58 - cmdstanpy - INFO - Chain [1] start processing
01:19:58 - cmdstanpy - INFO - Chain [1] done processing
```python
# Python
m_linear.plot_components(preds_linear);
```
![png](/prophet/static/additional_topics_files/additional_topics_16_0.png)
```python
# Python
m_flat.plot_components(preds_flat);
```
![png](/prophet/static/additional_topics_files/additional_topics_17_0.png)
```python
# Python
fig, ax = plt.subplots(figsize=(11, 5))
ax.scatter(preds_linear["ds"], preds_linear["y"], color="black", marker=".")
ax.plot(preds_linear["ds"], preds_linear["yhat"], label=f"linear, mape={mape_linear:.1%}")
ax.plot(preds_flat["ds"], preds_flat["yhat"], label=f"flat, mape={mape_flat:.1%}")
plt.xticks(rotation=60)
ax.legend();
```
![png](/prophet/static/additional_topics_files/additional_topics_18_0.png)
In this example, trends in the target sensor location can be mostly explained by the exogenous regressor (a nearby sensor). The model with linear growth assumes a growing trend and this leads to larger and larger over-predictions in the test period, while the model with the flat trend is mostly driven by trends in the exogenous regressor, which results in a sizeable MAPE improvement.
Note that forecasting with exogenous regressors is only effective when we can be confident in the future values of the regressor -- the example above is most relevant to time series causal inference, where we want to forecast what a time series would have looked like in the past, and hence the exogenous regressor values are known.
If the flat trend is used on a time series that doesn't have a constant trend, without exogenous regressors, any trend will be fit with the noise term and so there will be high predictive uncertainty in the forecast.
<a id="custom-trends"> </a>
### Custom trends
@ -129,6 +231,412 @@ As can be seen, the parameters from the previous model are passed in to the fitt
There are few caveats that should be kept in mind when considering warm-starting. First, warm-starting may work well for small updates to the data (like the addition of one day in the example above) but can be worse than fitting from scratch if there are large changes to the data (i.e., a lot of days have been added). This is because when a large amount of history is added, the location of the changepoints will be very different between the two models, and so the parameters from the previous model may actually produce a bad trend initialization. Second, as a detail, the number of changepoints need to be consistent from one model to the next or else an error will be raised because the changepoint prior parameter `delta` will be the wrong size.
<a id="'minmax'-scaling-(new-in-1.1.5)"> </a>
### 'minmax' scaling (new in 1.1.5)
Before model fitting, Prophet scales `y` by dividing by the maximum value in the history. For datasets with very large `y` values, the scaled `y` values may be compressed to a very small range (i.e. `[0.99999... - 1.0]`), which causes a bad fit. This can be fixed by setting `scaling='absmax'` in the Prophet constructor.
```python
# Python
large_y = pd.read_csv("https://raw.githubusercontent.com/facebook/prophet/main/python/prophet/tests/data3.csv", parse_dates=["ds"])
```
```python
# Python
m1 = Prophet(scaling="absmax")
m1.fit(large_y)
```
01:42:10 - cmdstanpy - INFO - Chain [1] start processing
01:42:10 - cmdstanpy - INFO - Chain [1] done processing
<prophet.forecaster.Prophet at 0x7f253353bee0>
```python
# Python
m2 = Prophet(scaling="minmax")
m2.fit(large_y)
```
01:42:19 - cmdstanpy - INFO - Chain [1] start processing
01:42:19 - cmdstanpy - INFO - Chain [1] done processing
<prophet.forecaster.Prophet at 0x7f253352d910>
```python
# Python
m1.plot(m1.predict(large_y));
```
![png](/prophet/static/additional_topics_files/additional_topics_28_0.png)
```python
# Python
m2.plot(m2.predict(large_y));
```
![png](/prophet/static/additional_topics_files/additional_topics_29_0.png)
<a id="inspecting-transformed-data-(new-in-1.1.5)"> </a>
### Inspecting transformed data (new in 1.1.5)
For debugging, it's useful to understand how the raw data has been transformed before being passed to the underlying generalized additive model. We can call the `.preprocess()` method to see the data that will be passed to the stan fit routine, and `.calculate_init_params()` to see how the parameters are initialized in the fit routine.
```python
# Python
df = pd.read_csv('../examples/example_wp_log_peyton_manning.csv')
m = Prophet()
transformed = m.preprocess(df)
```
```python
# Python
transformed.y.head(n=10)
```
0 0.746552
1 0.663171
2 0.637023
3 0.628367
4 0.614441
5 0.605884
6 0.654956
7 0.687273
8 0.652501
9 0.628148
Name: y_scaled, dtype: float64
```python
# Python
transformed.X.head(n=10)
```
<div>
<style scoped>
.dataframe tbody tr th:only-of-type {
vertical-align: middle;
}
.dataframe tbody tr th {
vertical-align: top;
}
.dataframe thead th {
text-align: right;
}
</style>
<table border="1" class="dataframe">
<thead>
<tr style="text-align: right;">
<th></th>
<th>yearly_delim_1</th>
<th>yearly_delim_2</th>
<th>yearly_delim_3</th>
<th>yearly_delim_4</th>
<th>yearly_delim_5</th>
<th>yearly_delim_6</th>
<th>yearly_delim_7</th>
<th>yearly_delim_8</th>
<th>yearly_delim_9</th>
<th>yearly_delim_10</th>
<th>...</th>
<th>yearly_delim_17</th>
<th>yearly_delim_18</th>
<th>yearly_delim_19</th>
<th>yearly_delim_20</th>
<th>weekly_delim_1</th>
<th>weekly_delim_2</th>
<th>weekly_delim_3</th>
<th>weekly_delim_4</th>
<th>weekly_delim_5</th>
<th>weekly_delim_6</th>
</tr>
</thead>
<tbody>
<tr>
<th>0</th>
<td>-0.377462</td>
<td>0.926025</td>
<td>-0.699079</td>
<td>0.715044</td>
<td>-0.917267</td>
<td>0.398272</td>
<td>-0.999745</td>
<td>0.022576</td>
<td>-0.934311</td>
<td>-0.356460</td>
<td>...</td>
<td>0.335276</td>
<td>-0.942120</td>
<td>0.666089</td>
<td>-0.745872</td>
<td>-4.338837e-01</td>
<td>-0.900969</td>
<td>7.818315e-01</td>
<td>0.623490</td>
<td>-9.749279e-01</td>
<td>-0.222521</td>
</tr>
<tr>
<th>1</th>
<td>-0.361478</td>
<td>0.932381</td>
<td>-0.674069</td>
<td>0.738668</td>
<td>-0.895501</td>
<td>0.445059</td>
<td>-0.995827</td>
<td>0.091261</td>
<td>-0.961479</td>
<td>-0.274879</td>
<td>...</td>
<td>0.185987</td>
<td>-0.982552</td>
<td>0.528581</td>
<td>-0.848883</td>
<td>-9.749279e-01</td>
<td>-0.222521</td>
<td>4.338837e-01</td>
<td>-0.900969</td>
<td>7.818315e-01</td>
<td>0.623490</td>
</tr>
<tr>
<th>2</th>
<td>-0.345386</td>
<td>0.938461</td>
<td>-0.648262</td>
<td>0.761418</td>
<td>-0.871351</td>
<td>0.490660</td>
<td>-0.987196</td>
<td>0.159513</td>
<td>-0.981538</td>
<td>-0.191266</td>
<td>...</td>
<td>0.032249</td>
<td>-0.999480</td>
<td>0.375470</td>
<td>-0.926834</td>
<td>-7.818315e-01</td>
<td>0.623490</td>
<td>-9.749279e-01</td>
<td>-0.222521</td>
<td>-4.338837e-01</td>
<td>-0.900969</td>
</tr>
<tr>
<th>3</th>
<td>-0.329192</td>
<td>0.944263</td>
<td>-0.621687</td>
<td>0.783266</td>
<td>-0.844881</td>
<td>0.534955</td>
<td>-0.973892</td>
<td>0.227011</td>
<td>-0.994341</td>
<td>-0.106239</td>
<td>...</td>
<td>-0.122261</td>
<td>-0.992498</td>
<td>0.211276</td>
<td>-0.977426</td>
<td>5.505235e-14</td>
<td>1.000000</td>
<td>1.101047e-13</td>
<td>1.000000</td>
<td>1.984146e-12</td>
<td>1.000000</td>
</tr>
<tr>
<th>4</th>
<td>-0.312900</td>
<td>0.949786</td>
<td>-0.594376</td>
<td>0.804187</td>
<td>-0.816160</td>
<td>0.577825</td>
<td>-0.955979</td>
<td>0.293434</td>
<td>-0.999791</td>
<td>-0.020426</td>
<td>...</td>
<td>-0.273845</td>
<td>-0.961774</td>
<td>0.040844</td>
<td>-0.999166</td>
<td>7.818315e-01</td>
<td>0.623490</td>
<td>9.749279e-01</td>
<td>-0.222521</td>
<td>4.338837e-01</td>
<td>-0.900969</td>
</tr>
<tr>
<th>5</th>
<td>-0.296516</td>
<td>0.955028</td>
<td>-0.566362</td>
<td>0.824157</td>
<td>-0.785267</td>
<td>0.619157</td>
<td>-0.933542</td>
<td>0.358468</td>
<td>-0.997850</td>
<td>0.065537</td>
<td>...</td>
<td>-0.418879</td>
<td>-0.908042</td>
<td>-0.130793</td>
<td>-0.991410</td>
<td>9.749279e-01</td>
<td>-0.222521</td>
<td>-4.338837e-01</td>
<td>-0.900969</td>
<td>-7.818315e-01</td>
<td>0.623490</td>
</tr>
<tr>
<th>6</th>
<td>-0.280044</td>
<td>0.959987</td>
<td>-0.537677</td>
<td>0.843151</td>
<td>-0.752283</td>
<td>0.658840</td>
<td>-0.906686</td>
<td>0.421806</td>
<td>-0.988531</td>
<td>0.151016</td>
<td>...</td>
<td>-0.553893</td>
<td>-0.832588</td>
<td>-0.298569</td>
<td>-0.954388</td>
<td>4.338837e-01</td>
<td>-0.900969</td>
<td>-7.818315e-01</td>
<td>0.623490</td>
<td>9.749279e-01</td>
<td>-0.222521</td>
</tr>
<tr>
<th>7</th>
<td>-0.263489</td>
<td>0.964662</td>
<td>-0.508356</td>
<td>0.861147</td>
<td>-0.717295</td>
<td>0.696769</td>
<td>-0.875539</td>
<td>0.483147</td>
<td>-0.971904</td>
<td>0.235379</td>
<td>...</td>
<td>-0.675656</td>
<td>-0.737217</td>
<td>-0.457531</td>
<td>-0.889193</td>
<td>-4.338837e-01</td>
<td>-0.900969</td>
<td>7.818315e-01</td>
<td>0.623490</td>
<td>-9.749279e-01</td>
<td>-0.222521</td>
</tr>
<tr>
<th>8</th>
<td>-0.246857</td>
<td>0.969052</td>
<td>-0.478434</td>
<td>0.878124</td>
<td>-0.680398</td>
<td>0.732843</td>
<td>-0.840248</td>
<td>0.542202</td>
<td>-0.948090</td>
<td>0.318001</td>
<td>...</td>
<td>-0.781257</td>
<td>-0.624210</td>
<td>-0.602988</td>
<td>-0.797750</td>
<td>-9.749279e-01</td>
<td>-0.222521</td>
<td>4.338837e-01</td>
<td>-0.900969</td>
<td>7.818315e-01</td>
<td>0.623490</td>
</tr>
<tr>
<th>9</th>
<td>-0.230151</td>
<td>0.973155</td>
<td>-0.447945</td>
<td>0.894061</td>
<td>-0.641689</td>
<td>0.766965</td>
<td>-0.800980</td>
<td>0.598691</td>
<td>-0.917267</td>
<td>0.398272</td>
<td>...</td>
<td>-0.868168</td>
<td>-0.496271</td>
<td>-0.730644</td>
<td>-0.682758</td>
<td>-7.818315e-01</td>
<td>0.623490</td>
<td>-9.749279e-01</td>
<td>-0.222521</td>
<td>-4.338837e-01</td>
<td>-0.900969</td>
</tr>
</tbody>
</table>
<p>10 rows × 26 columns</p>
</div>
```python
# Python
m.calculate_initial_params(num_total_regressors=transformed.K)
```
ModelParams(k=-0.05444079622224118, m=0.7465517318876905, delta=array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0.]), beta=array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0.]), sigma_obs=1.0)
<a id="external-references"> </a>
### External references

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examples/example_pedestrians_multivariate.csv Normal file
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@ -0,0 +1,721 @@
ds,location_4,location_41
2023-04-01 00:00:00,903,975
2023-04-01 01:00:00,490,652
2023-04-01 02:00:00,377,434
2023-04-01 03:00:00,216,336
2023-04-01 04:00:00,124,115
2023-04-01 05:00:00,72,195
2023-04-01 06:00:00,138,328
2023-04-01 07:00:00,249,466
2023-04-01 08:00:00,733,1094
2023-04-01 09:00:00,1370,2006
2023-04-01 10:00:00,2150,2691
2023-04-01 11:00:00,3187,3565
2023-04-01 12:00:00,3746,3671
2023-04-01 13:00:00,4264,4022
2023-04-01 14:00:00,4827,4472
2023-04-01 15:00:00,4868,4266
2023-04-01 16:00:00,4399,4233
2023-04-01 17:00:00,4237,4199
2023-04-01 18:00:00,4594,4682
2023-04-01 19:00:00,4205,4253
2023-04-01 20:00:00,3584,3039
2023-04-01 21:00:00,2821,2972
2023-04-01 22:00:00,2380,2834
2023-04-01 23:00:00,1502,1775
2023-04-02 00:00:00,945,1227
2023-04-02 01:00:00,697,852
2023-04-02 02:00:00,543,663
2023-04-02 03:00:00,249,178
2023-04-02 04:00:00,86,135
2023-04-02 05:00:00,86,202
2023-04-02 06:00:00,153,329
2023-04-02 07:00:00,343,618
2023-04-02 08:00:00,651,952
2023-04-02 09:00:00,1173,1615
2023-04-02 10:00:00,2073,2478
2023-04-02 11:00:00,3127,3344
2023-04-02 12:00:00,3563,3829
2023-04-02 13:00:00,3723,3794
2023-04-02 14:00:00,4525,4232
2023-04-02 15:00:00,3913,3798
2023-04-02 16:00:00,3823,3583
2023-04-02 17:00:00,3781,3609
2023-04-02 18:00:00,3759,4137
2023-04-02 19:00:00,3375,3462
2023-04-02 20:00:00,2031,2102
2023-04-02 21:00:00,1734,1918
2023-04-02 22:00:00,854,1118
2023-04-02 23:00:00,459,516
2023-04-03 00:00:00,235,233
2023-04-03 01:00:00,119,139
2023-04-03 02:00:00,69,62
2023-04-03 03:00:00,36,58
2023-04-03 04:00:00,65,70
2023-04-03 05:00:00,73,159
2023-04-03 06:00:00,174,526
2023-04-03 07:00:00,444,1097
2023-04-03 08:00:00,1033,2343
2023-04-03 09:00:00,1414,2278
2023-04-03 10:00:00,2247,2585
2023-04-03 11:00:00,3131,3079
2023-04-03 12:00:00,3636,3628
2023-04-03 13:00:00,4102,3815
2023-04-03 14:00:00,3511,3436
2023-04-03 15:00:00,3389,3349
2023-04-03 16:00:00,3243,3393
2023-04-03 17:00:00,3166,3847
2023-04-03 18:00:00,2614,2675
2023-04-03 19:00:00,1829,1916
2023-04-03 20:00:00,1279,1476
2023-04-03 21:00:00,1071,1177
2023-04-03 22:00:00,695,747
2023-04-03 23:00:00,306,430
2023-04-04 00:00:00,105,156
2023-04-04 01:00:00,39,68
2023-04-04 02:00:00,39,63
2023-04-04 03:00:00,25,55
2023-04-04 04:00:00,24,39
2023-04-04 05:00:00,59,201
2023-04-04 06:00:00,197,577
2023-04-04 07:00:00,514,1312
2023-04-04 08:00:00,1099,2630
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