@@ -189,19 +175,84 @@ forecast[(forecast['playoff'] + forecast['superbowl']).abs() > 0][
The holiday effects will also show up in the components plot, where we see that there is a spike on the days around playoff appearances, with an especially large spike for the superbowl:
-```python
-# Python
-m.plot_components(forecast);
-```
```R
# R
-prophet_plot_components(m, forecast);
+prophet_plot_components(m, forecast)
+```
+```python
+# Python
+fig = m.plot_components(forecast)
```
-
+
-Individual holidays can be plotted using the `plot_forecast_component` method (Python) or function (R). For example, `m.plot_forecast_component(forecast, 'superbowl')` in Python and `plot_forecast_component(forecast, 'superbowl')` in R to plot just the superbowl holiday component.
+Individual holidays can be plotted using the `plot_forecast_component` function (imported from `fbprophet.plot` in Python) like `plot_forecast_component(forecast, 'superbowl')` to plot just the superbowl holiday component.
+
+### Fourier Order for Seasonalities
+
+Seasonalities are estimated using a partial Fourier sum. See [the paper](https://peerj.com/preprints/3190/) for complete details, and [this figure on Wikipedia](https://en.wikipedia.org/wiki/Fourier_series#/media/File:Fourier_Series.svg) for an illustration of how a partial Fourier sum can approximate an aribtrary periodic signal. The number of terms in the partial sum (the order) is a parameter that determines how quickly the seasonality can change. To illustrate this, consider the Peyton Manning data from the Quickstart. The default Fourier order for yearly seasonality is 10, which produces this fit:
+
+```R
+# R
+m <- prophet(df)
+prophet:::plot_yearly(m)
+```
+```python
+# Python
+from fbprophet.plot import plot_yearly
+m = Prophet().fit(df)
+a = plot_yearly(m)
+```
+
+
+
+
+The default values are often appropriate, but they can be increased when the seasonality needs to fit higher-frequency changes, and generally be less smooth. The Fourier order can be specified for each built-in seasonality when instantiating the model, here it is increased to 20:
+
+```R
+# R
+m <- prophet(df, yearly.seasonality = 20)
+prophet:::plot_yearly(m)
+```
+```python
+# Python
+from fbprophet.plot import plot_yearly
+m = Prophet(yearly_seasonality=20).fit(df)
+a = plot_yearly(m)
+```
+
+
+
+
+Increasing the number of Fourier terms allows the seasonality to fit faster changing cycles, but can also lead to overfitting: N Fourier terms corresponds to 2N variables used for modeling the cycle
+
+### Specifying Custom Seasonalities
+
+Prophet will by default fit weekly and yearly seasonalities, if the time series is more than two cycles long. It will also fit daily seasonality for a sub-daily time series. You can add other seasonalities (monthly, quarterly, hourly) using the `add_seasonality` method (Python) or function (R).
+
+The inputs to this function are a name, the period of the seasonality in days, and the Fourier order for the seasonality. For reference, by default Prophet uses a Fourier order of 3 for weekly seasonality and 10 for yearly seasonality. An optional input to `add_seasonality` is the prior scale for that seasonal component - this is discussed below.
+
+As an example, here we fit the Peyton Manning data from the Quickstart, but replace the weekly seasonality with monthly seasonality. The monthly seasonality then will appear in the components plot:
+
+```R
+# R
+m <- prophet(weekly.seasonality=FALSE)
+m <- add_seasonality(m, name='monthly', period=30.5, fourier.order=5)
+m <- fit.prophet(m, df)
+forecast <- predict(m, future)
+prophet_plot_components(m, forecast)
+```
+```python
+# Python
+m = Prophet(weekly_seasonality=False)
+m.add_seasonality(name='monthly', period=30.5, fourier_order=5)
+forecast = m.fit(df).predict(future)
+fig = m.plot_components(forecast)
+```
+
+
+
### Prior scale for holidays and seasonality
If you find that the holidays are overfitting, you can adjust their prior scale to smooth them using the parameter `holidays_prior_scale`. By default this parameter is 10, which provides very little regularization. Reducing this parameter dampens holiday effects:
@@ -226,6 +277,19 @@ forecast[(forecast['playoff'] + forecast['superbowl']).abs() > 0][
+
@@ -239,62 +303,62 @@ forecast[(forecast['playoff'] + forecast['superbowl']).abs() > 0][
| 2190 |
2014-02-02 |
- 1.200631 |
- 0.957093 |
+ 1.205344 |
+ 0.963327 |
| 2191 |
2014-02-03 |
- 1.841906 |
- 0.979777 |
+ 1.851992 |
+ 0.991010 |
| 2532 |
2015-01-11 |
- 1.200631 |
+ 1.205344 |
0.000000 |
| 2533 |
2015-01-12 |
- 1.841906 |
+ 1.851992 |
0.000000 |
| 2901 |
2016-01-17 |
- 1.200631 |
+ 1.205344 |
0.000000 |
| 2902 |
2016-01-18 |
- 1.841906 |
+ 1.851992 |
0.000000 |
| 2908 |
2016-01-24 |
- 1.200631 |
+ 1.205344 |
0.000000 |
| 2909 |
2016-01-25 |
- 1.841906 |
+ 1.851992 |
0.000000 |
| 2922 |
2016-02-07 |
- 1.200631 |
- 0.957093 |
+ 1.205344 |
+ 0.963327 |
| 2923 |
2016-02-08 |
- 1.841906 |
- 0.979777 |
+ 1.851992 |
+ 0.991010 |
@@ -306,18 +370,19 @@ The magnitude of the holiday effect has been reduced compared to before, especia
Prior scales can be set separately for individual holidays by including a column `prior_scale` in the holidays dataframe. Prior scales for individual seasonalities can be passed as an argument to `add_seasonality`. For instance, the prior scale for just weekly seasonality can be set using:
-```python
-# Python
-m = Prophet()
-m.add_seasonality(
- name='weekly', period=7, fourier_order=3, prior_scale=0.1);
-```
```R
# R
m <- prophet()
m <- add_seasonality(
m, name='weekly', period=7, fourier.order=3, prior.scale=0.1)
```
+```python
+# Python
+m = Prophet()
+m.add_seasonality(
+ name='weekly', period=7, fourier_order=3, prior_scale=0.1)
+```
+
### Additional regressors
Additional regressors can be added to the linear part of the model using the `add_regressor` method or function. A column with the regressor value will need to be present in both the fitting and prediction dataframes. For example, we can add an additional effect on Sundays during the NFL season. On the components plot, this effect will show up in the 'extra_regressors' plot:
@@ -356,12 +421,16 @@ m.fit(df)
future['nfl_sunday'] = future['ds'].apply(nfl_sunday)
forecast = m.predict(future)
-m.plot_components(forecast);
+fig = m.plot_components(forecast)
```
-
+
NFL Sundays could also have been handled using the "holidays" interface described above, by creating a list of past and future NFL Sundays. The `add_regressor` function provides a more general interface for defining extra linear regressors, and in particular does not require that the regressor be a binary indicator. Another time series could be used as a regressor, although its future values would have to be known. The regressor cannot be constant in the training data; fitting will exit with an error if it is.
-The `add_regressor` function has optional arguments for specifying the prior scale (holiday prior scale is used by default) and whether or not the regressor is standardized - see the docstring with `help(Prophet.add_regressor)` in Python and `?add_regressor` in R.
+The `add_regressor` function has optional arguments for specifying the prior scale (holiday prior scale is used by default) and whether or not the regressor is standardized - see the docstring with `help(Prophet.add_regressor)` in Python and `?add_regressor` in R. Note that regressors must be added prior to model fitting.
+
+The extra regressor must be known for both the history and for future dates. It thus must either be something that has known future values (such as `nfl_sunday`), or something that has separately been forecasted elsewhere. Prophet will also raise an error if the regressor is constant throughout the history, since there is nothing to fit from it.
+
+Extra regressors are put in the linear component of the model, so the underlying model is that the time series depends on the extra regressor as either an additive or multiplicative factor (see the next section for multiplicativity).
diff --git a/docs/_docs/trend_changepoints.md b/docs/_docs/trend_changepoints.md
index 6ba8121..e255a98 100644
--- a/docs/_docs/trend_changepoints.md
+++ b/docs/_docs/trend_changepoints.md
@@ -19,7 +19,23 @@ Even though we have a lot of places where the rate can possibly change, because
-The number of potential changepoints can be set using the argument `n_changepoints`, but this is better tuned by adjusting the regularization.
+The number of potential changepoints can be set using the argument `n_changepoints`, but this is better tuned by adjusting the regularization. The locations of the signification changepoints can be visualized with:
+
+```R
+# R
+plot(m, forecast) + add_changepoints_to_plot(m)
+```
+```python
+# Python
+from fbprophet.plot import add_changepoints_to_plot
+fig = m.plot(forecast)
+a = add_changepoints_to_plot(fig.gca(), m, forecast)
+```
+
+
+
+
+By default changepoints are only inferred for the first 80% of the time series in order to have plenty of runway for projecting the trend forward and to avoid overfitting fluctuations at the end of the time series. This default works in many situations but not all, and can be change using the `changepoint_range` argument. For example, `m = Prophet(changepoint_range=0.9)` in Python or `m <- prophet(changepoint.range = 0.9)` in R will place potential changepoints in the first 90% of the time series.
### Adjusting trend flexibility
If the trend changes are being overfit (too much flexibility) or underfit (not enough flexibility), you can adjust the strength of the sparse prior using the input argument `changepoint_prior_scale`. By default, this parameter is set to 0.05. Increasing it will make the trend *more* flexible:
@@ -28,16 +44,16 @@ If the trend changes are being overfit (too much flexibility) or underfit (not e
# R
m <- prophet(df, changepoint.prior.scale = 0.5)
forecast <- predict(m, future)
-plot(m, forecast);
+plot(m, forecast)
```
```python
# Python
m = Prophet(changepoint_prior_scale=0.5)
forecast = m.fit(df).predict(future)
-m.plot(forecast);
+fig = m.plot(forecast)
```
-
+
Decreasing it will make the trend *less* flexible:
@@ -46,34 +62,34 @@ Decreasing it will make the trend *less* flexible:
# R
m <- prophet(df, changepoint.prior.scale = 0.001)
forecast <- predict(m, future)
-plot(m, forecast);
+plot(m, forecast)
```
```python
# Python
m = Prophet(changepoint_prior_scale=0.001)
forecast = m.fit(df).predict(future)
-m.plot(forecast);
+fig = m.plot(forecast)
```
-
+
### Specifying the locations of the changepoints
-If you wish, rather than using automatic changepoint detection you can manually specify the locations of potential changepoints with the `changepoints` argument.
+If you wish, rather than using automatic changepoint detection you can manually specify the locations of potential changepoints with the `changepoints` argument. Slope changes will then be allowed only at these points, with the same sparse regularization as before. One could, for instance, create a grid of points as is done automatically, but then augment that grid with some specific dates that are known to be likely to have changes. As another example, the changepoints could be entirely limited to a small set of dates, as is done here:
```R
# R
m <- prophet(df, changepoints = c('2014-01-01'))
forecast <- predict(m, future)
-plot(m, forecast);
+plot(m, forecast)
```
```python
# Python
m = Prophet(changepoints=['2014-01-01'])
forecast = m.fit(df).predict(future)
-m.plot(forecast);
+fig = m.plot(forecast)
```
-
+
diff --git a/docs/_docs/uncertainty_intervals.md b/docs/_docs/uncertainty_intervals.md
index a671f11..d10a6b2 100644
--- a/docs/_docs/uncertainty_intervals.md
+++ b/docs/_docs/uncertainty_intervals.md
@@ -15,39 +15,39 @@ One property of this way of measuring uncertainty is that allowing higher flexib
The width of the uncertainty intervals (by default 80%) can be set using the parameter `interval_width`:
-```python
-# Python
-forecast = Prophet(interval_width=0.95).fit(df).predict(future)
-```
```R
# R
m <- prophet(df, interval.width = 0.95)
forecast <- predict(m, future)
```
+```python
+# Python
+forecast = Prophet(interval_width=0.95).fit(df).predict(future)
+```
Again, these intervals assume that the future will see the same frequency and magnitude of rate changes as the past. This assumption is probably not true, so you should not expect to get accurate coverage on these uncertainty intervals.
### Uncertainty in seasonality
-By default Prophet will only return uncertainty in the trend and observation noise. To get uncertainty in seasonality, you must do full Bayesian sampling. This is done using the parameter `mcmc.samples` (which defaults to 0). We do this here for the Peyton Manning data from the Quickstart:
+By default Prophet will only return uncertainty in the trend and observation noise. To get uncertainty in seasonality, you must do full Bayesian sampling. This is done using the parameter `mcmc.samples` (which defaults to 0). We do this here for the first six months of the Peyton Manning data from the Quickstart:
-```python
-# Python
-m = Prophet(mcmc_samples=300)
-forecast = m.fit(df).predict(future)
-```
```R
# R
m <- prophet(df, mcmc.samples = 300)
forecast <- predict(m, future)
```
-This replaces the typical MAP estimation with MCMC sampling, and takes much longer - think 10 minutes instead of 10 seconds. If you do full sampling, then you will see the uncertainty in seasonal components when you plot them:
-
```python
# Python
-m.plot_components(forecast);
+m = Prophet(mcmc_samples=300)
+forecast = m.fit(df).predict(future)
```
+This replaces the typical MAP estimation with MCMC sampling, and can take much longer depending on how many observations there are - expect several minutes instead of several seconds. If you do full sampling, then you will see the uncertainty in seasonal components when you plot them:
+
```R
# R
-prophet_plot_components(m, forecast);
+prophet_plot_components(m, forecast)
+```
+```python
+# Python
+fig = m.plot_components(forecast)
```
diff --git a/docs/index.md b/docs/index.md
index 162d2c4..349ef17 100644
--- a/docs/index.md
+++ b/docs/index.md
@@ -4,7 +4,7 @@ title: Prophet
id: home
---
-Prophet is a procedure for forecasting time series data. It is based on an additive model where non-linear trends are fit with yearly and weekly seasonality, plus holidays. It works best with daily periodicity data with at least one year of historical data. Prophet is robust to missing data, shifts in the trend, and large outliers.
+Prophet is a procedure for forecasting time series data based on an additive model where non-linear trends are fit with yearly, weekly, and daily seasonality, plus holiday effects. It works best with time series that have strong seasonal effects and several seasons of historical data. Prophet is robust to missing data and shifts in the trend, and typically handles outliers well.
Prophet is [open source software](https://code.facebook.com/projects/) released by Facebook's [Core Data Science team](https://research.fb.com/category/data-science/). It is available for download on [CRAN](https://cran.r-project.org/package=prophet) and [PyPI](https://pypi.python.org/pypi/fbprophet/).
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index 59c68ba..f6b5211 100644
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index 1931801..51637fe 100644
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diff --git a/notebooks/non-daily_data.ipynb b/notebooks/non-daily_data.ipynb
index 145af32..a36eb84 100644
--- a/notebooks/non-daily_data.ipynb
+++ b/notebooks/non-daily_data.ipynb
@@ -506,7 +506,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "The seasonality has low uncertainty at the start of each month where there are data points, but has very high posterior variance in between. When fitting Prophet to monthly data, only make monthly forecasts, which can be done by passing the frequency into make_future_dataframe:"
+ "The seasonality has low uncertainty at the start of each month where there are data points, but has very high posterior variance in between. When fitting Prophet to monthly data, only make monthly forecasts, which can be done by passing the frequency into `make_future_dataframe`:"
]
},
{
@@ -570,7 +570,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
- "version": "2.7.14+"
+ "version": "2.7.13"
}
},
"nbformat": 4,
diff --git a/notebooks/quick_start.ipynb b/notebooks/quick_start.ipynb
index bd7c2ec..6b4c0a0 100644
--- a/notebooks/quick_start.ipynb
+++ b/notebooks/quick_start.ipynb
@@ -394,7 +394,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "More details about the options available for each method are available in the docstrings, for example, via `help(Prophet)` or `help(Prophet.fit)`."
+ "More details about the options available for each method are available in the docstrings, for example, via `help(Prophet)` or `help(Prophet.fit)`. The [R reference manual](https://cran.r-project.org/web/packages/prophet/prophet.pdf) on CRAN provides a concise list of all of the available functions, each of which has a Python equivalent."
]
},
{
@@ -612,7 +612,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
- "version": "2.7.14+"
+ "version": "2.7.13"
}
},
"nbformat": 4,
diff --git a/notebooks/seasonality,_holiday_effects,_and_regressors.ipynb b/notebooks/seasonality,_holiday_effects,_and_regressors.ipynb
index 2cc4e1d..60ad863 100644
--- a/notebooks/seasonality,_holiday_effects,_and_regressors.ipynb
+++ b/notebooks/seasonality,_holiday_effects,_and_regressors.ipynb
@@ -357,9 +357,7 @@
{
"cell_type": "code",
"execution_count": 10,
- "metadata": {
- "output_hidden": true
- },
+ "metadata": {},
"outputs": [
{
"data": {
@@ -380,7 +378,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "Individual holidays can be plotted using the `plot_forecast_component` method (Python) or function (R). For example, `m.plot_forecast_component(forecast, 'superbowl')` in Python and `plot_forecast_component(forecast, 'superbowl')` in R to plot just the superbowl holiday component."
+ "Individual holidays can be plotted using the `plot_forecast_component` function (imported from `fbprophet.plot` in Python) like `plot_forecast_component(forecast, 'superbowl')` to plot just the superbowl holiday component."
]
},
{
@@ -511,7 +509,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "Increasing the number of Fourier terms allows the seasonality to fit faster changing cycles, but can also lead to overfitting: $N$ Fourier terms corresponds to $2N$ variables used for modeling the cycle\n",
+ "Increasing the number of Fourier terms allows the seasonality to fit faster changing cycles, but can also lead to overfitting: N Fourier terms corresponds to 2N variables used for modeling the cycle\n",
"\n",
"### Specifying Custom Seasonalities\n",
"\n",
@@ -801,6 +799,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
+ "\n",
"### Additional regressors\n",
"Additional regressors can be added to the linear part of the model using the `add_regressor` method or function. A column with the regressor value will need to be present in both the fitting and prediction dataframes. For example, we can add an additional effect on Sundays during the NFL season. On the components plot, this effect will show up in the 'extra_regressors' plot:"
]
@@ -915,7 +914,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
- "version": "2.7.14+"
+ "version": "2.7.13"
}
},
"nbformat": 4,