Eric D. BrownOct 08 2019 UTC

Forecasting Time Series Data With Prophet I & II

Introduction

A lot of what I do in my data analytics work is understanding time series data, modeling that data and trying to forecast what might come next in that data. Over the years I’ve used many different approaches, libraries, and modeling techniques for modeling and forecasting with some success… and a lot of failure.

Recently, I’ve been looking for a simpler approach for my initial modeling and think I’ve found a very nice library in Facebook’s Prophet (available for both Python and R). While this particular library isn’t terribly robust, it is quick and gives some very good results for that initial pass at modeling / forecasting time series data. An added bonus with Prophet for those that like to understand the theory behind things is this white paper with a very good description of the math / statistical approach behind Prophet.

If you are interested in learning more about time-series forecasting, check out the books / websites below.

Part I

Getting Started

Using Prophet is extremely straightforward. You import it, load some data into a Pandas dataframe, set the data up into the proper format and then start modeling / forecasting.

First, import the module (plus some other modules that we’ll need):

import pandas as pd
import numpy as np
from fbprophet import Prophet
import matplotlib.pyplot as plt
 
plt.rcParams['figure.figsize']=(20,10)
plt.style.use('ggplot')

Matplotlib must be manually registered with Pandas due to a conflict between Prophet and Pandas.

pd.plotting.register_matplotlib_converters()

Read in the data

retail_sales.csv

Read the data in from the retail_sales.csv file and set the index to the date column. We are also parsing dates in the data file.

sales_df = pd.read_csv(
retail_sales.csv
, index_col='date', parse_dates=True)

Now, we have a Pandas dataframe with our data that looks something like this:

sales_df.head()
datesales
2009-10-01338630
2009-11-01339386
2009-12-01400264
2010-01-01314640
2010-02-01311022
5 items

Prepare for Prophet

For Prophet to work, we need to change the names of these columns to ds and y, so lets just create a new dataframe and keep our old one handy (you'll see why later). The new dataframe will initially be created with an integer index so we can rename the columns

df = sales_df.reset_index()

Your dataframe should now look like the following:

df.head()
datesales
02009-10-01338630
12009-11-01339386
22009-12-01400264
32010-01-01314640
42010-02-01311022
5 items

Let's rename the columns as required by fbprophet. Additionally, fbprophet doesn't like the index to be a datetime... it wants to see ds as a non-index column, so we won't set an index differently than the integer index.

df=df.rename(columns={'date':'ds', 'sales':'y'})
df.head()
dsy
02009-10-01338630
12009-11-01339386
22009-12-01400264
32010-01-01314640
42010-02-01311022
5 items

Now's a good time to take a look at your data. Plot the data using Pandas' plot function.

df.set_index('ds').y.plot().get_figure()

When working with time series data, its good to take a look at the data to determine if trends exist, whether it is stationary, has any outliers and/or any other anomalies. Facebook Prophet's example uses the log-transform as a way to remove some of these anomalies but it isn't the absolute 'best' way to do this... but given that its the example and a simple data series, I'll follow their lead for now. Taking the log of a number is easily reversible to be able to see your original data.

To log-transform your data, you can use Numpy's log() function

df['y'] = np.log(df['y'])
df.tail()
dsy
672015-05-0113.044650453675313
682015-06-0113.013059541513272
692015-07-0113.033991074775358
702015-08-0113.030993424699561
712015-09-0112.973670775134828
5 items
df.set_index('ds').y.plot().get_figure()

As you can see in the above chart, the plot looks the same as the first one but just at a different scale.

Part II

Running Prophet

Now, let's set Prophet up to begin modeling our data.

Note: Since we are using monthly data, you'll see a message from Prophet saying Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this. This is OK since we are working with monthly data but you can disable it by using weekly_seasonality=True in the instantiation of Prophet.

model = Prophet()
model.fit(df);
<fbprophet.fo...x7f2c11972f60>

Forecasting is fairly useless unless you can look into the future, so we need to add some future dates to our dataframe. For this example, I want to forecast 2 years into the future, so I'll built a future dataframe with 24 periods since we are working with monthly data. Note the freq='m' inclusion to ensure we are adding 24 months of data.

This can be done with the following code:

future = model.make_future_dataframe(periods=24, freq = 'm')
future.tail()
ds
912017-04-30
922017-05-31
932017-06-30
942017-07-31
952017-08-31
5 items

To forecast this future data, we need to run it through Prophet's model.

forecast = model.predict(future)

The resulting forecast dataframe contains quite a bit of data, but we really only care about a few columns. First, let's look at the full dataframe:

forecast.tail()

We really only want to look at yhat, yhat_lower, and yhat_upper, so we can do that with:

forecast[['ds', 'yhat', 'yhat_lower', 'yhat_upper']].tail()
dsyhatyhat_loweryhat_upper
912017-04-3013.0596009114299212.86983077136156713.255463589763021
922017-05-3113.05587420563058412.85043726905510513.270689789903539
932017-06-3013.07632518223537812.85253366550388813.31003696452107
942017-07-3113.05605291521129812.82136319062715313.308538566200477
952017-08-3113.02737031004898112.77331656504801313.292583771318434
5 items

Plotting Prophet results

Prophet has a plotting mechanism called plot. This plot functionality draws the original data (black dots), the model (blue line), and the error of the forecast (shaded blue area).

model.plot(forecast);

Personally, I'm not a fan of this visualization so I like to break the data up and build a chart myself. The next section describes how I build my own visualization for Prophet modeling.

Visualizing Prophet models

In order to build a useful dataframe to visualize our model versus our original data, we need to combine the output of the Prophet model with our original data set, then we'll build a new chart manually using Pandas and Matplotlib.

First, let's set our dataframes to have the same index of ds.

df.set_index('ds', inplace=True)
forecast.set_index('ds', inplace=True)

Now, we'll combine the original data and our forecast model data.

viz_df = sales_df.join(forecast[['yhat', 'yhat_lower','yhat_upper']], how = 'outer')

If we look at the head(), we see the data has been joined correctly but the scales of our original data (sales) and our model (yhat) are different. We need to rescale the yhat column(s) to get the same scale, so we'll use Numpy's exp function to do that.

viz_df.head()
salesyhatyhat_loweryhat_upper
2009-10-01338630.012.7289162996766412.71936452418300312.73949007973038
2009-11-01339386.012.74943508787369212.73876288538901512.75984775702255
2009-12-01400264.012.88744365640661512.8772276748452612.899177627363834
2010-01-01314640.012.66246940243891712.6519408107834712.67338564231148
2010-02-01311022.012.65582528105592912.6456361895563212.665771587151028
5 items
viz_df['yhat_rescaled'] = np.exp(viz_df['yhat'])
viz_df.head()
salesyhatyhat_loweryhat_upperyhat_rescaled
2009-10-01338630.012.7289162996766412.71936452418300312.73949007973038337363.51235967537
2009-11-01339386.012.74943508787369212.73876288538901512.75984775702255344357.3095608864
2009-12-01400264.012.88744365640661512.8772276748452612.899177627363834395317.159207676
2010-01-01314640.012.66246940243891712.6519408107834712.67338564231148315675.2904628142
2010-02-01311022.012.65582528105592912.6456361895563212.665771587151028313584.8577497736
5 items

Let's take a look at the sales and yhat_rescaled data together in a chart.

viz_df[['sales', 'yhat_rescaled']].plot().get_figure()

You can see from the chart that the model (blue) is pretty good when plotted against the actual signal (orange) but I like to make my visualizations a little easier to understand. To build my 'better' visualization, we'll need to go back to our original sales_df and forecast dataframes.

First things first - we need to find the 2nd to last date of the original sales data in sales_df in order to ensure the original sales data and model data charts are connected.

sales_df.index = pd.to_datetime(sales_df.index) #make sure our index as a datetime object
connect_date = sales_df.index[-2] #select the 2nd to last date

Using the connect_date we can now grab only the model data that after that date (you'll see why in a minute). To do this, we'll mask the forecast data.

mask = (forecast.index > connect_date)
predict_df = forecast.loc[mask]
predict_df.head()

Now, let's build a dataframe to use in our new visualization. We'll follow the same steps we did before.

viz_df = sales_df.join(predict_df[['yhat', 'yhat_lower','yhat_upper']], how = 'outer')
viz_df['yhat_scaled']=np.exp(viz_df['yhat'])

Now, if we take a look at the head() of viz_df we'll see NaNs everywhere except for our original data rows.

viz_df.head()
salesyhatyhat_loweryhat_upperyhat_scaled
2009-10-01338630.0
2009-11-01339386.0
2009-12-01400264.0
2010-01-01314640.0
2010-02-01311022.0
5 items

If we take a look at the tail() of the viz_df you'll see we have data for the forecast data and NaNs for the original data series.

viz_df.tail()
salesyhatyhat_loweryhat_upperyhat_scaled
2017-04-3013.0596009114299212.86983077136156713.255463589763021469583.26560153335
2017-05-3113.05587420563058412.85043726905510513.270689789903539467836.5237404679
2017-06-3013.07632518223537812.85253366550388813.31003696452107477502.74244912295
2017-07-3113.05605291521129812.82136319062715313.308538566200477467920.13808058767
2017-08-3113.02737031004898112.77331656504801313.292583771318434454689.61942474794
5 items

Time to plot

Now, let's plot everything to get the 'final' visualization of our sales data and forecast with errors.

fig, ax1 = plt.subplots()
ax1.plot(viz_df.sales)
ax1.plot(viz_df.yhat_scaled, color='black', linestyle=':')
ax1.fill_between(viz_df.index, np.exp(viz_df['yhat_upper']), np.exp(viz_df['yhat_lower']), alpha=0.5, color='darkgray')
ax1.set_title('Sales (Orange) vs Sales Forecast (Black)')
ax1.set_ylabel('Dollar Sales')
ax1.set_xlabel('Date')

L=ax1.legend() #get the legend
L.get_texts()[0].set_text('Actual Sales') #change the legend text for 1st plot
L.get_texts()[1].set_text('Forecasted Sales') #change the legend text for 2nd plot
fig

This visualization is much better (in my opinion) than the default fbprophet plot. It is much easier to quickly understand and describe what's happening. The orange line is actual sales data and the black dotted line is the forecast. The gray shaded area is the uncertainty estimation of the forecast.