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Forecasting with Prophet
Resources consulted: YouTube Tutorial & Kaggle Notebook

Evan Marie online: | EvanMarie.com| EvanMarie@Proton.me | Linked In | GitHub | Hugging Face | Mastadon | Jovian.ai | TikTok | CodeWars | Discord ⇨ ✨ EvanMarie ✨#6114 |

from helpers_elegant import *
import_all()
plt.style.use('elegant.mplstyle')
import seaborn as sns
from prophet import Prophet
from sklearn.metrics import mean_squared_error as mse
from sklearn.metrics import mean_absolute_error as mae
from sklearn.metrics import mean_absolute_percentage_error as mape
import warnings
from tqdm import tqdm
warnings.filterwarnings("ignore")
%matplotlib inline

colors = sns.color_palette("husl", 20)
clr = list(map(mpl.colors.rgb2hex, colors))
from random import choice as rc

/Users/evancarr/opt/anaconda3/envs/sktime_project_02_05_23/lib/python3.10/site-packages/tqdm/auto.py:22: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html
  from .autonotebook import tqdm as notebook_tqdm

%%html
<style>
a:link {color: pink !important; font-weight: 600 !important;}
a:visited {color: pink !important; font-weight: 600 !important;}
</style>

data = pd.read_csv('pjme.csv',
                   index_col=[0],
                  parse_dates=[0])

df_overview(data, 'imported data')

imported data Columns

	PJME_MW
datatype	float64
missing values	0
count	145,366.00
mean	32,080.22
std	6,464.01
min	14,544.00
25%	27,573.00
50%	31,421.00
75%	35,650.00
max	62,009.00

   

imported data Key Points

total rows	145,366
total columns	1
column names	PJME_MW
index start	2002-12-31 01:00:00
index end	2018-01-02 00:00:00
total missing values	0

   

imported data Head and Tail

head(3)

	PJME_MW
Datetime
2002-12-31	26,498.00
2002-12-31	25,147.00
2002-12-31	24,574.00

   

tail(3)

	PJME_MW
Datetime
2018-01-01	42,402.00
2018-01-01	40,164.00
2018-01-02	38,608.00

   

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Initial Data Visualization

fix, axes = plt.subplots(5, 1, figsize = (12, 17))
data.plot(ax = axes[0], title = 'PJME: Energy Consumption Hourly', ms=.5, c = rc(clr))
data.resample('D').mean().plot(ax = axes[1], title = 'PJME: Daily Avg', c = rc(clr))
data.resample('W').mean().plot(ax = axes[2], title = 'PJME: Weekly Avg', c = rc(clr))
data.resample('M').mean().plot(ax = axes[3], title = 'PJME: Monthly Avg', c = rc(clr))
data.resample('A').mean().plot(ax = axes[4], title = 'PJME: Yearly Avg', c = rc(clr))
axes[0].legend().remove(); axes[1].legend().remove();
axes[2].legend().remove(); axes[3].legend().remove();
axes[4].legend().remove();
plt.tight_layout()

Featurized Data

featurized = featurize_dt_index(data)

df_overview(featurized, 'featurized_data')

featurized_data Columns

	PJME_MW	hour	weekday	weekday_name	month	month_name	quarter	year	week_of_year	day_of_year	date_offset	season	time_of_day
datatype	float64	int64	int64	category	int64	category	int64	int64	float64	int64	int64	category	category
missing values	0	0	0	0	0	0	0	0	0	0	0	408	0
count	145,366.00	145,366.00	145,366.00	nan	145,366.00	nan	145,366.00	145,366.00	145,366.00	145,366.00	145,366.00	nan	nan
mean	32,080.22	11.50	3.00	nan	6.44	nan	2.48	2,009.80	26.22	180.46	624.66	nan	nan
std	6,464.01	6.92	2.00	nan	3.44	nan	1.11	4.79	15.02	105.14	380.84	nan	nan
min	14,544.00	0.00	0.00	nan	1.00	nan	1.00	2,002.00	1.00	1.00	0.00	nan	nan
25%	27,573.00	6.00	1.00	nan	3.00	nan	1.00	2,006.00	13.00	90.00	297.00	nan	nan
50%	31,421.00	12.00	3.00	nan	6.00	nan	2.00	2,010.00	26.00	179.00	596.00	nan	nan
75%	35,650.00	18.00	5.00	nan	9.00	nan	3.00	2,014.00	39.00	271.00	900.00	nan	nan
max	62,009.00	23.00	6.00	nan	12.00	nan	4.00	2,018.00	53.00	366.00	1,299.00	nan	nan

   

featurized_data Key Points

total rows	145,366
total columns	13
column names	PJME_MW, hour, weekday, weekday_name, month, month_name, quarter, year, week_of_year, day_of_year, date_offset, season, time_of_day
index start	2002-12-31 01:00:00
index end	2018-01-02 00:00:00
total missing values	408

   

featurized_data Head and Tail

head(3)

	PJME_MW	hour	weekday	weekday_name	month	month_name	quarter	year	week_of_year	day_of_year	date_offset	season	time_of_day
Datetime
2002-12-31	26,498.00	1	1	Tuesday	12	December	4	2,002	1.00	365	911	Winter	midnight
2002-12-31	25,147.00	2	1	Tuesday	12	December	4	2,002	1.00	365	911	Winter	midnight
2002-12-31	24,574.00	3	1	Tuesday	12	December	4	2,002	1.00	365	911	Winter	midnight

   

tail(3)

	PJME_MW	hour	weekday	weekday_name	month	month_name	quarter	year	week_of_year	day_of_year	date_offset	season	time_of_day
Datetime
2018-01-01	42,402.00	22	0	Monday	1	January	1	2,018	1.00	1	1,081	Winter	night
2018-01-01	40,164.00	23	0	Monday	1	January	1	2,018	1.00	1	1,081	Winter	night
2018-01-02	38,608.00	0	1	Tuesday	1	January	1	2,018	1.00	2	1,082	Winter	midnight

   

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Feature Visualization

def box_plot_me(df, column, target, hue, palette = 'cool'):
	fig, ax = plt.subplots(figsize=(10, 5))
	sns.boxplot(data = featurized.dropna(),
				x = column,
				y = target,
				hue = hue,
				ax = ax,
				linewidth = 1,
			   palette = palette)
	ax.set_title(f'Energy Consumption by {column}')
	ax.set_xlabel(f'{column}')
	ax.set_ylabel(f'{target}')
	ax.legend(bbox_to_anchor=(1, 1))

box_plot_me(featurized, 'weekday', 'PJME_MW', 'season')
box_plot_me(featurized, 'month', 'PJME_MW', 'weekday', palette = 'bright')

Train-Test Split

split_date = '1-Jan-2015'
train_data = data.loc[data.index <= split_date].copy()
test_data = data.loc[data.index > split_date].copy()

fig, ax = plt.subplots()
train_data.plot(ax = ax, c = rc(clr), ms = 4, style='.');
test_data.plot(ax = ax, c = rc(clr), ms = 4, style='.');
plt.title('Train-Test Split');
plt.legend(labels = ['training', 'testing']);

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| Top | Initial Data Visualization | Visualizing Features | Prophet Model | Incoporating Holidays | Future Predictions |

---

Prophet Model
- Prophet requires the datetime index to be a column named ds and the metric or target column to be named y

prophet_data = data.reset_index()\
		   .rename(columns = {'Datetime': 'ds', 'PJME_MW': 'y'})

head_tail_horz(prophet_data, 5, 'Data Prepped for Prophet')

Data Prepped for Prophet

head(5)

	ds	y
0	2002-12-31	26,498.00
1	2002-12-31	25,147.00
2	2002-12-31	24,574.00
3	2002-12-31	24,393.00
4	2002-12-31	24,860.00

   

tail(5)

	ds	y
145361	2018-01-01	44,284.00
145362	2018-01-01	43,751.00
145363	2018-01-01	42,402.00
145364	2018-01-01	40,164.00
145365	2018-01-02	38,608.00

   

Documentation on Prophet

# help(Prophet)

Prepping the testing and training data

prophet_train = train_data.reset_index()\
						  .rename(columns = {'Datetime': 'ds', 'PJME_MW': 'y'})
prophet_test = test_data.reset_index()\
						.rename(columns = {'Datetime': 'ds', 'PJME_MW': 'y'})

Fitting the model

%%time
model = Prophet()
model.fit(prophet_train)

15:32:20 - cmdstanpy - INFO - Chain [1] start processing
15:33:05 - cmdstanpy - INFO - Chain [1] done processing

CPU times: user 5.1 s, sys: 276 ms, total: 5.37 s
Wall time: 50 s

<prophet.forecaster.Prophet at 0x7f8069cc4ca0>

Forecasting

prophet_forecast = model.predict(prophet_test)

head_tail_vert(prophet_forecast, 5, title = "Prophet Forecast")

Prophet Forecast: head(5)

	ds	trend	yhat_lower	yhat_upper	trend_lower	trend_upper	additive_terms	additive_terms_lower	additive_terms_upper	daily	daily_lower	daily_upper	weekly	weekly_lower	weekly_upper	yearly	yearly_lower	yearly_upper	multiplicative_terms	multiplicative_terms_lower	multiplicative_terms_upper	yhat
0	2015-01-01	31,210.66	23,657.45	32,593.63	31,210.66	31,210.66	-2,836.55	-2,836.55	-2,836.55	-4,430.26	-4,430.26	-4,430.26	1,281.38	1,281.38	1,281.38	312.33	312.33	312.33	0.00	0.00	0.00	28,374.11
1	2015-01-01	31,210.62	22,226.58	31,323.26	31,210.62	31,210.62	-4,340.88	-4,340.88	-4,340.88	-5,927.14	-5,927.14	-5,927.14	1,272.62	1,272.62	1,272.62	313.64	313.64	313.64	0.00	0.00	0.00	26,869.74
2	2015-01-01	31,210.58	21,536.55	30,689.50	31,210.58	31,210.58	-5,212.57	-5,212.57	-5,212.57	-6,790.21	-6,790.21	-6,790.21	1,262.66	1,262.66	1,262.66	314.99	314.99	314.99	0.00	0.00	0.00	25,998.01
3	2015-01-01	31,210.54	21,080.78	30,011.51	31,210.54	31,210.54	-5,354.14	-5,354.14	-5,354.14	-6,922.12	-6,922.12	-6,922.12	1,251.61	1,251.61	1,251.61	316.38	316.38	316.38	0.00	0.00	0.00	25,856.40
4	2015-01-01	31,210.51	21,753.91	30,900.70	31,210.51	31,210.51	-4,679.83	-4,679.83	-4,679.83	-6,237.25	-6,237.25	-6,237.25	1,239.62	1,239.62	1,239.62	317.81	317.81	317.81	0.00	0.00	0.00	26,530.68

Prophet Forecast: tail(5)

	ds	trend	yhat_lower	yhat_upper	trend_lower	trend_upper	additive_terms	additive_terms_lower	additive_terms_upper	daily	daily_lower	daily_upper	weekly	weekly_lower	weekly_upper	yearly	yearly_lower	yearly_upper	multiplicative_terms	multiplicative_terms_lower	multiplicative_terms_upper	yhat
31434	2018-08-02	30,036.72	-8,445.77	88,610.31	-18,755.46	76,102.03	11,263.15	11,263.15	11,263.15	4,451.04	4,451.04	4,451.04	1,033.85	1,033.85	1,033.85	5,778.26	5,778.26	5,778.26	0.00	0.00	0.00	41,299.88
31435	2018-08-02	30,036.69	-9,223.74	86,786.42	-18,758.70	76,105.59	10,490.38	10,490.38	10,490.38	3,695.84	3,695.84	3,695.84	1,021.23	1,021.23	1,021.23	5,773.32	5,773.32	5,773.32	0.00	0.00	0.00	40,527.07
31436	2018-08-02	30,036.65	-10,586.11	85,253.92	-18,761.94	76,109.15	8,861.20	8,861.20	8,861.20	2,084.37	2,084.37	2,084.37	1,008.45	1,008.45	1,008.45	5,768.37	5,768.37	5,768.37	0.00	0.00	0.00	38,897.84
31437	2018-08-02	30,036.61	-12,486.18	84,076.65	-18,765.17	76,112.70	6,653.49	6,653.49	6,653.49	-105.25	-105.25	-105.25	995.32	995.32	995.32	5,763.42	5,763.42	5,763.42	0.00	0.00	0.00	36,690.10
31438	2018-08-03	30,036.57	-15,782.19	80,735.46	-18,768.41	76,116.26	4,327.99	4,327.99	4,327.99	-2,412.10	-2,412.10	-2,412.10	981.61	981.61	981.61	5,758.47	5,758.47	5,758.47	0.00	0.00	0.00	34,364.56

Customized Prophet Plot Function (adapted from Prophet documentation)

def customized_plot(model, 
					forecast, 
					ax=None,  
					uncertainty=True, 
					plot_cap=True, 
					xlabel='datetime', 
					ylabel='target metric',
):
	
    if ax is None:
        fig = plt.figure()
        ax = fig.add_subplot(111)
    else:
        fig = ax.get_figure()
    fcst_t = forecast['ds'].dt.to_pydatetime()
    ax.plot(model.history['ds'].dt.to_pydatetime(), model.history['y'], c=rc(clr))
    ax.plot(fcst_t, forecast['yhat'], ls='-', c=rc(clr))
    if 'cap' in forecast and plot_cap:
        ax.plot(fcst_t, forecast['cap'], ls='--', c=rc(clr))
    if model.logistic_floor and 'floor' in forecast and plot_cap:
        ax.plot(fcst_t, forecast['floor'], ls='--', c=rc(clr))
    if uncertainty:
        ax.fill_between(fcst_t, forecast['yhat_lower'], forecast['yhat_upper'],
                        color=rc(clr), alpha=0.4)
		
    ax.grid(True, which='major', c=rc(clr), ls='-', lw=1, alpha=0.4)
    ax.set_xlabel(xlabel)
    ax.set_ylabel(ylabel)
    fig.tight_layout()
    return fig

fig, ax = plt.subplots(figsize=(10, 5))
fig = customized_plot(model = model, forecast = prophet_forecast, ax=ax);
ax.set_title('Prophet Forecast');

Confidence interval becomes wider the farther a prediction is into the future

(Source) Confidence Intervals are estimates that are calculated from sample data to determine ranges likely to contain the population parameter(mean, standard deviation)of interest. For example, if our population is (2,6), a confidence interval of the mean suggests that the population mean is likely between 2 and 6. And how confidently can we say this? Obviously 100%, right? Because we know all the values and we can calculate it very easily. But in real-life problems, this is not the case. It is not always feasible or possible to study the whole population. So what do we do? We take sample data. But can we rely on one sample? No, because different samples from the same data will produce different mean. So we take numerous random samples (from the same population) and calculate confidence intervals for each sample and a certain percentage of these ranges will contain the true population parameter. This certain percentage is called the confidence level. A 95% confidence level means that out of 100 random samples taken, I expect 95 of the confidence intervals to contain the true population parameter.

Visualizing Components

import matplotlib
matplotlib.rcParams.update(matplotlib.rcParamsDefault)

fig = model.plot_components(prophet_forecast)
plt.show()

Model Evaluation

fig, ax = plt.subplots()
ax.scatter(test_data.index, test_data['PJME_MW'], color='yellow')
customized_plot(model = model, forecast = prophet_forecast, ax=ax)
plt.show()

Zoom in to date range within predictions and actual values

def zoom_in_prophet(forecast, 
					test_data,
					start_date, 
					end_date, 
					title, 
					legend_loc = 1
				   ):
	forecast_segment = forecast.set_index('ds')
	forecast_segment = forecast_segment.loc[start_date : end_date]
	test_segment = test_data.loc[start_date : end_date]
	plt.style.use('elegant.mplstyle')
	fig, ax = plt.subplots(figsize = (15, 4))
	ax.scatter(test_segment.index, 
		   test_segment['PJME_MW'], 
		   color = 'yellow',
		  label = "Actual Values",
		  s = 20)
	ax.scatter(forecast_segment.index, 
		   forecast_segment['yhat'], 
		   color = 'deeppink',
		  label = 'Predicted Values',
		  s = 20)
	plt.title(title + ' Actual Values vs Predicted');
	plt.xticks(rotation = 40)
	plt.legend(loc = legend_loc)
	plt.show()

Monthly Comparison: Earliest Predictions

zoom_in_prophet(prophet_forecast, test_data, 
				'2015-01-01', '2015-02-01', 'January 2015:')
zoom_in_prophet(prophet_forecast, test_data, 
				'2015-02-01', '2015-03-01', 'February 2015:', legend_loc = 2)
zoom_in_prophet(prophet_forecast, test_data, 
				'2015-03-01', '2015-04-01', 'March 2015:')
zoom_in_prophet(prophet_forecast, test_data, 
				'2015-04-01', '2015-05-01', 'April 2015:', legend_loc = 4)

Weekly Comparison: Earliest Predictions

zoom_in_prophet(prophet_forecast, test_data, 
				'2015-01-01', '2015-01-08', 'January 2015 Week 1:', legend_loc = 2)
zoom_in_prophet(prophet_forecast, test_data, 
				'2015-01-08', '2015-01-15', 'January 2015 Week 2:', legend_loc = 4)
zoom_in_prophet(prophet_forecast, test_data, 
				'2015-01-15', '2015-01-22', 'January 2015 Week 3:', legend_loc = 4)
zoom_in_prophet(prophet_forecast, test_data, 
				'2015-01-22', '2015-01-29', 'January 2015 Week 4:', legend_loc = 4)

Monthly Comparison: Latest Predictions

zoom_in_prophet(prophet_forecast, test_data, 
				'2018-04-01', '2018-05-01', 'April 2018:')
zoom_in_prophet(prophet_forecast, test_data, 
				'2018-05-01', '2018-06-01', 'May 2018:', legend_loc = 2)
zoom_in_prophet(prophet_forecast, test_data, 
				'2018-06-01', '2018-07-01', 'June 2018:')
zoom_in_prophet(prophet_forecast, test_data, 
				'2018-07-01', '2018-08-01', 'July 2018:', legend_loc = 4)

Weekly Comparison: Latest Predictions

zoom_in_prophet(prophet_forecast, test_data, 
				'2018-07-01', '2018-07-08', 'July 2018 Week 1:', legend_loc = 2)
zoom_in_prophet(prophet_forecast, test_data, 
				'2018-07-08', '2018-07-15', 'July 2018 Week 2:', legend_loc = 4)
zoom_in_prophet(prophet_forecast, test_data, 
				'2018-07-15', '2018-07-22', 'July 2018 Week 3:', legend_loc = 4)
zoom_in_prophet(prophet_forecast, test_data, 
				'2018-07-22', '2018-07-29', 'July 2018 Week 4:', legend_loc = 4)

Error Metric Evaluation

actual_values = test_data.PJME_MW
predictions = prophet_forecast.yhat

pretty(np.sqrt(mse(actual_values, predictions)), 'Mean Squared Error Score:')
pretty(mae(actual_values, predictions), 'Mean Absolute Error Score:')
pretty(f'{mape(actual_values, predictions)*100:.3f}%', 
	   'Mean Absolute Percenage Error:')

Mean Squared Error Score:
6615.820557

Mean Absolute Error Score:
5182.108151

Mean Absolute Percenage Error:
16.509%

---

| Top | Initial Data Visualization | Visualizing Features | Prophet Model | Incoporating Holidays | Future Predictions |

---

Incorporating Holidays

# Rob used another library, but I am just using the Prophet method
# to add holidays

holiday_model = Prophet()
holiday_model.add_country_holidays(country_name='US')
holiday_model = holiday_model.fit(prophet_train)

15:37:44 - cmdstanpy - INFO - Chain [1] start processing
15:38:32 - cmdstanpy - INFO - Chain [1] done processing

pretty('US Holidays from Prophet')
pd.DataFrame(holiday_model.train_holiday_names).style\
									   .hide(axis = 'index')\
									   .hide(axis = 'columns')

US Holidays from Prophet

New Year's Day
Martin Luther King Jr. Day
Washington's Birthday
Memorial Day
Independence Day
Labor Day
Columbus Day
Veterans Day
Thanksgiving
Christmas Day
New Year's Day (Observed)
Independence Day (Observed)
Christmas Day (Observed)
Veterans Day (Observed)

Predictions: Accounting for holidays

holidays_forecast = holiday_model.predict(df = prophet_test)

head_tail_vert(holidays_forecast, 5, 'Holidays Forecast')

Holidays Forecast: head(5)

	ds	trend	yhat_lower	yhat_upper	trend_lower	trend_upper	Christmas Day	Christmas Day_lower	Christmas Day_upper	Christmas Day (Observed)	Christmas Day (Observed)_lower	Christmas Day (Observed)_upper	Columbus Day	Columbus Day_lower	Columbus Day_upper	Independence Day	Independence Day_lower	Independence Day_upper	Independence Day (Observed)	Independence Day (Observed)_lower	Independence Day (Observed)_upper	Labor Day	Labor Day_lower	Labor Day_upper	Martin Luther King Jr. Day	Martin Luther King Jr. Day_lower	Martin Luther King Jr. Day_upper	Memorial Day	Memorial Day_lower	Memorial Day_upper	New Year's Day	New Year's Day_lower	New Year's Day_upper	New Year's Day (Observed)	New Year's Day (Observed)_lower	New Year's Day (Observed)_upper	Thanksgiving	Thanksgiving_lower	Thanksgiving_upper	Veterans Day	Veterans Day_lower	Veterans Day_upper	Veterans Day (Observed)	Veterans Day (Observed)_lower	Veterans Day (Observed)_upper	Washington's Birthday	Washington's Birthday_lower	Washington's Birthday_upper	additive_terms	additive_terms_lower	additive_terms_upper	daily	daily_lower	daily_upper	holidays	holidays_lower	holidays_upper	weekly	weekly_lower	weekly_upper	yearly	yearly_lower	yearly_upper	multiplicative_terms	multiplicative_terms_lower	multiplicative_terms_upper	yhat
0	2015-01-01	31,266.52	21,382.75	30,266.37	31,266.52	31,266.52	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	-3,057.33	-3,057.33	-3,057.33	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	-5,514.97	-5,514.97	-5,514.97	-4,430.34	-4,430.34	-4,430.34	-3,057.33	-3,057.33	-3,057.33	1,317.81	1,317.81	1,317.81	654.90	654.90	654.90	0.00	0.00	0.00	25,751.55
1	2015-01-01	31,266.48	19,692.07	28,486.71	31,266.48	31,266.48	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	-3,057.33	-3,057.33	-3,057.33	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	-7,016.75	-7,016.75	-7,016.75	-5,927.22	-5,927.22	-5,927.22	-3,057.33	-3,057.33	-3,057.33	1,312.01	1,312.01	1,312.01	655.80	655.80	655.80	0.00	0.00	0.00	24,249.74
2	2015-01-01	31,266.45	19,271.15	27,719.36	31,266.45	31,266.45	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	-3,057.33	-3,057.33	-3,057.33	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	-7,886.21	-7,886.21	-7,886.21	-6,790.28	-6,790.28	-6,790.28	-3,057.33	-3,057.33	-3,057.33	1,304.67	1,304.67	1,304.67	656.73	656.73	656.73	0.00	0.00	0.00	23,380.24
3	2015-01-01	31,266.41	18,873.50	27,643.08	31,266.41	31,266.41	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	-3,057.33	-3,057.33	-3,057.33	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	-8,025.93	-8,025.93	-8,025.93	-6,922.19	-6,922.19	-6,922.19	-3,057.33	-3,057.33	-3,057.33	1,295.91	1,295.91	1,295.91	657.69	657.69	657.69	0.00	0.00	0.00	23,240.49
4	2015-01-01	31,266.38	19,529.33	28,463.87	31,266.38	31,266.38	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	-3,057.33	-3,057.33	-3,057.33	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	-7,350.14	-7,350.14	-7,350.14	-6,237.33	-6,237.33	-6,237.33	-3,057.33	-3,057.33	-3,057.33	1,285.83	1,285.83	1,285.83	658.68	658.68	658.68	0.00	0.00	0.00	23,916.23

Holidays Forecast: tail(5)

	ds	trend	yhat_lower	yhat_upper	trend_lower	trend_upper	Christmas Day	Christmas Day_lower	Christmas Day_upper	Christmas Day (Observed)	Christmas Day (Observed)_lower	Christmas Day (Observed)_upper	Columbus Day	Columbus Day_lower	Columbus Day_upper	Independence Day	Independence Day_lower	Independence Day_upper	Independence Day (Observed)	Independence Day (Observed)_lower	Independence Day (Observed)_upper	Labor Day	Labor Day_lower	Labor Day_upper	Martin Luther King Jr. Day	Martin Luther King Jr. Day_lower	Martin Luther King Jr. Day_upper	Memorial Day	Memorial Day_lower	Memorial Day_upper	New Year's Day	New Year's Day_lower	New Year's Day_upper	New Year's Day (Observed)	New Year's Day (Observed)_lower	New Year's Day (Observed)_upper	Thanksgiving	Thanksgiving_lower	Thanksgiving_upper	Veterans Day	Veterans Day_lower	Veterans Day_upper	Veterans Day (Observed)	Veterans Day (Observed)_lower	Veterans Day (Observed)_upper	Washington's Birthday	Washington's Birthday_lower	Washington's Birthday_upper	additive_terms	additive_terms_lower	additive_terms_upper	daily	daily_lower	daily_upper	holidays	holidays_lower	holidays_upper	weekly	weekly_lower	weekly_upper	yearly	yearly_lower	yearly_upper	multiplicative_terms	multiplicative_terms_lower	multiplicative_terms_upper	yhat
31434	2018-08-02	30,132.09	1,910.44	85,032.05	-8,671.05	73,917.88	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	11,265.73	11,265.73	11,265.73	4,451.12	4,451.12	4,451.12	0.00	0.00	0.00	1,067.63	1,067.63	1,067.63	5,746.99	5,746.99	5,746.99	0.00	0.00	0.00	41,397.82
31435	2018-08-02	30,132.05	1,379.49	84,542.92	-8,671.33	73,920.14	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	10,490.17	10,490.17	10,490.17	3,695.91	3,695.91	3,695.91	0.00	0.00	0.00	1,052.16	1,052.16	1,052.16	5,742.09	5,742.09	5,742.09	0.00	0.00	0.00	40,622.22
31436	2018-08-02	30,132.01	-795.26	82,982.56	-8,671.61	73,922.40	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	8,858.04	8,858.04	8,858.04	2,084.42	2,084.42	2,084.42	0.00	0.00	0.00	1,036.43	1,036.43	1,036.43	5,737.19	5,737.19	5,737.19	0.00	0.00	0.00	38,990.06
31437	2018-08-02	30,131.98	-4,276.75	81,395.76	-8,671.89	73,924.66	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	6,647.30	6,647.30	6,647.30	-105.26	-105.26	-105.26	0.00	0.00	0.00	1,020.27	1,020.27	1,020.27	5,732.29	5,732.29	5,732.29	0.00	0.00	0.00	36,779.28
31438	2018-08-03	30,131.94	-4,482.38	78,794.76	-8,672.17	73,926.92	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	4,318.70	4,318.70	4,318.70	-2,412.16	-2,412.16	-2,412.16	0.00	0.00	0.00	1,003.47	1,003.47	1,003.47	5,727.39	5,727.39	5,727.39	0.00	0.00	0.00	34,450.64

header_text('Forecast: Incorporating Holidays')
customized_plot(model = holiday_model, 
			   forecast = holidays_forecast)

Forecast: Incorporating Holidays

Visualizing Components: Incorporating Holidays

import matplotlib
matplotlib.rcParams.update(matplotlib.rcParamsDefault)

fig = holiday_model.plot_components(holidays_forecast)
plt.show()

Monthly Comparison (incorporating holidays): Earliest Predictions

zoom_in_prophet(holidays_forecast, test_data, 
				'2015-01-01', '2015-02-01', 'January 2015:')
zoom_in_prophet(holidays_forecast, test_data, 
				'2015-02-01', '2015-03-01', 'February 2015:', legend_loc = 2)
zoom_in_prophet(holidays_forecast, test_data, 
				'2015-03-01', '2015-04-01', 'March 2015:')
zoom_in_prophet(holidays_forecast, test_data, 
				'2015-04-01', '2015-05-01', 'April 2015:', legend_loc = 4)

Weekly Comparison (incorporating holidays): Earliest Predictions

zoom_in_prophet(holidays_forecast, test_data, 
				'2015-01-01', '2015-01-08', 'January 2015 Week 1:', legend_loc = 2)
zoom_in_prophet(holidays_forecast, test_data, 
				'2015-01-08', '2015-01-15', 'January 2015 Week 2:', legend_loc = 4)
zoom_in_prophet(holidays_forecast, test_data, 
				'2015-01-15', '2015-01-22', 'January 2015 Week 3:', legend_loc = 4)
zoom_in_prophet(holidays_forecast, test_data, 
				'2015-01-22', '2015-01-29', 'January 2015 Week 4:', legend_loc = 4)

Monthly Comparison (incorporating holidays): Latest Predictions

zoom_in_prophet(holidays_forecast, test_data, 
				'2018-04-01', '2018-05-01', 'April 2018:')
zoom_in_prophet(holidays_forecast, test_data, 
				'2018-05-01', '2018-06-01', 'May 2018:', legend_loc = 2)
zoom_in_prophet(holidays_forecast, test_data, 
				'2018-06-01', '2018-07-01', 'June 2018:')
zoom_in_prophet(holidays_forecast, test_data, 
				'2018-07-01', '2018-08-01', 'July 2018:', legend_loc = 4)

Weekly Comparison (incorporating holidays): Latest Predictions

zoom_in_prophet(holidays_forecast, test_data, 
				'2018-07-01', '2018-07-08', 'July 2018 Week 1:', legend_loc = 2)
zoom_in_prophet(holidays_forecast, test_data, 
				'2018-07-08', '2018-07-15', 'July 2018 Week 2:', legend_loc = 4)
zoom_in_prophet(holidays_forecast, test_data, 
				'2018-07-15', '2018-07-22', 'July 2018 Week 3:', legend_loc = 4)
zoom_in_prophet(holidays_forecast, test_data, 
				'2018-07-22', '2018-07-29', 'July 2018 Week 4:', legend_loc = 4)

actual_values = test_data.PJME_MW
predictions = holidays_forecast.yhat

pretty(np.sqrt(mse(actual_values, predictions)), 'Mean Squared Error Score:')
pretty(mae(actual_values, predictions), 'Mean Absolute Error Score:')
pretty(f'{mape(actual_values, predictions)*100:.3f}%', 
	   'Mean Absolute Percenage Error:')

Mean Squared Error Score:
6634.361847

Mean Absolute Error Score:
5197.493614

Mean Absolute Percenage Error:
16.566%

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| Top | Initial Data Visualization | Visualizing Features | Prophet Model | Incoporating Holidays | Future Predictions |

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Future Predictions

# retraining model on entirety of the data # Rob didn't do this, but I do not see a reason not to

future_model = Prophet()
future_model = future_model.fit(prophet_data)

15:57:59 - cmdstanpy - INFO - Chain [1] start processing
15:58:40 - cmdstanpy - INFO - Chain [1] done processing

future = future_model.make_future_dataframe(periods = 365*24, 
										    freq='h', 
										    include_history=False)

future_forecast = future_model.predict(future)

head_tail_vert(future_forecast, 5, 'Future Prediction Forecast')

Future Prediction Forecast: head(5)

	ds	trend	yhat_lower	yhat_upper	trend_lower	trend_upper	additive_terms	additive_terms_lower	additive_terms_upper	daily	daily_lower	daily_upper	weekly	weekly_lower	weekly_upper	yearly	yearly_lower	yearly_upper	multiplicative_terms	multiplicative_terms_lower	multiplicative_terms_upper	yhat
0	2018-08-03	30,824.25	28,762.81	38,351.27	30,824.25	30,824.25	2,392.84	2,392.84	2,392.84	-4,336.67	-4,336.67	-4,336.67	944.13	944.13	944.13	5,785.38	5,785.38	5,785.38	0.00	0.00	0.00	33,217.09
1	2018-08-03	30,824.22	27,377.33	36,294.35	30,824.22	30,824.22	912.37	912.37	912.37	-5,801.94	-5,801.94	-5,801.94	933.11	933.11	933.11	5,781.20	5,781.20	5,781.20	0.00	0.00	0.00	31,736.59
2	2018-08-03	30,824.20	25,963.22	35,700.36	30,824.20	30,824.20	47.62	47.62	47.62	-6,649.93	-6,649.93	-6,649.93	920.52	920.52	920.52	5,777.02	5,777.02	5,777.02	0.00	0.00	0.00	30,871.81
3	2018-08-03	30,824.17	26,051.66	34,994.86	30,824.17	30,824.17	-96.59	-96.59	-96.59	-6,775.47	-6,775.47	-6,775.47	906.04	906.04	906.04	5,772.84	5,772.84	5,772.84	0.00	0.00	0.00	30,727.58
4	2018-08-03	30,824.15	26,540.61	35,902.12	30,824.15	30,824.15	567.80	567.80	567.80	-6,090.15	-6,090.15	-6,090.15	889.29	889.29	889.29	5,768.66	5,768.66	5,768.66	0.00	0.00	0.00	31,391.95

Future Prediction Forecast: tail(5)

	ds	trend	yhat_lower	yhat_upper	trend_lower	trend_upper	additive_terms	additive_terms_lower	additive_terms_upper	daily	daily_lower	daily_upper	weekly	weekly_lower	weekly_upper	yearly	yearly_lower	yearly_upper	multiplicative_terms	multiplicative_terms_lower	multiplicative_terms_upper	yhat
8755	2019-08-02	30,604.14	35,590.82	46,949.20	27,292.16	33,586.28	10,391.84	10,391.84	10,391.84	4,425.20	4,425.20	4,425.20	135.17	135.17	135.17	5,831.48	5,831.48	5,831.48	0.00	0.00	0.00	40,995.98
8756	2019-08-02	30,604.12	34,210.36	45,933.98	27,290.99	33,586.67	9,517.51	9,517.51	9,517.51	3,649.72	3,649.72	3,649.72	40.51	40.51	40.51	5,827.28	5,827.28	5,827.28	0.00	0.00	0.00	40,121.62
8757	2019-08-02	30,604.09	32,466.65	43,588.31	27,289.83	33,587.06	7,805.73	7,805.73	7,805.73	2,042.67	2,042.67	2,042.67	-60.02	-60.02	-60.02	5,823.09	5,823.09	5,823.09	0.00	0.00	0.00	38,409.83
8758	2019-08-02	30,604.07	30,087.02	41,862.48	27,288.66	33,587.45	5,540.35	5,540.35	5,540.35	-112.31	-112.31	-112.31	-166.23	-166.23	-166.23	5,818.89	5,818.89	5,818.89	0.00	0.00	0.00	36,144.42
8759	2019-08-03	30,604.04	28,144.76	39,567.14	27,287.49	33,587.84	3,169.70	3,169.70	3,169.70	-2,367.12	-2,367.12	-2,367.12	-277.88	-277.88	-277.88	5,814.70	5,814.70	5,814.70	0.00	0.00	0.00	33,773.74

future_forecast.yhat.plot(c='cyan', title = 'Future Predictions')
plt.show()

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| Top | Initial Data Visualization | Visualizing Features | Prophet Model | Incoporating Holidays | Future Predictions |

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