Note
Click here to download the full example code
Example for monthly data¶
This is a basic example for monthly data using Silverkite. Note that here we are fitting a few simple models and the goal is not to optimize the results as much as possible.
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | import warnings
from collections import defaultdict
import plotly
import pandas as pd
from greykite.framework.benchmark.data_loader_ts import DataLoaderTS
from greykite.framework.templates.autogen.forecast_config import EvaluationPeriodParam
from greykite.framework.templates.autogen.forecast_config import ForecastConfig
from greykite.framework.templates.autogen.forecast_config import MetadataParam
from greykite.framework.templates.autogen.forecast_config import ModelComponentsParam
from greykite.framework.templates.forecaster import Forecaster
from greykite.framework.utils.result_summary import summarize_grid_search_results
from greykite.framework.input.univariate_time_series import UnivariateTimeSeries
warnings.filterwarnings("ignore")
|
Loads dataset into UnivariateTimeSeries.
29 30 31 32 33 34 35 36 37 38 39 40 | dl = DataLoaderTS()
agg_func = {"count": "sum"}
df = dl.load_bikesharing(agg_freq="monthly", agg_func=agg_func)
# In this monthly data the last month data is incomplete, therefore we drop it
df.drop(df.tail(1).index,inplace=True)
df.reset_index(drop=True)
ts = UnivariateTimeSeries()
ts.load_data(
df=df,
time_col="ts",
value_col="count",
freq="MS")
|
Out:
<greykite.framework.input.univariate_time_series.UnivariateTimeSeries object at 0x1b07d4c50>
Exploratory data analysis (EDA)¶
After reading in a time series, we could first do some exploratory data analysis.
The UnivariateTimeSeries class is
used to store a timeseries and perform EDA.
A quick description of the data can be obtained as follows.
51 52 53 | print(ts.describe_time_col())
print(ts.describe_value_col())
print(df.head())
|
Out:
{'data_points': 108, 'mean_increment_secs': 2629143.925233645, 'min_timestamp': Timestamp('2010-09-01 00:00:00'), 'max_timestamp': Timestamp('2019-08-01 00:00:00')}
count 108.000000
mean 231254.101852
std 106017.804606
min 4001.000000
25% 144661.750000
50% 227332.000000
75% 327851.250000
max 404811.000000
Name: y, dtype: float64
ts count
0 2010-09-01 4001
1 2010-10-01 35949
2 2010-11-01 47391
3 2010-12-01 28253
4 2011-01-01 37499
Let’s plot the original timeseries.
(The interactive plot is generated by plotly: click to zoom!)
58 59 | fig = ts.plot()
plotly.io.show(fig)
|
Exploratory plots can be plotted to reveal the time series’s properties. Monthly overlay plot can be used to inspect the annual patterns. This plot overlays various years on top of each other.
65 66 67 68 69 70 71 72 73 74 75 76 | fig = ts.plot_quantiles_and_overlays(
groupby_time_feature="month",
show_mean=False,
show_quantiles=False,
show_overlays=True,
overlay_label_time_feature="year",
overlay_style={"line": {"width": 1}, "opacity": 0.5},
center_values=False,
xlabel="month of year",
ylabel=ts.original_value_col,
title="yearly seasonality for each year (centered)",)
plotly.io.show(fig)
|
Specify common metadata.
80 81 82 83 84 85 86 87 |
Specify common evaluation parameters. Set minimum input data for training.
92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 | cv_min_train_periods = 24
# Let CV use most recent splits for cross-validation.
cv_use_most_recent_splits = True
# Determine the maximum number of validations.
cv_max_splits = 5
evaluation_period_param = EvaluationPeriodParam(
test_horizon=forecast_horizon,
cv_horizon=forecast_horizon,
periods_between_train_test=0,
cv_min_train_periods=cv_min_train_periods,
cv_expanding_window=True,
cv_use_most_recent_splits=cv_use_most_recent_splits,
cv_periods_between_splits=None,
cv_periods_between_train_test=0,
cv_max_splits=cv_max_splits,
)
|
Fit a simple model without autoregression.
The important modeling parameters for monthly data are as follows.
These are plugged into ModelComponentsParam.
The extra_pred_cols is used to specify growth and annual seasonality
Growth is modelled with both “ct_sqrt”, “ct1” for extra flexibility as we have
longterm data and ridge regularization will avoid over-fitting the trend.
The annual seasonality is modelled categorically with “C(month)” instead of
Fourier series. This is because in monthly data, the number of data points in
year is rather small (12) as opposed to daily data where there are many points in
the year, which makes categorical representation non-feasible.
The categorical representation of monthly also is more explainable/interpretable in the model
summary.
122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 | extra_pred_cols = ["ct_sqrt", "ct1", "C(month, levels=list(range(1, 13)))"]
autoregression = None
# Specify the model parameters
model_components = ModelComponentsParam(
growth=dict(growth_term=None),
seasonality=dict(
yearly_seasonality=[False],
quarterly_seasonality=[False],
monthly_seasonality=[False],
weekly_seasonality=[False],
daily_seasonality=[False]
),
custom=dict(
fit_algorithm_dict=dict(fit_algorithm="ridge"),
extra_pred_cols=extra_pred_cols
),
regressors=dict(regressor_cols=None),
autoregression=autoregression,
uncertainty=dict(uncertainty_dict=None),
events=dict(holiday_lookup_countries=None),
)
# Run the forecast model
forecaster = Forecaster()
result = forecaster.run_forecast_config(
df=df,
config=ForecastConfig(
model_template="SILVERKITE",
coverage=0.95,
forecast_horizon=forecast_horizon,
metadata_param=meta_data_params,
evaluation_period_param=evaluation_period_param,
model_components_param=model_components
)
)
# Get the useful fields from the forecast result
model = result.model[-1]
backtest = result.backtest
forecast = result.forecast
grid_search = result.grid_search
# Check model coefficients / variables
# Get model summary with p-values
print(model.summary())
# Get cross-validation results
cv_results = summarize_grid_search_results(
grid_search=grid_search,
decimals=2,
cv_report_metrics=None,
column_order=[
"rank", "mean_test", "split_test", "mean_train", "split_train",
"mean_fit_time", "mean_score_time", "params"])
# Transposes to save space in the printed output
print(cv_results.transpose())
# Check historical evaluation metrics (on the historical training/test set).
backtest_eval = defaultdict(list)
for metric, value in backtest.train_evaluation.items():
backtest_eval[metric].append(value)
backtest_eval[metric].append(backtest.test_evaluation[metric])
metrics = pd.DataFrame(backtest_eval, index=["train", "test"]).T
print(metrics)
|
Out:
Fitting 5 folds for each of 1 candidates, totalling 5 fits
================================ Model Summary =================================
Number of observations: 108, Number of features: 14
Method: Ridge regression
Number of nonzero features: 14
Regularization parameter: 0.1748
Residuals:
Min 1Q Median 3Q Max
-7.121e+04 -2.265e+04 -322.6 2.499e+04 6.327e+04
Pred_col Estimate Std. Err Pr(>)_boot sig. code 95%CI
Intercept -1.061e+05 2.287e+04 <2e-16 *** (-1.470e+05, -5.655e+04)
C(month,... 13)))_2 -1.271e+04 1.856e+04 0.496 (-5.010e+04, 2.011e+04)
C(month,... 13)))_3 4.549e+04 1.532e+04 0.004 ** (1.089e+04, 7.071e+04)
C(month,... 13)))_4 1.148e+05 1.545e+04 <2e-16 *** (8.001e+04, 1.397e+05)
C(month,... 13)))_5 1.314e+05 1.608e+04 <2e-16 *** (9.314e+04, 1.549e+05)
C(month,... 13)))_6 1.448e+05 1.674e+04 <2e-16 *** (1.060e+05, 1.723e+05)
C(month,... 13)))_7 1.525e+05 1.722e+04 <2e-16 *** (1.154e+05, 1.821e+05)
C(month,... 13)))_8 1.523e+05 1.713e+04 <2e-16 *** (1.148e+05, 1.823e+05)
C(month,... 13)))_9 1.318e+05 1.716e+04 <2e-16 *** (9.244e+04, 1.599e+05)
C(month,...13)))_10 1.167e+05 1.676e+04 <2e-16 *** (7.905e+04, 1.440e+05)
C(month,...13)))_11 4.323e+04 1.538e+04 0.006 ** (8837.0, 6.864e+04)
C(month,...13)))_12 -3090.0 1.614e+04 0.858 (-4.027e+04, 2.172e+04)
ct_sqrt 1.748e+05 2.143e+04 <2e-16 *** (1.268e+05, 2.088e+05)
ct1 -2.117e+04 5697.0 <2e-16 *** (-3.035e+04, -7805.0)
Signif. Code: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Multiple R-squared: 0.9104, Adjusted R-squared: 0.8986
F-statistic: 72.821 on 12 and 94 DF, p-value: 1.110e-16
Model AIC: 2770.5, model BIC: 2806.7
WARNING: the condition number is large, 4.02e+03. This might indicate that there are strong multicollinearity or other numerical problems.
WARNING: the F-ratio and its p-value on regularized methods might be misleading, they are provided only for reference purposes.
0
rank_test_MAPE 1
mean_test_MAPE 19.93
split_test_MAPE (16.83, 23.32, 4.26, 24.84, 30.4)
mean_train_MAPE 28.41
split_train_MAPE (29.02, 30.0, 28.61, 28.08, 26.34)
mean_fit_time 3.51
mean_score_time 0.27
params []
train test
CORR 0.952305 0.99193
R2 0.905847 -9.01706
MSE 1.03449e+09 7.3309e+08
RMSE 32163.5 27075.6
MAE 26827.1 27035.7
MedAE 25350.2 26717.7
MAPE 24.9649 7.69857
MedAPE 9.59447 7.62733
sMAPE 10.7097 3.70635
Q80 13413.5 5407.14
Q95 13413.5 1351.78
Q99 13413.5 270.357
OutsideTolerance1p 0.980769 1
OutsideTolerance2p 0.865385 1
OutsideTolerance3p 0.836538 1
OutsideTolerance4p 0.798077 1
OutsideTolerance5p 0.778846 1
Outside Tolerance (fraction) None None
R2_null_model_score None None
Prediction Band Width (%) 107.402 36.1039
Prediction Band Coverage (fraction) 0.971154 1
Coverage: Lower Band 0.442308 1
Coverage: Upper Band 0.528846 0
Coverage Diff: Actual_Coverage - Intended_Coverage 0.0211538 0.05
Fit/backtest plot:
190 191 | fig = backtest.plot()
plotly.io.show(fig)
|
Forecast plot:
195 196 | fig = forecast.plot()
plotly.io.show(fig)
|
The components plot:
200 201 | fig = forecast.plot_components()
plotly.io.show(fig)
|
Fit a simple model with autoregression.
This is done by specifying the autoregression parameter in ModelComponentsParam.
Note that the auto-regressive structure can be customized further depending on your data.
207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 | extra_pred_cols = ["ct_sqrt", "ct1", "C(month, levels=list(range(1, 13)))"]
autoregression = {
"autoreg_dict": {
"lag_dict": {"orders": [1]},
"agg_lag_dict": None
}
}
# Specify the model parameters
model_components = ModelComponentsParam(
growth=dict(growth_term=None),
seasonality=dict(
yearly_seasonality=[False],
quarterly_seasonality=[False],
monthly_seasonality=[False],
weekly_seasonality=[False],
daily_seasonality=[False]
),
custom=dict(
fit_algorithm_dict=dict(fit_algorithm="ridge"),
extra_pred_cols=extra_pred_cols
),
regressors=dict(regressor_cols=None),
autoregression=autoregression,
uncertainty=dict(uncertainty_dict=None),
events=dict(holiday_lookup_countries=None),
)
# Run the forecast model
forecaster = Forecaster()
result = forecaster.run_forecast_config(
df=df,
config=ForecastConfig(
model_template="SILVERKITE",
coverage=0.95,
forecast_horizon=forecast_horizon,
metadata_param=meta_data_params,
evaluation_period_param=evaluation_period_param,
model_components_param=model_components
)
)
# Get the useful fields from the forecast result
model = result.model[-1]
backtest = result.backtest
forecast = result.forecast
grid_search = result.grid_search
# Check model coefficients / variables
# Get model summary with p-values
print(model.summary())
# Get cross-validation results
cv_results = summarize_grid_search_results(
grid_search=grid_search,
decimals=2,
cv_report_metrics=None,
column_order=[
"rank", "mean_test", "split_test", "mean_train", "split_train",
"mean_fit_time", "mean_score_time", "params"])
# Transposes to save space in the printed output
print(cv_results.transpose())
# Check historical evaluation metrics (on the historical training/test set).
backtest_eval = defaultdict(list)
for metric, value in backtest.train_evaluation.items():
backtest_eval[metric].append(value)
backtest_eval[metric].append(backtest.test_evaluation[metric])
metrics = pd.DataFrame(backtest_eval, index=["train", "test"]).T
print(metrics)
|
Out:
Fitting 5 folds for each of 1 candidates, totalling 5 fits
================================ Model Summary =================================
Number of observations: 108, Number of features: 15
Method: Ridge regression
Number of nonzero features: 15
Regularization parameter: 1.789
Residuals:
Min 1Q Median 3Q Max
-7.679e+04 -1.328e+04 484.7 1.489e+04 8.141e+04
Pred_col Estimate Std. Err Pr(>)_boot sig. code 95%CI
Intercept 1.126e+04 8251.0 0.164 (-4075.0, 2.896e+04)
C(month,... 13)))_2 -3806.0 7278.0 0.566 (-1.786e+04, 9454.0)
C(month,... 13)))_3 4.103e+04 9708.0 <2e-16 *** (2.173e+04, 5.846e+04)
C(month,... 13)))_4 6.078e+04 1.298e+04 <2e-16 *** (3.265e+04, 8.378e+04)
C(month,... 13)))_5 2.803e+04 7113.0 <2e-16 *** (1.404e+04, 4.028e+04)
C(month,... 13)))_6 2.831e+04 9133.0 0.002 ** (1.050e+04, 4.435e+04)
C(month,... 13)))_7 2.573e+04 6008.0 <2e-16 *** (1.418e+04, 3.659e+04)
C(month,... 13)))_8 2.047e+04 5086.0 <2e-16 *** (9764.0, 2.985e+04)
C(month,... 13)))_9 2659.0 6845.0 0.680 (-1.294e+04, 1.457e+04)
C(month,...13)))_10 6175.0 5267.0 0.224 (-5288.0, 1.533e+04)
C(month,...13)))_11 -4.795e+04 1.115e+04 <2e-16 *** (-6.957e+04, -2.654e+04)
C(month,...13)))_12 -3.795e+04 7610.0 <2e-16 *** (-5.289e+04, -2.326e+04)
ct_sqrt 1.162e+04 9479.0 0.222 (-8136.0, 2.886e+04)
ct1 1226.0 2609.0 0.604 (-4019.0, 6408.0)
y_lag1 0.7948 0.04584 <2e-16 *** (0.7042, 0.8868)
Signif. Code: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Multiple R-squared: 0.9297, Adjusted R-squared: 0.9219
F-statistic: 114.62 on 10 and 96 DF, p-value: 1.110e-16
Model AIC: 2740.7, model BIC: 2772.1
WARNING: the condition number is large, 3.26e+12. This might indicate that there are strong multicollinearity or other numerical problems.
WARNING: the F-ratio and its p-value on regularized methods might be misleading, they are provided only for reference purposes.
0
rank_test_MAPE 1
mean_test_MAPE 20.74
split_test_MAPE (24.08, 11.08, 6.87, 40.51, 21.13)
mean_train_MAPE 17.03
split_train_MAPE (17.8, 17.99, 17.19, 16.64, 15.55)
mean_fit_time 3.23
mean_score_time 1.93
params []
train test
CORR 0.96174 0.950079
R2 0.92443 -3.5984
MSE 8.30317e+08 3.3653e+08
RMSE 28815.2 18344.7
MAE 21411.4 18101.4
MedAE 15294.8 19253
MAPE 15.177 5.17313
MedAPE 7.1528 5.44632
sMAPE 6.84121 2.51932
Q80 10705.7 3620.29
Q95 10705.7 905.072
Q99 10705.7 181.014
OutsideTolerance1p 0.894231 1
OutsideTolerance2p 0.826923 1
OutsideTolerance3p 0.778846 1
OutsideTolerance4p 0.721154 0.75
OutsideTolerance5p 0.625 0.75
Outside Tolerance (fraction) None None
R2_null_model_score None None
Prediction Band Width (%) 96.2213 35.563
Prediction Band Coverage (fraction) 0.932692 1
Coverage: Lower Band 0.461538 1
Coverage: Upper Band 0.471154 0
Coverage Diff: Actual_Coverage - Intended_Coverage -0.0173077 0.05
Fit/backtest plot:
280 281 | fig = backtest.plot()
plotly.io.show(fig)
|
Forecast plot:
285 286 | fig = forecast.plot()
plotly.io.show(fig)
|
The components plot:
290 291 | fig = forecast.plot_components()
plotly.io.show(fig)
|
Fit a model with time-varying seasonality (month effect).
This is achieved by adding "ct1*C(month)" to ModelComponentsParam.
Note that this feature may or may not be useful in your use case.
We have included this for demonstration purposes only.
In this example, while the fit has improved the backtest is inferior to the previous setting.
299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 | extra_pred_cols = ["ct_sqrt", "ct1", "C(month, levels=list(range(1, 13)))",
"ct1*C(month, levels=list(range(1, 13)))"]
autoregression = {
"autoreg_dict": {
"lag_dict": {"orders": [1]},
"agg_lag_dict": None
}
}
# Specify the model parameters
model_components = ModelComponentsParam(
growth=dict(growth_term=None),
seasonality=dict(
yearly_seasonality=[False],
quarterly_seasonality=[False],
monthly_seasonality=[False],
weekly_seasonality=[False],
daily_seasonality=[False]
),
custom=dict(
fit_algorithm_dict=dict(fit_algorithm="ridge"),
extra_pred_cols=extra_pred_cols
),
regressors=dict(regressor_cols=None),
autoregression=autoregression,
uncertainty=dict(uncertainty_dict=None),
events=dict(holiday_lookup_countries=None),
)
# Run the forecast model
forecaster = Forecaster()
result = forecaster.run_forecast_config(
df=df,
config=ForecastConfig(
model_template="SILVERKITE",
coverage=0.95,
forecast_horizon=forecast_horizon,
metadata_param=meta_data_params,
evaluation_period_param=evaluation_period_param,
model_components_param=model_components
)
)
# Get the useful fields from the forecast result
model = result.model[-1]
backtest = result.backtest
forecast = result.forecast
grid_search = result.grid_search
# Check model coefficients / variables
# Get model summary with p-values
print(model.summary())
# Get cross-validation results
cv_results = summarize_grid_search_results(
grid_search=grid_search,
decimals=2,
cv_report_metrics=None,
column_order=[
"rank", "mean_test", "split_test", "mean_train", "split_train",
"mean_fit_time", "mean_score_time", "params"])
# Transposes to save space in the printed output
print(cv_results.transpose())
# Check historical evaluation metrics (on the historical training/test set).
backtest_eval = defaultdict(list)
for metric, value in backtest.train_evaluation.items():
backtest_eval[metric].append(value)
backtest_eval[metric].append(backtest.test_evaluation[metric])
metrics = pd.DataFrame(backtest_eval, index=["train", "test"]).T
print(metrics)
|
Out:
Fitting 5 folds for each of 1 candidates, totalling 5 fits
================================ Model Summary =================================
Number of observations: 108, Number of features: 26
Method: Ridge regression
Number of nonzero features: 26
Regularization parameter: 29.15
Residuals:
Min 1Q Median 3Q Max
-6.180e+04 -1.322e+04 -3030.0 1.151e+04 7.759e+04
Pred_col Estimate Std. Err Pr(>)_boot sig. code 95%CI
Intercept 2.042e+04 5108.0 <2e-16 *** (1.089e+04, 3.136e+04)
C(month,... 13)))_2 -812.5 637.9 0.190 (-2171.0, 263.9)
C(month,... 13)))_3 3127.0 1000.0 0.006 ** (1228.0, 4998.0)
C(month,... 13)))_4 3959.0 1258.0 0.002 ** (1143.0, 6190.0)
C(month,... 13)))_5 2999.0 945.6 0.002 ** (1115.0, 4774.0)
C(month,... 13)))_6 832.2 593.5 0.172 (-340.2, 2055.0)
C(month,... 13)))_7 1253.0 604.7 0.038 * (-19.94, 2270.0)
C(month,... 13)))_8 925.9 576.6 0.114 (-199.6, 2067.0)
C(month,... 13)))_9 -19.3 779.5 0.982 (-1641.0, 1420.0)
C(month,...13)))_10 -782.2 640.9 0.232 (-1925.0, 638.7)
C(month,...13)))_11 -2595.0 601.4 <2e-16 *** (-3768.0, -1386.0)
C(month,...13)))_12 -3451.0 968.8 0.002 ** (-5306.0, -1478.0)
ct_sqrt 1832.0 938.3 0.052 . (-108.7, 3610.0)
ct1 -234.7 1302.0 0.834 (-2448.0, 2551.0)
ct1:C(mo... 13)))_2 1611.0 1700.0 0.328 (-1900.0, 4798.0)
ct1:C(mo... 13)))_3 9752.0 2252.0 <2e-16 *** (5250.0, 1.445e+04)
ct1:C(mo... 13)))_4 1.313e+04 2323.0 <2e-16 *** (8620.0, 1.754e+04)
ct1:C(mo... 13)))_5 4360.0 1712.0 0.010 * (1334.0, 7937.0)
ct1:C(mo... 13)))_6 6085.0 1999.0 0.006 ** (1896.0, 9525.0)
ct1:C(mo... 13)))_7 4815.0 1196.0 0.002 ** (2685.0, 7548.0)
ct1:C(mo... 13)))_8 3663.0 921.1 <2e-16 *** (1661.0, 5497.0)
ct1:C(mo... 13)))_9 -289.7 1995.0 0.874 (-4080.0, 3232.0)
ct1:C(mo...13)))_10 1967.0 1447.0 0.148 (-1511.0, 3938.0)
ct1:C(mo...13)))_11 -1.156e+04 1506.0 <2e-16 *** (-1.397e+04, -7563.0)
ct1:C(mo...13)))_12 -6430.0 1650.0 <2e-16 *** (-9555.0, -3487.0)
y_lag1 0.8629 0.04046 <2e-16 *** (0.7897, 0.9453)
Signif. Code: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Multiple R-squared: 0.9441, Adjusted R-squared: 0.9375
F-statistic: 139.81 on 11 and 95 DF, p-value: 1.110e-16
Model AIC: 2717.0, model BIC: 2749.8
WARNING: the condition number is large, 2.34e+11. This might indicate that there are strong multicollinearity or other numerical problems.
WARNING: the F-ratio and its p-value on regularized methods might be misleading, they are provided only for reference purposes.
0
rank_test_MAPE 1
mean_test_MAPE 11.34
split_test_MAPE (6.0, 15.75, 6.39, 21.63, 6.94)
mean_train_MAPE 12.05
split_train_MAPE (16.46, 15.58, 9.15, 8.5, 10.53)
mean_fit_time 3.2
mean_score_time 1.9
params []
train test
CORR 0.982006 0.989264
R2 0.96433 -59.3175
MSE 3.9192e+08 4.41428e+09
RMSE 19797 66440.1
MAE 15499.4 62905.1
MedAE 13399.1 72193
MAPE 9.98505 17.7785
MedAPE 6.6598 20.4163
sMAPE 4.66599 8.09662
Q80 7749.68 12581
Q95 7749.68 3145.26
Q99 7749.68 629.051
OutsideTolerance1p 0.923077 1
OutsideTolerance2p 0.826923 1
OutsideTolerance3p 0.721154 1
OutsideTolerance4p 0.634615 1
OutsideTolerance5p 0.557692 1
Outside Tolerance (fraction) None None
R2_null_model_score None None
Prediction Band Width (%) 66.1071 18.5954
Prediction Band Coverage (fraction) 0.932692 0.25
Coverage: Lower Band 0.471154 0.25
Coverage: Upper Band 0.461538 0
Coverage Diff: Actual_Coverage - Intended_Coverage -0.0173077 -0.7
Fit/backtest plot:
373 374 | fig = backtest.plot()
plotly.io.show(fig)
|
Forecast plot:
378 379 | fig = forecast.plot()
plotly.io.show(fig)
|
The components plot:
383 384 | fig = forecast.plot_components()
plotly.io.show(fig)
|
Total running time of the script: ( 1 minutes 42.667 seconds)