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 26 | 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.templates.model_templates import ModelTemplateEnum
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.
30 31 32 33 34 35 36 37 38 39 40 41 | 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 0x19ed3f3d0>
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.
52 53 54 | 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!)
59 60 | 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.
66 67 68 69 70 71 72 73 74 75 76 77 | 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.
81 82 83 84 85 86 87 88 |
Specify common evaluation parameters. Set minimum input data for training.
93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 | 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.
123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 | 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=ModelTemplateEnum.SILVERKITE.name,
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: 21
Method: Ridge regression
Number of nonzero features: 21
Regularization parameter: 0.01269
Residuals:
Min 1Q Median 3Q Max
-5.631e+04 -2.219e+04 2946.0 2.172e+04 6.649e+04
Pred_col Estimate Std. Err Pr(>)_boot sig. code 95%CI
Intercept -9.460e+04 3.439e+04 0.010 * (-1.464e+05, -1.203e+04)
C(month,... 13)))_2 5660.0 1.875e+04 0.740 (-3.299e+04, 4.029e+04)
C(month,... 13)))_3 6.530e+04 1.754e+04 <2e-16 *** (3.438e+04, 1.028e+05)
C(month,... 13)))_4 1.362e+05 1.590e+04 <2e-16 *** (1.045e+05, 1.677e+05)
C(month,... 13)))_5 1.534e+05 1.657e+04 <2e-16 *** (1.215e+05, 1.872e+05)
C(month,... 13)))_6 1.675e+05 1.782e+04 0.002 ** (1.370e+05, 2.002e+05)
C(month,... 13)))_7 1.756e+05 1.671e+04 <2e-16 *** (1.417e+05, 2.069e+05)
C(month,... 13)))_8 1.758e+05 1.689e+04 <2e-16 *** (1.427e+05, 2.092e+05)
C(month,... 13)))_9 1.477e+05 1.749e+04 <2e-16 *** (1.112e+05, 1.828e+05)
C(month,...13)))_10 1.345e+05 1.645e+04 <2e-16 *** (1.019e+05, 1.675e+05)
C(month,...13)))_11 6.066e+04 1.500e+04 <2e-16 *** (3.115e+04, 8.971e+04)
C(month,...13)))_12 1.422e+04 1.748e+04 0.404 (-1.796e+04, 4.928e+04)
ct_sqrt 3.313e+05 1.175e+05 0.004 ** (3.869e+04, 4.618e+05)
ct1 3.895e+04 1.280e+05 0.782 (-1.761e+05, 2.901e+05)
cp0_2011_12_31_00 2.954e+04 8.431e+04 0.726 (-1.244e+05, 2.166e+05)
cp1_2012_01_30_00 1.218e+04 8.109e+04 0.880 (-1.390e+05, 1.885e+05)
cp2_2012_12_31_00 -7.390e+04 1.024e+05 0.472 (-2.949e+05, 1.051e+05)
cp3_2014_12_30_00 -1.254e+04 6.107e+04 0.822 (-1.265e+05, 1.166e+05)
cp4_2015_02_01_00 4.932e+04 4.751e+04 0.310 (-4.634e+04, 1.330e+05)
cp5_2015_04_29_00 -3.631e+04 9.086e+04 0.708 (-2.161e+05, 1.553e+05)
cp6_2017_08_31_00 -7.053e+04 2.199e+04 0.002 ** (-1.126e+05, -2.873e+04)
Signif. Code: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Multiple R-squared: 0.9248, Adjusted R-squared: 0.9113
F-statistic: 68.337 on 16 and 90 DF, p-value: 1.110e-16
Model AIC: 2759.1, model BIC: 2805.3
WARNING: the condition number is large, 2.44e+04. 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 17.95
split_test_MAPE (16.97, 21.68, 5.09, 23.25, 22.77)
mean_train_MAPE 30.74
split_train_MAPE (34.41, 28.6, 31.42, 29.18, 30.07)
mean_fit_time 1.5
mean_score_time 0.24
params []
train test
CORR 0.959601 0.959809
R2 0.920783 -2.06113
MSE 8.70384e+08 2.24026e+08
RMSE 29502.3 14967.5
MAE 25057.5 14721.3
MedAE 23885.3 13428.2
MAPE 31.1795 4.18228
MedAPE 9.40904 3.79933
sMAPE 10.5786 2.13708
Q80 12528.8 11777
Q95 12528.8 13985.2
Q99 12528.8 14574.1
OutsideTolerance1p 0.980769 1
OutsideTolerance2p 0.894231 1
OutsideTolerance3p 0.836538 1
OutsideTolerance4p 0.826923 0.25
OutsideTolerance5p 0.740385 0.25
Outside Tolerance (fraction) None None
R2_null_model_score None None
Prediction Band Width (%) 98.5155 33.1166
Prediction Band Coverage (fraction) 0.980769 1
Coverage: Lower Band 0.5 0
Coverage: Upper Band 0.480769 1
Coverage Diff: Actual_Coverage - Intended_Coverage 0.0307692 0.05
Fit/backtest plot:
191 192 | fig = backtest.plot()
plotly.io.show(fig)
|
Forecast plot:
196 197 | fig = forecast.plot()
plotly.io.show(fig)
|
The components plot:
201 202 | 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.
208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 | 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=ModelTemplateEnum.SILVERKITE.name,
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: 22
Method: Ridge regression
Number of nonzero features: 22
Regularization parameter: 0.0621
Residuals:
Min 1Q Median 3Q Max
-5.655e+04 -1.618e+04 -1849.0 1.957e+04 6.007e+04
Pred_col Estimate Std. Err Pr(>)_boot sig. code 95%CI
Intercept -2.605e+04 1.765e+04 0.128 (-6.082e+04, 5663.0)
C(month,... 13)))_2 1.142e+04 1.253e+04 0.336 (-1.417e+04, 3.417e+04)
C(month,... 13)))_3 6.686e+04 1.407e+04 <2e-16 *** (4.060e+04, 9.746e+04)
C(month,... 13)))_4 1.060e+05 1.553e+04 <2e-16 *** (7.367e+04, 1.327e+05)
C(month,... 13)))_5 8.563e+04 1.535e+04 <2e-16 *** (5.626e+04, 1.173e+05)
C(month,... 13)))_6 9.056e+04 1.626e+04 <2e-16 *** (5.808e+04, 1.204e+05)
C(month,... 13)))_7 9.126e+04 1.611e+04 <2e-16 *** (5.848e+04, 1.234e+05)
C(month,... 13)))_8 8.720e+04 1.615e+04 <2e-16 *** (5.631e+04, 1.183e+05)
C(month,... 13)))_9 6.215e+04 1.638e+04 <2e-16 *** (3.267e+04, 9.527e+04)
C(month,...13)))_10 6.108e+04 1.480e+04 <2e-16 *** (3.271e+04, 9.215e+04)
C(month,...13)))_11 -6119.0 1.718e+04 0.688 (-4.439e+04, 2.556e+04)
C(month,...13)))_12 -1.324e+04 1.319e+04 0.286 (-4.037e+04, 1.257e+04)
ct_sqrt 9.290e+04 3.920e+04 0.012 * (8616.0, 1.634e+05)
ct1 4.863e+04 2.159e+04 0.024 * (7906.0, 9.485e+04)
cp0_2011_12_31_00 2.021e+04 2.720e+04 0.430 (-2.641e+04, 7.852e+04)
cp1_2012_01_30_00 1.920e+04 2.499e+04 0.412 (-2.329e+04, 7.171e+04)
cp2_2012_12_31_00 -3.002e+04 3.298e+04 0.370 (-9.062e+04, 3.715e+04)
cp3_2014_12_30_00 -945.8 1.874e+04 0.966 (-3.848e+04, 3.266e+04)
cp4_2015_02_01_00 1769.0 1.357e+04 0.892 (-2.739e+04, 2.510e+04)
cp5_2015_04_29_00 -1.569e+04 3.222e+04 0.630 (-7.719e+04, 5.183e+04)
cp6_2017_08_31_00 -3.195e+04 1.898e+04 0.090 . (-6.886e+04, 7482.0)
y_lag1 2.133e+05 2.997e+04 <2e-16 *** (1.530e+05, 2.681e+05)
Signif. Code: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Multiple R-squared: 0.9451, Adjusted R-squared: 0.9355
F-statistic: 97.446 on 15 and 91 DF, p-value: 1.110e-16
Model AIC: 2724.5, model BIC: 2769.8
WARNING: the condition number is large, 5.60e+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 16.81
split_test_MAPE (14.18, 11.56, 9.9, 29.35, 19.04)
mean_train_MAPE 22.43
split_train_MAPE (23.53, 22.22, 22.94, 22.04, 21.44)
mean_fit_time 1.34
mean_score_time 1.84
params []
train test
CORR 0.970891 0.810576
R2 0.942621 0.171875
MSE 6.30447e+08 6.06056e+07
RMSE 25108.7 7784.96
MAE 20697 6872.87
MedAE 18654.1 6918.05
MAPE 20.9768 1.95055
MedAPE 8.37506 1.99794
sMAPE 8.81036 0.983418
Q80 10348.5 4526.72
Q95 10348.5 5071.85
Q99 10348.5 5217.22
OutsideTolerance1p 0.932692 0.75
OutsideTolerance2p 0.875 0.5
OutsideTolerance3p 0.788462 0.25
OutsideTolerance4p 0.75 0
OutsideTolerance5p 0.673077 0
Outside Tolerance (fraction) None None
R2_null_model_score None None
Prediction Band Width (%) 83.8443 18.4221
Prediction Band Coverage (fraction) 0.951923 1
Coverage: Lower Band 0.490385 0.25
Coverage: Upper Band 0.461538 0.75
Coverage Diff: Actual_Coverage - Intended_Coverage 0.00192308 0.05
Fit/backtest plot:
281 282 | fig = backtest.plot()
plotly.io.show(fig)
|
Forecast plot:
286 287 | fig = forecast.plot()
plotly.io.show(fig)
|
The components plot:
291 292 | fig = forecast.plot_components()
plotly.io.show(fig)
|