def test_weights_for_airline_averaging():
y = load_airline()
y_train, y_test = temporal_train_test_split(y)
forecaster = OnlineEnsembleForecaster([
("ses", ExponentialSmoothing(seasonal="multiplicative", sp=12)),
(
"holt",
ExponentialSmoothing(trend="add",
damped_trend=False,
seasonal="multiplicative",
sp=12),
),
(
"damped_trend",
ExponentialSmoothing(trend="add",
damped_trend=True,
seasonal="multiplicative",
sp=12),
),
])
forecaster.fit(y_train)
expected = np.array([1 / 3, 1 / 3, 1 / 3])
np.testing.assert_allclose(forecaster.weights, expected, rtol=1e-8)
def test_FittedParamExtractor(param_names):
forecaster = ExponentialSmoothing()
t = FittedParamExtractor(forecaster=forecaster, param_names=param_names)
Xt = t.fit_transform(X_train)
assert Xt.shape == (X_train.shape[0],
len(t._check_param_names(param_names)))
# check specific value
forecaster.fit(X_train.iloc[47, 0])
fitted_param = forecaster.get_fitted_params()[param_names]
assert Xt.iloc[47, 0] == fitted_param
def train_model_expSmooting(y, x, output: bool = True) -> ExponentialSmoothing:
if output:
logger.info("Training Exponential Smoothing model...")
timer = Timer()
model = ExponentialSmoothing(sp=24, seasonal='mul')
y = pd.Series(data=np.delete(y, 0))
x = pd.DataFrame(data=x[:-1])
model.fit(y, x)
if output:
logger.info(f'Done in {timer}')
return model
def run_sktimes(dept_id, store_id):
# create timeseries for fbprophet
ts = CreateTimeSeries(dept_id, store_id)
# sktime ensembler
forecaster = EnsembleForecaster([
('naive_ses', NaiveForecaster(sp=28, strategy="seasonal_last")),
('naive', NaiveForecaster(strategy="last")),
('theta_ses', ThetaForecaster(sp=28)), ('theta', ThetaForecaster()),
("exp_ses", ExponentialSmoothing(seasonal="additive", sp=28)),
("exp_damped",
ExponentialSmoothing(trend='additive',
damped=True,
seasonal="additive",
sp=28))
])
forecaster.fit(ts.y + 1)
y_pred = forecaster.predict(np.arange(1, 29))
return np.append(np.array([dept_id, store_id]), y_pred - 1)
def get_test_params(cls):
"""Return testing parameter settings for the estimator.
Returns
-------
params : dict or list of dict, default = {}
Parameters to create testing instances of the class
Each dict are parameters to construct an "interesting" test instance, i.e.,
`MyClass(**params)` or `MyClass(**params[i])` creates a valid test instance.
`create_test_instance` uses the first (or only) dictionary in `params`
"""
from sktime.forecasting.exp_smoothing import ExponentialSmoothing
return {"forecaster": ExponentialSmoothing()}
def test_exponential_smoothing():
"""Test bug in 1876.
https://github.com/alan-turing-institute/sktime/issues/1876#issue-1103752402.
"""
y = load_airline()
# Change index to 10 min interval
freq = "10Min"
time_range = pd.date_range(
pd.to_datetime("2019-01-01 00:00"),
pd.to_datetime("2019-01-01 23:55"),
freq=freq,
)
# Period Index does not work
y.index = time_range.to_period()
forecaster = ExponentialSmoothing(trend="add",
seasonal="multiplicative",
sp=12)
forecaster.fit(y, fh=[1, 2, 3, 4, 5, 6])
y_pred = forecaster.predict()
pd.testing.assert_index_equal(
y_pred.index, pd.period_range("2019-01-02 00:00", periods=6,
freq=freq))
def select_regressor(selection):
regressors = {
'LR': LinearRegression(),
'KNN': KNeighborsRegressor(),
'RF': RandomForestRegressor(),
'GB': GradientBoostingRegressor(),
'XGBoost': XGBRegressor(verbosity = 0),
'SVM': LinearSVR(),
'Extra Trees': ExtraTreesRegressor(),
'Naive' : NaiveForecaster(strategy="last", sp=12),
'Theta': ThetaForecaster(sp=12),
'Exp_Smoothing': ExponentialSmoothing(trend="add", seasonal="multiplicative", sp=12),
'TBATS': TBATS(sp=12, use_trend=True, use_box_cox=False)
}
return regressors[selection]
def get_test_params(cls, parameter_set="default"):
"""Return testing parameter settings for the estimator.
Parameters
----------
parameter_set : str, default="default"
Name of the set of test parameters to return, for use in tests. If no
special parameters are defined for a value, will return `"default"` set.
Returns
-------
params : dict or list of dict, default = {}
Parameters to create testing instances of the class
Each dict are parameters to construct an "interesting" test instance, i.e.,
`MyClass(**params)` or `MyClass(**params[i])` creates a valid test instance.
`create_test_instance` uses the first (or only) dictionary in `params`
"""
from sktime.forecasting.exp_smoothing import ExponentialSmoothing
return {"forecaster": ExponentialSmoothing()}
type(y) plot_series(y) y.index y_train, y_test = temporal_train_test_split(y, test_size = 24) plot_series(y_train, y_test) fh = ForecastingHorizon(y_test.index, is_relative=False) fh ets_frcstr = ExponentialSmoothing(trend='additive', seasonal='additive', sp=12) ets_frcstr.fit(y_train) y_pred = ets_frcstr.predict(fh) plot_series(y_train, y_test, y_pred, labels=['Обучающая', 'т', 'п']) ets_frcstr.get_fitted_params() ets_frcstr.get_params() smape_loss(y_test, y_pred) auto_ets_frr = AutoETS() auto_ets_frr.fit(y_pred)
plot_ys(train, test, y_pred, labels=['train', 'test', 'preds'])
plt.title(
f'strategy : {strategy} - smape_loss : {round(smape_loss(test,y_pred),4)}'
)
# ## Tuning
# ### Tune Forecaster
# In[44]:
from sktime.forecasting.model_selection import SlidingWindowSplitter, ForecastingGridSearchCV
# In[33]:
forecaster = ExponentialSmoothing()
# In[39]:
forecaster_param_grid = {
'trend': ['add', 'mul'],
'seasonal': ['add', 'mul'],
'sp': [12]
}
# In[40]:
cv = SlidingWindowSplitter(initial_window=int(len(train) * 0.5))
gscv = ForecastingGridSearchCV(forecaster,
cv=cv,
param_grid=forecaster_param_grid)
def forecast(data,
customer_id,
start='2017-01',
end='2019-04',
model_type='NaiveForecaster',
test_size_month=5,
model_storage_path=''):
"""
Main function for build forecasting model on selected customer and time interval, save the model and plotting
Parameters
----------
data: pandas DataFrame
main dataset with customer_id, product_id and Timestamp
customer_id: int
start: string
start year and month in '2020-01' format
end: string
end year and month in '2020-01' format *** this month will not be included ***
model_type:
type of model to use in forecasting
select from : ['NaiveForecaster', 'PolynomialTrendForecaster', 'ThetaForecaster', 'KNeighborsRegressor',
'ExponentialSmoothing', 'AutoETS', 'AutoARIMA', 'TBATS', 'BATS', 'EnsembleForecaster']
test_size_month:
number of month that will be excluded from end of interval to use as test dataset
model_storage_path: string
the folder that you want to store saved models
Returns
-------
sMAPE Loss: print
plot: matplotlib figure
plot train, test and predicted values
"""
y_train, y_test = temporal_train_test_split(prepare_data(data,
customer_id,
start=start,
end=end),
test_size=test_size_month)
fh = ForecastingHorizon(y_test.index, is_relative=False)
if model_type == 'NaiveForecaster':
forecaster = NaiveForecaster(strategy="last", sp=12)
elif model_type == 'PolynomialTrendForecaster':
forecaster = PolynomialTrendForecaster(degree=2)
elif model_type == 'ThetaForecaster':
forecaster = ThetaForecaster(sp=6)
elif model_type == 'KNeighborsRegressor':
regressor = KNeighborsRegressor(n_neighbors=1)
forecaster = ReducedRegressionForecaster(regressor=regressor,
window_length=12,
strategy="recursive")
elif model_type == 'ExponentialSmoothing':
forecaster = ExponentialSmoothing(trend="add",
seasonal="multiplicative",
sp=12)
elif model_type == 'AutoETS':
forecaster = AutoETS(auto=True, sp=12, n_jobs=-1)
elif model_type == 'AutoARIMA':
forecaster = AutoARIMA(sp=12, suppress_warnings=True)
elif model_type == 'TBATS':
forecaster = TBATS(sp=12, use_trend=True, use_box_cox=False)
elif model_type == 'BATS':
forecaster = BATS(sp=12, use_trend=True, use_box_cox=False)
elif model_type == 'EnsembleForecaster':
forecaster = EnsembleForecaster([
("ses", ExponentialSmoothing(seasonal="multiplicative", sp=12)),
(
"holt",
ExponentialSmoothing(trend="add",
damped_trend=False,
seasonal="multiplicative",
sp=12),
),
(
"damped",
ExponentialSmoothing(trend="add",
damped_trend=True,
seasonal="multiplicative",
sp=12),
),
])
try:
forecaster.fit(y_train)
except:
forecaster.fit(y_train + 1)
y_pred = forecaster.predict(fh)
dump(
forecaster,
f'{model_storage_path}/{customer_id}_{model_type}_{start}_{end}_{test_size_month}.model'
)
print('sMAPE Loss :', smape_loss(y_pred, y_test))
plot = plot_series(y_train,
y_test,
y_pred,
labels=["y_train", "y_test", "y_pred"])
return plot
def genforecast(data):
from sktime.forecasting.model_selection import temporal_train_test_split
import numpy as np
import math
y_train, y_test = temporal_train_test_split(data)
fh = np.arange(1, len(y_test) + 1)
testct = len(y_test)
from sktime.forecasting.naive import NaiveForecaster
forecaster = NaiveForecaster(strategy="drift")
forecaster.fit(y_train)
y_pred_naive = forecaster.predict(fh)
from sktime.performance_metrics.forecasting import smape_loss
naive_acc = round(smape_loss(y_pred_naive, y_test), 4)
#full model dev and forecast next 5 days
forecaster.fit(data)
futurewin = np.arange(1, 6) # 5 day in future prediction
fut_pred = forecaster.predict(futurewin)
min_naive = round(min(fut_pred), 2)
max_naive = round(max(fut_pred), 2)
from sktime.forecasting.trend import PolynomialTrendForecaster
forecaster = PolynomialTrendForecaster(degree=1)
forecaster.fit(y_train)
y_pred_poly = forecaster.predict(fh)
from sktime.performance_metrics.forecasting import smape_loss
poly_acc = round(smape_loss(y_pred_poly, y_test), 4)
#full model dev and forecast next 5 days
forecaster.fit(data)
futurewin = np.arange(1, 6) # 5 day in future prediction
fut_pred = forecaster.predict(futurewin)
min_poly = round(min(fut_pred), 2)
max_poly = round(max(fut_pred), 2)
from sktime.forecasting.compose import EnsembleForecaster
from sktime.forecasting.exp_smoothing import ExponentialSmoothing
sp1 = math.floor(len(y_test) / 4)
sp2 = min(sp1, 12)
spval = max(2, sp2)
forecaster = EnsembleForecaster([
("ses", ExponentialSmoothing(seasonal="multiplicative", sp=spval)),
("holt",
ExponentialSmoothing(trend="add",
damped=False,
seasonal="multiplicative",
sp=spval)),
("damped",
ExponentialSmoothing(trend="add",
damped=True,
seasonal="multiplicative",
sp=spval))
])
forecaster.fit(y_train)
y_pred_ensem = forecaster.predict(fh)
ensem_acc = round(smape_loss(y_test, y_pred_ensem), 4)
#full model dev and forecast next 5 days
forecaster.fit(data)
futurewin = np.arange(1, 6) # 5 day in future prediction
fut_pred = forecaster.predict(futurewin)
min_ensem = round(min(fut_pred), 2)
max_ensem = round(max(fut_pred), 2)
from sklearn.neighbors import KNeighborsRegressor
regressor = KNeighborsRegressor(n_neighbors=1)
from sktime.forecasting.compose import ReducedRegressionForecaster
forecaster = ReducedRegressionForecaster(regressor=regressor,
window_length=15,
strategy="recursive")
param_grid = {"window_length": [5, 10, 15]}
from sktime.forecasting.model_selection import SlidingWindowSplitter
from sktime.forecasting.model_selection import ForecastingGridSearchCV
# we fit the forecaster on the initial window, and then use temporal cross-validation to find the optimal parameter
cv = SlidingWindowSplitter(initial_window=int(len(y_train) * 0.5))
gscv = ForecastingGridSearchCV(forecaster, cv=cv, param_grid=param_grid)
gscv.fit(y_train)
y_pred_redreg = gscv.predict(fh)
redreg_acc = round(smape_loss(y_test, y_pred_redreg), 4)
#full model dev and forecast next 5 days
gscv.fit(data)
futurewin = np.arange(1, 6) # 5 day in future prediction
fut_pred = gscv.predict(futurewin)
min_redreg = round(min(fut_pred), 2)
max_redreg = round(max(fut_pred), 2)
return min_naive, max_naive, min_poly, max_poly, min_ensem, max_ensem, min_redreg, max_redreg, y_test, testct, y_pred_naive, naive_acc, y_pred_poly, poly_acc, y_pred_ensem, ensem_acc, y_pred_redreg, redreg_acc
"steps": STEPS
},
ForecastingPipeline: {
"steps": STEPS
},
EnsembleForecaster: {
"forecasters": FORECASTERS
},
StackingForecaster: {
"forecasters": FORECASTERS
},
AutoEnsembleForecaster: {
"forecasters": FORECASTERS
},
Detrender: {
"forecaster": ExponentialSmoothing()
},
ForecastingGridSearchCV: {
"forecaster": NaiveForecaster(strategy="mean"),
"cv": SingleWindowSplitter(fh=1),
"param_grid": {
"window_length": [2, 5]
},
"scoring": MeanAbsolutePercentageError(symmetric=True),
},
ForecastingRandomizedSearchCV: {
"forecaster": NaiveForecaster(strategy="mean"),
"cv": SingleWindowSplitter(fh=1),
"param_distributions": {
"window_length": [2, 5]
},
import pandas as pd
import pytest
from sktime.forecasting.compose import EnsembleForecaster
from sktime.forecasting.compose._ensemble import VALID_AGG_FUNCS
from sktime.forecasting.exp_smoothing import ExponentialSmoothing
from sktime.forecasting.naive import NaiveForecaster
from sktime.forecasting.trend import PolynomialTrendForecaster
from sktime.utils._testing.forecasting import make_forecasting_problem
@pytest.mark.parametrize(
"forecasters",
[
[("trend", PolynomialTrendForecaster()), ("naive", NaiveForecaster())],
[("trend", PolynomialTrendForecaster()), ("ses", ExponentialSmoothing())],
],
)
def test_avg_mean(forecasters):
"""Assert `mean` aggfunc returns the same values as `average` with equal weights."""
y = make_forecasting_problem()
forecaster = EnsembleForecaster(forecasters)
forecaster.fit(y, fh=[1, 2, 3])
mean_pred = forecaster.predict()
forecaster_1 = EnsembleForecaster(forecasters, aggfunc="mean", weights=[1, 1])
forecaster_1.fit(y, fh=[1, 2, 3])
avg_pred = forecaster_1.predict()
pd.testing.assert_series_equal(mean_pred, avg_pred)
[0 1 2 3 4 5 6 7 8 9] [10]
''')
st.write('''
### 4.2 Statistical forecasters
sktime基于statsmodels中的实现，具有多种统计预测算法。
例如，要将指数平滑与可加趋势成分和可乘季节性一起使用，我们可以编写以下内容。注意，由于这是每月数据，所以季节性周期（sp）或每年的周期数为12。
''')
from sktime.forecasting.exp_smoothing import ExponentialSmoothing
forecaster = ExponentialSmoothing(trend="add",
seasonal="multiplicative",
sp=12)
forecaster.fit(y_train)
y_pred = forecaster.predict(fh)
plot_ys(y_train, y_test, y_pred, labels=["y_train", "y_test", "y_pred"])
st.pyplot()
st.write("smape_loss(y_test, y_pred):", smape_loss(y_test, y_pred))
st.write('''
另一个常见模型是ARIMA模型。
在sktime中，我们连接pmdarima，这是一个用于自动选择最佳ARIMA模型的软件包。
这是因为搜索了许多可能的模型参数，因此可能需要更长的时间。
''')
from sktime.forecasting.arima import AutoARIMA
def main():
df = datasets.load_airline(
) #Univariate, monthly records from 1949 to 60 (144 records)
y_train, y_test = temporal_train_test_split(
df, test_size=36) #36 months for testing
forecaster = NaiveForecaster(
strategy='seasonal_last', sp=12
) #model strategy: last, mean, seasonal_last. sp=12months (yearly season)
forecaster.fit(y_train) #fit
fh = np.arange(1,
len(y_test) +
1) #forecast horizon: array with the same lenght of y_test
y_pred = forecaster.predict(fh) #pred
forecaster2 = AutoARIMA(sp=12, suppress_warnings=True, trace=1)
forecaster2.fit(y_train)
y_pred2 = forecaster2.predict(fh)
forecaster3 = ExponentialSmoothing(trend='add',
damped='True',
seasonal='multiplicative',
sp=12)
forecaster3.fit(y_train)
y_pred3 = forecaster3.predict(fh)
forecaster4 = ThetaForecaster(sp=12)
forecaster4.fit(y_train)
y_pred4 = forecaster4.predict(fh)
forecaster5 = EnsembleForecaster([
('NaiveForecaster', NaiveForecaster(strategy='seasonal_last', sp=12)),
('AutoARIMA', AutoARIMA(sp=12, suppress_warnings=True)),
('Exp Smoothing',
ExponentialSmoothing(trend='add',
damped='True',
seasonal='multiplicative',
sp=12)), ('Theta', ThetaForecaster(sp=12))
])
forecaster5.fit(y_train)
y_pred5 = forecaster5.predict(fh)
plot_ys(y_train,
y_test,
y_pred,
y_pred2,
y_pred3,
y_pred4,
y_pred5,
labels=[
'Train', 'Test', 'Naive Forecaster', 'AutoARIMA',
'Exp Smoothing', 'Theta', 'Ensemble'
])
plt.xlabel('Months')
plt.ylabel('Number of flights')
plt.title(
'Time series of the number of international flights in function of time'
)
plt.show()
print('SMAPE Error for NaiveForecaster is:',
100 * round(smape_loss(y_test, y_pred), 3), '%')
print('SMAPE Error for AutoARIMA is:',
100 * round(smape_loss(y_test, y_pred2), 3), '%')
print('SMAPE Error for Exp Smoothing is:',
100 * round(smape_loss(y_test, y_pred3), 3), '%')
print('SMAPE Error for Theta is:',
100 * round(smape_loss(y_test, y_pred4), 3), '%')
print('SMAPE Error for Ensemble is:',
100 * round(smape_loss(y_test, y_pred5), 3), '%')
from scipy.stats import gmean
from sktime.forecasting.compose import EnsembleForecaster
from sktime.forecasting.exp_smoothing import ExponentialSmoothing
from sktime.forecasting.naive import NaiveForecaster
from sktime.forecasting.trend import PolynomialTrendForecaster
from sktime.utils._testing.forecasting import make_forecasting_problem
@pytest.mark.parametrize(
"forecasters",
[
[("trend", PolynomialTrendForecaster()), ("naive", NaiveForecaster())],
[("trend", PolynomialTrendForecaster()),
("ses", ExponentialSmoothing())],
],
)
def test_avg_mean(forecasters):
"""Assert `mean` aggfunc returns the same values as `average` with equal weights."""
y = make_forecasting_problem()
forecaster = EnsembleForecaster(forecasters)
forecaster.fit(y, fh=[1, 2, 3])
mean_pred = forecaster.predict()
forecaster_1 = EnsembleForecaster(forecasters,
aggfunc="mean",
weights=[1, 1])
forecaster_1.fit(y, fh=[1, 2, 3])
avg_pred = forecaster_1.predict()
import pandas as pd
import pytest
from sktime.forecasting.compose import ColumnEnsembleForecaster
from sktime.forecasting.exp_smoothing import ExponentialSmoothing
from sktime.forecasting.naive import NaiveForecaster
from sktime.forecasting.trend import PolynomialTrendForecaster
@pytest.mark.parametrize(
"forecasters",
[
[
("trend", PolynomialTrendForecaster(), 0),
("naive", NaiveForecaster(), 1),
("ses", ExponentialSmoothing(), 2),
]
],
)
@pytest.mark.parametrize(
"fh", [(np.arange(1, 11)), (np.arange(1, 33)), (np.arange(1, 3))]
)
def test_column_ensemble_shape(forecasters, fh):
"""Check the shape of the returned prediction."""
y = pd.DataFrame(np.random.randint(0, 100, size=(100, 3)), columns=list("ABC"))
forecaster = ColumnEnsembleForecaster(forecasters)
forecaster.fit(y, fh=fh)
actual = forecaster.predict()
assert actual.shape == (len(fh), y.shape[1])
def test_set_params():
params = {"trend": "additive"}
f = ExponentialSmoothing(**params)
f.fit(y_train, fh=1)
expected = f.predict()
f = ExponentialSmoothing()
f.set_params(**params)
f.fit(y_train, fh=1)
y_pred = f.predict()
assert_array_equal(y_pred, expected)
from sktime.forecasting.theta import ThetaForecaster
from sktime.forecasting.trend import PolynomialTrendForecaster
from sktime.transformers.single_series.boxcox import BoxCoxTransformer
from sktime.transformers.single_series.detrend import ConditionalDeseasonalizer
from sktime.transformers.single_series.detrend import Detrender
from xgboost import XGBRegressor
from sktime.performance_metrics.forecasting import mase_loss
from sktime.performance_metrics.forecasting import smape_loss
from sktime.utils.validation.forecasting import check_sp
from sktime.utils.validation.forecasting import check_y
from statsmodels.tsa.stattools import acf
SEASONAL_MODEL = "multiplicative"
ses = ExponentialSmoothing()
holt = ExponentialSmoothing(trend="add", damped=False)
damped = ExponentialSmoothing(trend="add", damped=True)
def M4_owa_loss(mase, smape, naive2_mase, naive2_smape):
"""overall weighted average of sMAPE and MASE loss used in M4 competition
References
----------
..[1] https://github.com/Mcompetitions/M4-methods/blob/master
/Benchmarks%20and%20Evaluation.R
"""
return ((np.nanmean(smape) / np.mean(naive2_smape)) +
(np.nanmean(mase) / np.mean(naive2_mase))) / 2
SeriesToSeriesRowTransformer(SERIES_TO_SERIES_TRANSFORMER,
check_transformer=False),
),
(
"transformer2",
SeriesToSeriesRowTransformer(SERIES_TO_SERIES_TRANSFORMER,
check_transformer=False),
),
]
REGRESSOR = LinearRegression()
TIME_SERIES_CLASSIFIER = TimeSeriesForest(n_estimators=3)
TIME_SERIES_CLASSIFIERS = [
("tsf1", TIME_SERIES_CLASSIFIER),
("tsf2", TIME_SERIES_CLASSIFIER),
]
FORECASTER = ExponentialSmoothing()
FORECASTERS = [("ses1", FORECASTER), ("ses2", FORECASTER)]
STEPS = [
("transformer", Detrender(ThetaForecaster())),
("forecaster", NaiveForecaster()),
]
ESTIMATOR_TEST_PARAMS = {
OnlineEnsembleForecaster: {
"forecasters": FORECASTERS
},
FeatureUnion: {
"transformer_list": TRANSFORMERS
},
DirectRegressionForecaster: {
"regressor": REGRESSOR
},
if uploaded_file is not None:
df, df2 = load_data(uploaded_file)
# prepare models
models = []
models.append(('LR', LinearRegression()))
models.append(('KNN', KNeighborsRegressor()))
models.append(('RF', RandomForestRegressor()))
models.append(('GB', GradientBoostingRegressor()))
models.append(('XGBoost', XGBRegressor(verbosity = 0)))
models.append(('SVM', LinearSVR()))
models.append(('Extra Trees', ExtraTreesRegressor()))
models.append(('Naive', NaiveForecaster(strategy="last", sp=12)))
models.append(('Theta', ThetaForecaster(sp=12)))
models.append(('Exp_Smoothing', ExponentialSmoothing(trend="add", seasonal="additive", sp=12)))
models.append(('TBATS', TBATS(sp=12, use_trend=True, use_box_cox=False)))
forecast_horizon = st.sidebar.slider(label = 'Forecast Length (months)',min_value = 3, max_value = 36, value = 12)
window_length = st.sidebar.slider(label = 'Sliding Window Length ',min_value = 1, value = 12)
# evaluate each model in turn
results1 = []
names = []
dn_forecast = []
dn_test =[]
for name, model in models:
if name == 'LR' or name == 'KNN' or name == 'RF' or name == 'GB' or name == 'XGBoost' or name == 'SVM' or name == 'Extra Trees':
forecaster = ReducedRegressionForecaster(regressor=model, window_length=window_length,strategy='recursive')
else:
