
from sktime.datasets import load_airline
from sktime.forecasting.arima import AutoARIMA
from sktime.forecasting.model_evaluation import evaluate
from sktime.forecasting.model_selection import ExpandingWindowSplitter
from sktime.forecasting.model_selection import SlidingWindowSplitter
from sktime.utils.plotting import plot_series


# load data
y = load_airline()

# create a forecaster
forecaster = AutoARIMA(sp=12, suppress_warnings=True)

# define cross validation parameters
# step_length, growing step of training data size
# fh, forecasting horizon
#     fh represent the distance to the end of training data
#     training data, 1949.01 to 1954.12
#     [1, 3, 5, 7], represent 1955.01, 1955.03, 1955.05, 1955.07
# initial_window, initial training data windows
cv = ExpandingWindowSplitter(step_length=12, fh=[1, 3, 5, 7], initial_window=72)

# implement cross validation
df = evaluate(forecaster=forecaster, y=y, cv=cv, strategy="refit", return_data=True)

df['test_MeanAbsolutePercentageError'].mean()

0.04592431316985412

df


plot_series(df['y_train'][1], df['y_test'][1], df['y_pred'][1], labels=["y_train", "y_test", "y_pred"])

(<Figure size 1600x400 with 1 Axes>,
 <Axes: ylabel='Number of airline passengers'>)


# load data
y = load_airline()

# create a forecaster
forecaster = AutoARIMA(sp=12, suppress_warnings=True)

# define cross validation parameters
# step_length, growing step of training data size
# fh, forecasting horizon
#     fh represent the distance to the end of training data
#     training data, 1949.01 to 1954.12
#     [1, 3, 5, 7], represent 1955.01, 1955.03, 1955.05, 1955.07
# initial_window, initial training data windows
cv = SlidingWindowSplitter(step_length=12, fh=[1, 3, 5, 7], window_length=72)

# implement cross validation
df = evaluate(forecaster=forecaster, y=y, cv=cv, strategy="refit", return_data=True)

df['test_MeanAbsolutePercentageError'].mean()

0.05076923937663073

df


plot_series(df['y_train'][1], df['y_test'][1], df['y_pred'][1], labels=["y_train", "y_test", "y_pred"])

(<Figure size 1600x400 with 1 Axes>,
 <Axes: ylabel='Number of airline passengers'>)

	test_MeanAbsolutePercentageError	fit_time	pred_time	len_train_window	cutoff	y_train	y_test	y_pred
0	0.046795	2.511999	0.006742	72	1954-12	Period 1949-01 112.0 1949-02 118.0 1949-...	Period 1955-01 242.0 1955-03 267.0 1955-...	1955-01 232.146575 1955-03 267.401294 19...
1	0.046369	3.020546	0.005270	84	1955-12	Period 1949-01 112.0 1949-02 118.0 1949-...	Period 1956-01 284.0 1956-03 317.0 1956-...	1956-01 282.568762 1956-03 302.619870 19...
2	0.026692	4.549398	0.004204	96	1956-12	Period 1949-01 112.0 1949-02 118.0 1949-...	Period 1957-01 315.0 1957-03 356.0 1957-...	1957-01 314.174145 1957-03 345.253673 19...
3	0.039624	2.149422	0.005393	108	1957-12	Period 1949-01 112.0 1949-02 118.0 1949-...	Period 1958-01 340.0 1958-03 362.0 1958-...	1958-01 345.964471 1958-03 386.787992 19...
4	0.073457	2.956735	0.005959	120	1958-12	Period 1949-01 112.0 1949-02 118.0 1949-...	Period 1959-01 360.0 1959-03 406.0 1959-...	1959-01 345.739350 1959-03 372.828949 19...
5	0.042609	6.139920	0.005772	132	1959-12	Period 1949-01 112.0 1949-02 118.0 1949-...	Period 1960-01 417.0 1960-03 419.0 1960-...	1960-01 419.967172 1960-03 457.994381 19...

	test_MeanAbsolutePercentageError	fit_time	pred_time	len_train_window	cutoff	y_train	y_test	y_pred
0	0.046795	2.478890	0.005060	72	1954-12	Period 1949-01 112.0 1949-02 118.0 1949-...	Period 1955-01 242.0 1955-03 267.0 1955-...	1955-01 232.146575 1955-03 267.401294 19...
1	0.043258	2.542394	0.005163	72	1955-12	1950-01 115.0 1950-02 126.0 1950-03 1...	1956-01 284.0 1956-03 317.0 1956-05 3...	1956-01 282.583134 1956-03 303.210321 19...
2	0.029347	1.015556	0.004076	72	1956-12	Period 1951-01 145.0 1951-02 150.0 1951-...	Period 1957-01 315.0 1957-03 356.0 1957-...	1957-01 312.0 1957-03 345.0 1957-05 3...
3	0.037439	1.116795	0.004227	72	1957-12	Period 1952-01 171.0 1952-02 180.0 1952-...	Period 1958-01 340.0 1958-03 362.0 1958-...	1958-01 345.0 1958-03 386.0 1958-05 3...
4	0.106939	6.440724	0.003960	72	1958-12	Period 1953-01 196.0 1953-02 196.0 1953-...	Period 1959-01 360.0 1959-03 406.0 1959-...	1959-01 340.315698 1959-03 354.387886 19...
5	0.040837	1.720588	0.005030	72	1959-12	Period 1954-01 204.0 1954-02 188.0 1954-...	Period 1960-01 417.0 1960-03 419.0 1960-...	1960-01 421.971103 1960-03 459.472694 19...

Cross-Validation¶

ExpandingWindowSplitter¶

SlidingWindowSplitter¶

Reference¶