Air Passenger Benchmark¶

from warnings import simplefilter
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd

import scipy.signal.signaltools


def _centered(arr, newsize):
    # Return the center newsize portion of the array.
    newsize = np.asarray(newsize)
    currsize = np.array(arr.shape)
    startind = (currsize - newsize) // 2
    endind = startind + newsize
    myslice = [slice(startind[k], endind[k]) for k in range(len(endind))]
    return arr[tuple(myslice)]


scipy.signal.signaltools._centered = _centered

from sysidentpy.model_structure_selection import FROLS
from sysidentpy.model_structure_selection import AOLS
from sysidentpy.model_structure_selection import MetaMSS
from sysidentpy.basis_function import Polynomial
from sysidentpy.utils.plotting import plot_results
from torch import nn

# from sysidentpy.metrics import mean_squared_error
from sysidentpy.neural_network import NARXNN

from sktime.datasets import load_airline
from sktime.forecasting.ets import AutoETS
from sktime.forecasting.arima import ARIMA, AutoARIMA
from sktime.forecasting.base import ForecastingHorizon
from sktime.forecasting.exp_smoothing import ExponentialSmoothing
from sktime.forecasting.fbprophet import Prophet
from sktime.forecasting.tbats import TBATS
from sktime.forecasting.bats import BATS

# from sktime.forecasting.model_evaluation import evaluate
from sktime.forecasting.model_selection import temporal_train_test_split
from sktime.performance_metrics.forecasting import mean_squared_error
from sktime.utils.plotting import plot_series
from neuralprophet import NeuralProphet
from neuralprophet import set_random_seed

simplefilter("ignore", FutureWarning)
np.seterr(all="ignore")

%matplotlib inline

loss = mean_squared_error

c:\Users\wilso\miniconda3\envs\neural_prophet\lib\site-packages\sktime\datatypes\_series\_check.py:43: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  VALID_INDEX_TYPES = (pd.Int64Index, pd.RangeIndex, pd.PeriodIndex, pd.DatetimeIndex)
c:\Users\wilso\miniconda3\envs\neural_prophet\lib\site-packages\sktime\datatypes\_panel\_check.py:45: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  VALID_INDEX_TYPES = (pd.Int64Index, pd.RangeIndex, pd.PeriodIndex, pd.DatetimeIndex)
c:\Users\wilso\miniconda3\envs\neural_prophet\lib\site-packages\sktime\datatypes\_panel\_check.py:46: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  VALID_MULTIINDEX_TYPES = (pd.Int64Index, pd.RangeIndex)
c:\Users\wilso\miniconda3\envs\neural_prophet\lib\site-packages\sktime\utils\validation\series.py:18: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  VALID_INDEX_TYPES = (pd.Int64Index, pd.RangeIndex, pd.PeriodIndex, pd.DatetimeIndex)
c:\Users\wilso\miniconda3\envs\neural_prophet\lib\site-packages\sktime\forecasting\base\_fh.py:18: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  RELATIVE_TYPES = (pd.Int64Index, pd.RangeIndex)
c:\Users\wilso\miniconda3\envs\neural_prophet\lib\site-packages\sktime\forecasting\base\_fh.py:19: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  ABSOLUTE_TYPES = (pd.Int64Index, pd.RangeIndex, pd.DatetimeIndex, pd.PeriodIndex)
c:\Users\wilso\miniconda3\envs\neural_prophet\lib\site-packages\statsmodels\tsa\base\tsa_model.py:7: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import (to_datetime, Int64Index, DatetimeIndex, Period,
c:\Users\wilso\miniconda3\envs\neural_prophet\lib\site-packages\statsmodels\tsa\base\tsa_model.py:7: FutureWarning: pandas.Float64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import (to_datetime, Int64Index, DatetimeIndex, Period,

y = load_airline()
y_train, y_test = temporal_train_test_split(y, test_size=23)  # 23 samples for testing
plot_series(y_train, y_test, labels=["y_train", "y_test"])
fh = ForecastingHorizon(y_test.index, is_relative=False)
print(y_train.shape[0], y_test.shape[0])

121 23

y = load_airline()
y_train, y_test = temporal_train_test_split(y, test_size=23)
y_train = y_train.values.reshape(-1, 1)
y_test = y_test.values.reshape(-1, 1)

basis_function = Polynomial(degree=1)
sysidentpy = FROLS(
    order_selection=True,
    ylag=13,  # the lags for all models will be 13
    basis_function=basis_function,
    model_type="NAR",
)
sysidentpy.fit(y=y_train)
y_test = np.concatenate([y_train[-sysidentpy.max_lag :], y_test])

yhat = sysidentpy.predict(y=y_test, forecast_horizon=23)
frols_loss = loss(
    pd.Series(y_test.flatten()[sysidentpy.max_lag :]),
    pd.Series(yhat.flatten()[sysidentpy.max_lag :]),
)
print(frols_loss)

plot_results(y=y_test[sysidentpy.max_lag :], yhat=yhat[sysidentpy.max_lag :])

C:\Users\wilso\Desktop\projects\GitHub\sysidentpy\sysidentpy\model_structure_selection\forward_regression_orthogonal_least_squares.py:619: UserWarning:

n_info_values is greater than the maximum number of all regressors space considering the chosen y_lag, u_lag, and non_degree. We set as 14



805.9521186338106

y = load_airline()
y_train, y_test = temporal_train_test_split(y, test_size=23)
y_train = y_train.values.reshape(-1, 1)
y_test = y_test.values.reshape(-1, 1)

df_train, df_test = temporal_train_test_split(y, test_size=23)
df_train = df_train.reset_index()
df_train.columns = ["ds", "y"]
df_train["ds"] = pd.to_datetime(df_train["ds"].astype(str))
df_test = df_test.reset_index()
df_test.columns = ["ds", "y"]
df_test["ds"] = pd.to_datetime(df_test["ds"].astype(str))

sysidentpy_AOLS = AOLS(
    ylag=13, k=2, L=1, model_type="NAR", basis_function=basis_function
)
sysidentpy_AOLS.fit(y=y_train)
y_test = np.concatenate([y_train[-sysidentpy_AOLS.max_lag :], y_test])

yhat = sysidentpy_AOLS.predict(y=y_test, steps_ahead=None, forecast_horizon=23)
aols_loss = loss(
    pd.Series(y_test.flatten()[sysidentpy_AOLS.max_lag :]),
    pd.Series(yhat.flatten()[sysidentpy_AOLS.max_lag :]),
)
print(aols_loss)

plot_results(y=y_test[sysidentpy_AOLS.max_lag :], yhat=yhat[sysidentpy_AOLS.max_lag :])

476.64996316992523

set_random_seed(42)

y = load_airline()
y_train, y_test = temporal_train_test_split(y, test_size=23)
y_train = y_train.values.reshape(-1, 1)
y_test = y_test.values.reshape(-1, 1)

sysidentpy_metamss = MetaMSS(
    basis_function=basis_function, ylag=13, model_type="NAR", test_size=0.17
)
sysidentpy_metamss.fit(y=y_train)

y_test = np.concatenate([y_train[-sysidentpy_metamss.max_lag :], y_test])

yhat = sysidentpy_metamss.predict(y=y_test, steps_ahead=None, forecast_horizon=23)
metamss_loss = loss(
    pd.Series(y_test.flatten()[sysidentpy_metamss.max_lag :]),
    pd.Series(yhat.flatten()[sysidentpy_metamss.max_lag :]),
)
print(metamss_loss)

plot_results(
    y=y_test[sysidentpy_metamss.max_lag :], yhat=yhat[sysidentpy_metamss.max_lag :]
)

450.992127624293

import torch

torch.manual_seed(42)

y = load_airline()
y_train, y_test = temporal_train_test_split(y, test_size=36)
y_train = y_train.values.reshape(-1, 1)
y_test = y_test.values.reshape(-1, 1)
x_train = np.zeros_like(y_train)
x_test = np.zeros_like(y_test)


class NARX(nn.Module):
    def __init__(self):
        super().__init__()
        self.lin = nn.Linear(13, 20)
        self.lin2 = nn.Linear(20, 20)
        self.lin3 = nn.Linear(20, 20)
        self.lin4 = nn.Linear(20, 1)
        self.relu = nn.ReLU()

    def forward(self, xb):
        z = self.lin(xb)
        z = self.relu(z)
        z = self.lin2(z)
        z = self.relu(z)
        z = self.lin3(z)
        z = self.relu(z)
        z = self.lin4(z)
        return z


narx_net = NARXNN(
    net=NARX(),
    ylag=13,
    model_type="NAR",
    basis_function=Polynomial(degree=1),
    epochs=900,
    verbose=False,
    learning_rate=2.5e-02,
    optim_params={},  # optional parameters of the optimizer
)

narx_net.fit(y=y_train)
yhat = narx_net.predict(y=y_test, forecast_horizon=23)
narxnet_loss = loss(
    pd.Series(y_test.flatten()[narx_net.max_lag :]),
    pd.Series(yhat.flatten()[narx_net.max_lag :]),
)
print(narxnet_loss)
plot_results(y=y_test[narx_net.max_lag :], yhat=yhat[narx_net.max_lag :])

316.54086775668776

y = load_airline()
y_train, y_test = temporal_train_test_split(y, test_size=23)  # 23 samples for testing
plot_series(y_train, y_test, labels=["y_train", "y_test"])
fh = ForecastingHorizon(y_test.index, is_relative=False)
print(y_train.shape[0], y_test.shape[0])

121 23

es = ExponentialSmoothing(trend="add", seasonal="multiplicative", sp=12)
y = load_airline()
y_train, y_test = temporal_train_test_split(y, test_size=23)
es.fit(y_train)
y_pred_es = es.predict(fh)

plot_series(y_test, y_pred_es, labels=["y_test", "y_pred"])
es_loss = loss(y_test, y_pred_es)
es_loss

910.462659260655

y = load_airline()

y_train, y_test = temporal_train_test_split(y, test_size=23)
ets = AutoETS(auto=True, sp=12, n_jobs=-1)
ets.fit(y_train)
y_pred_ets = ets.predict(fh)

plot_series(y_test, y_pred_ets, labels=["y_test", "y_pred"])
ets_loss = loss(y_test, y_pred_ets)
ets_loss

1739.117296439066

auto_arima = AutoARIMA(sp=12, suppress_warnings=True)
y = load_airline()

y_train, y_test = temporal_train_test_split(y, test_size=23)
auto_arima.fit(y_train)
y_pred_auto_arima = auto_arima.predict(fh)

plot_series(y_test, y_pred_auto_arima, labels=["y_test", "y_pred"])
autoarima_loss = loss(y_test, y_pred_auto_arima)
autoarima_loss

1714.4753226965322

y = load_airline()

y_train, y_test = temporal_train_test_split(y, test_size=23)
manual_arima = ARIMA(
    order=(13, 1, 0), suppress_warnings=True
)  # seasonal_order=(0, 1, 0, 12)
manual_arima.fit(y_train)
y_pred_manual_arima = manual_arima.predict(fh)
plot_series(y_test, y_pred_manual_arima, labels=["y_test", "y_pred"])
manualarima_loss = loss(y_test, y_pred_manual_arima)
manualarima_loss

2085.425167938668

y = load_airline()

y_train, y_test = temporal_train_test_split(y, test_size=23)
bats = BATS(sp=12, use_trend=True, use_box_cox=False)
bats.fit(y_train)
y_pred_bats = bats.predict(fh)

plot_series(y_test, y_pred_bats, labels=["y_test", "y_pred"])
bats_loss = loss(y_test, y_pred_bats)
bats_loss

7286.6484525676415

y = load_airline()

y_train, y_test = temporal_train_test_split(y, test_size=23)
tbats = TBATS(sp=12, use_trend=True, use_box_cox=False)
tbats.fit(y_train)
y_pred_tbats = tbats.predict(fh)
plot_series(y_test, y_pred_tbats, labels=["y_test", "y_pred"])
tbats_loss = loss(y_test, y_pred_tbats)
tbats_loss

7448.434672875093

set_random_seed(42)

y = load_airline()

y_train, y_test = temporal_train_test_split(y, test_size=23)
z = y.copy()
z = z.to_timestamp(freq="M")
z_train, z_test = temporal_train_test_split(z, test_size=23)


prophet = Prophet(
    seasonality_mode="multiplicative",
    n_changepoints=int(len(y_train) / 12),
    add_country_holidays={"country_name": "Germany"},
    yearly_seasonality=True,
    weekly_seasonality=False,
    daily_seasonality=False,
)
prophet.fit(z_train)
y_pred_prophet = prophet.predict(fh.to_relative(cutoff=y_train.index[-1]))

y_pred_prophet.index = y_test.index
plot_series(y_test, y_pred_prophet, labels=["y_test", "y_pred"])
prophet_loss = loss(y_test, y_pred_prophet)
prophet_loss

1186.0045566050442

set_random_seed(42)

df = pd.read_csv(r".\datasets\air_passengers.csv")
m = NeuralProphet(seasonality_mode="multiplicative")
df_train = df.iloc[:-23, :].copy()
df_test = df.iloc[-23:, :].copy()

m = NeuralProphet(seasonality_mode="multiplicative")

metrics = m.fit(df_train, freq="MS")

future = m.make_future_dataframe(
    df_train, periods=23, n_historic_predictions=len(df_train)
)

forecast = m.predict(future)
plt.plot(forecast["yhat1"].values[-23:])
plt.plot(df_test["y"].values)
neuralprophet_loss = loss(forecast["yhat1"].values[-23:], df_test["y"].values)
neuralprophet_loss

WARNING: nprophet - fit: Parts of code may break if using other than daily data.


11-21 20:57:55 - WARNING - Parts of code may break if using other than daily data.


INFO: nprophet.utils - set_auto_seasonalities: Disabling weekly seasonality. Run NeuralProphet with weekly_seasonality=True to override this.


11-21 20:57:55 - INFO - Disabling weekly seasonality. Run NeuralProphet with weekly_seasonality=True to override this.


INFO: nprophet.utils - set_auto_seasonalities: Disabling daily seasonality. Run NeuralProphet with daily_seasonality=True to override this.


11-21 20:57:55 - INFO - Disabling daily seasonality. Run NeuralProphet with daily_seasonality=True to override this.


INFO: nprophet.config - set_auto_batch_epoch: Auto-set batch_size to 8


11-21 20:57:55 - INFO - Auto-set batch_size to 8


INFO: nprophet.config - set_auto_batch_epoch: Auto-set epochs to 264


11-21 20:57:55 - INFO - Auto-set epochs to 264


 83%|████████▎ | 83/100 [00:00<00:00, 1034.46it/s]
INFO: nprophet - _lr_range_test: learning rate range test found optimal lr: 1.87E-01


11-21 20:57:55 - INFO - learning rate range test found optimal lr: 1.87E-01


Epoch[264/264]: 100%|██████████| 264/264 [00:03<00:00, 66.42it/s, SmoothL1Loss=0.000325, MAE=6.38, RegLoss=0]





501.24794023767436

results = {
    "Exponential Smoothing": es_loss,
    "ETS": ets_loss,
    "AutoArima": autoarima_loss,
    "Manual Arima": manualarima_loss,
    "BATS": bats_loss,
    "TBATS": tbats_loss,
    "Prophet": prophet_loss,
    "SysIdentPy (Polynomial Model)": frols_loss,
    "SysIdentPy (Neural Model)": narxnet_loss,
    "SysIdentPy (AOLS)": aols_loss,
    "SysIdentPy (MetaMSS)": metamss_loss,
    "NeuralProphet": neuralprophet_loss,
}

sorted(results.items(), key=lambda result: result[1])

[('SysIdentPy (Neural Model)', 316.54086775668776),
 ('SysIdentPy (MetaMSS)', 450.992127624293),
 ('SysIdentPy (AOLS)', 476.64996316992523),
 ('NeuralProphet', 501.24794023767436),
 ('SysIdentPy (Polynomial Model)', 805.9521186338106),
 ('Exponential Smoothing', 910.462659260655),
 ('Prophet', 1186.0045566050442),
 ('AutoArima', 1714.4753226965322),
 ('ETS', 1739.117296439066),
 ('Manual Arima', 2085.425167938668),
 ('BATS', 7286.6484525676415),
 ('TBATS', 7448.434672875093)]