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enh(SES): improve implementation (#973)
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@christophertitchen
christophertitchen authored Feb 17, 2025
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8 changes: 4 additions & 4 deletions README.md
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Expand Up @@ -170,10 +170,10 @@ Uses a weighted average of all past observations where the weights decrease expo

|Model | Point Forecast | Probabilistic Forecast | Insample fitted values | Probabilistic fitted values |Exogenous features|
|:------|:-------------:|:----------------------:|:---------------------:|:----------------------------:|:----------------:|
|[SimpleExponentialSmoothing](https://nixtlaverse.nixtla.io/statsforecast/src/core/models.html#simpleexponentialsmoothing)|✅|||||
|[SimpleExponentialSmoothingOptimized](https://nixtlaverse.nixtla.io/statsforecast/src/core/models.html#simpleexponentialsmoothingoptimized)|✅|||||
|[SeasonalExponentialSmoothing](https://nixtlaverse.nixtla.io/statsforecast/src/core/models.html#seasonalexponentialsmoothing)|✅|||||
|[SeasonalExponentialSmoothingOptimized](https://nixtlaverse.nixtla.io/statsforecast/src/core/models.html#seasonalexponentialsmoothingoptimized)|✅|||||
|[SimpleExponentialSmoothing](https://nixtlaverse.nixtla.io/statsforecast/src/core/models.html#simpleexponentialsmoothing)|✅||✅|||
|[SimpleExponentialSmoothingOptimized](https://nixtlaverse.nixtla.io/statsforecast/src/core/models.html#simpleexponentialsmoothingoptimized)|✅||✅|||
|[SeasonalExponentialSmoothing](https://nixtlaverse.nixtla.io/statsforecast/src/core/models.html#seasonalexponentialsmoothing)|✅||✅|||
|[SeasonalExponentialSmoothingOptimized](https://nixtlaverse.nixtla.io/statsforecast/src/core/models.html#seasonalexponentialsmoothingoptimized)|✅||✅|||
|[Holt](https://nixtlaverse.nixtla.io/statsforecast/src/core/models.html#holt)|✅|✅|✅|✅||
|[HoltWinters](https://nixtlaverse.nixtla.io/statsforecast/src/core/models.html#holtwinters)|✅|✅|✅|✅||

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118 changes: 77 additions & 41 deletions nbs/src/core/models.ipynb
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Expand Up @@ -58,11 +58,11 @@
"#| export\n",
"import warnings\n",
"from math import trunc\n",
"from typing import Any, Dict, List, Optional, Sequence, Tuple, Union\n",
"from typing import Any, Dict, List, Optional, Tuple, Union\n",
"\n",
"import numpy as np\n",
"from numba import njit\n",
"from scipy.optimize import minimize\n",
"from scipy.optimize import minimize_scalar\n",
"from scipy.special import inv_boxcox\n",
"\n",
"from statsforecast.arima import (\n",
Expand Down Expand Up @@ -3649,37 +3649,61 @@
"source": [
"#| export\n",
"@njit(nogil=NOGIL, cache=CACHE)\n",
"def _ses_fcst_mse(x: np.ndarray, alpha: float) -> Tuple[float, float, np.ndarray]:\n",
" r\"\"\"Perform simple exponential smoothing on a series.\n",
"def _ses_sse(alpha: float, x: np.ndarray) -> float:\n",
" r\"\"\"Compute the residual sum of squares for a simple exponential smoothing fit.\n",
" \n",
" Parameters\n",
" ----------\n",
" alpha : float \n",
" Smoothing parameter.\n",
" x : numpy.array\n",
" Clean time series of shape (n, ).\n",
"\n",
" Returns\n",
" -------\n",
" sse : float\n",
" Residual sum of squares for the fit.\n",
"\n",
" This function returns the one step ahead prediction\n",
" as well as the mean squared error of the fit.\n",
" \"\"\"\n",
" smoothed = x[0]\n",
" n = x.size\n",
" mse = 0.\n",
" fitted = np.full(n, np.nan, dtype=x.dtype)\n",
" complement = 1 - alpha\n",
" forecast = x[0]\n",
" sse = 0.0\n",
" \n",
" for i in range(1, len(x)):\n",
" forecast = alpha * x[i - 1] + complement * forecast\n",
" sse += (x[i] - forecast) ** 2\n",
" \n",
" return sse\n",
"\n",
" for i in range(1, n):\n",
" smoothed = (alpha * x[i - 1] + (1 - alpha) * smoothed).item()\n",
" error = x[i] - smoothed\n",
" mse += error * error\n",
" fitted[i] = smoothed\n",
"\n",
" mse /= n\n",
" forecast = alpha * x[-1] + (1 - alpha) * smoothed\n",
" return forecast, mse, fitted\n",
"@njit(nogil=NOGIL, cache=CACHE)\n",
"def _ses_forecast(x: np.ndarray, alpha: float) -> Tuple[float, np.ndarray]:\n",
" r\"\"\"Compute the one-step ahead forecast for a simple exponential smoothing fit.\n",
"\n",
" Parameters\n",
" ----------\n",
" x : numpy.array\n",
" Clean time series of shape (n, ).\n",
" alpha : float\n",
" Smoothing parameter.\n",
"\n",
"def _ses_mse(alpha: float, x: np.ndarray) -> float:\n",
" r\"\"\"Compute the mean squared error of a simple exponential smoothing fit.\"\"\"\n",
" _, mse, _ = _ses_fcst_mse(x, alpha)\n",
" return mse\n",
" Returns\n",
" -------\n",
" tuple of (float, numpy.array)\n",
" One-step ahead forecast and in-sample fitted values.\n",
"\n",
" \"\"\"\n",
" complement = 1 - alpha\n",
" fitted = np.empty_like(x)\n",
" fitted[0] = x[0]\n",
" j = 0\n",
"\n",
"def _ses_forecast(x: np.ndarray, alpha: float) -> Tuple[float, np.ndarray]:\n",
" r\"\"\"One step ahead forecast with simple exponential smoothing.\"\"\"\n",
" forecast, _, fitted = _ses_fcst_mse(x, alpha)\n",
" for i in range(1, len(x)):\n",
" fitted[i] = alpha * x[j] + complement * fitted[j]\n",
" j += 1\n",
"\n",
" forecast = alpha * x[j] + complement * fitted[j]\n",
" fitted[0] = np.nan\n",
" return forecast, fitted\n",
"\n",
"\n",
Expand All @@ -3701,16 +3725,28 @@
"\n",
"def _optimized_ses_forecast(\n",
" x: np.ndarray,\n",
" bounds: Sequence[Tuple[float, float]] = [(0.1, 0.3)]\n",
" bounds: Tuple[float, float] = (0.1, 0.3)\n",
" ) -> Tuple[float, np.ndarray]:\n",
" r\"\"\"Searches for the optimal alpha and computes SES one step forecast.\"\"\"\n",
" alpha = minimize(\n",
" fun=_ses_mse,\n",
" x0=(0,),\n",
" args=(x,),\n",
" r\"\"\"Compute the one-step ahead forecast for an optimal simple exponential smoothing fit.\n",
" \n",
" Parameters\n",
" ----------\n",
" x : numpy.array\n",
" Clean time series of shape (n, ).\n",
" bounds : tuple of (float, float)\n",
" Lower and upper optimisation bounds for alpha.\n",
"\n",
" Returns\n",
" -------\n",
" tuple of (float, numpy.array)\n",
" One-step ahead forecast and in-sample fitted values.\n",
"\n",
" \"\"\"\n",
" alpha = minimize_scalar(\n",
" fun=_ses_sse,\n",
" bounds=bounds,\n",
" method='L-BFGS-B'\n",
" ).x[0]\n",
" args=(x,),\n",
" ).x\n",
" forecast, fitted = _ses_forecast(x, alpha)\n",
" return forecast, fitted\n",
"\n",
Expand All @@ -3737,11 +3773,11 @@
" fitted: bool, # fitted values\n",
" alpha: float, # smoothing parameter\n",
") -> Dict[str, np.ndarray]: \n",
" fcst, _, fitted_vals = _ses_fcst_mse(y, alpha)\n",
" fcst = {'mean': _repeat_val(val=fcst, h=h)}\n",
" fcst, fitted_vals = _ses_forecast(y, alpha)\n",
" out = {'mean': _repeat_val(val=fcst, h=h)}\n",
" if fitted:\n",
" fcst['fitted'] = fitted_vals\n",
" return fcst"
" out['fitted'] = fitted_vals\n",
" return out"
]
},
{
Expand Down Expand Up @@ -4057,7 +4093,7 @@
" h: int, # forecasting horizon\n",
" fitted: bool, # fitted values\n",
" ):\n",
" fcst_, fitted_vals = _optimized_ses_forecast(y, [(0.01, 0.99)])\n",
" fcst_, fitted_vals = _optimized_ses_forecast(y, (0.01, 0.99))\n",
" mean = _repeat_val(val=fcst_, h=h)\n",
" fcst = {'mean': mean}\n",
" if fitted:\n",
Expand Down Expand Up @@ -4746,7 +4782,7 @@
" fitted_vals = np.full_like(y, np.nan)\n",
" for i in range(season_length):\n",
" init_idx = (i + n % season_length)\n",
" season_vals[i], fitted_vals[init_idx::season_length] = _optimized_ses_forecast(y[init_idx::season_length], [(0.01, 0.99)])\n",
" season_vals[i], fitted_vals[init_idx::season_length] = _optimized_ses_forecast(y[init_idx::season_length], (0.01, 0.99))\n",
" out = _repeat_val_seas(season_vals=season_vals, h=h)\n",
" fcst = {'mean': out}\n",
" if fitted:\n",
Expand Down Expand Up @@ -13027,9 +13063,9 @@
],
"metadata": {
"kernelspec": {
"display_name": "python3",
"display_name": "statsforecast",
"language": "python",
"name": "python3"
"name": "statsforecast"
}
},
"nbformat": 4,
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4 changes: 1 addition & 3 deletions python/statsforecast/_modidx.py
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Expand Up @@ -720,13 +720,11 @@
'statsforecast.models._seasonal_window_average': ( 'src/core/models.html#_seasonal_window_average',
'statsforecast/models.py'),
'statsforecast.models._ses': ('src/core/models.html#_ses', 'statsforecast/models.py'),
'statsforecast.models._ses_fcst_mse': ( 'src/core/models.html#_ses_fcst_mse',
'statsforecast/models.py'),
'statsforecast.models._ses_forecast': ( 'src/core/models.html#_ses_forecast',
'statsforecast/models.py'),
'statsforecast.models._ses_mse': ('src/core/models.html#_ses_mse', 'statsforecast/models.py'),
'statsforecast.models._ses_optimized': ( 'src/core/models.html#_ses_optimized',
'statsforecast/models.py'),
'statsforecast.models._ses_sse': ('src/core/models.html#_ses_sse', 'statsforecast/models.py'),
'statsforecast.models._tsb': ('src/core/models.html#_tsb', 'statsforecast/models.py'),
'statsforecast.models._window_average': ( 'src/core/models.html#_window_average',
'statsforecast/models.py')},
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112 changes: 76 additions & 36 deletions python/statsforecast/models.py
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Expand Up @@ -12,11 +12,11 @@
# %% ../../nbs/src/core/models.ipynb 4
import warnings
from math import trunc
from typing import Any, Dict, List, Optional, Sequence, Tuple, Union
from typing import Any, Dict, List, Optional, Tuple, Union

import numpy as np
from numba import njit
from scipy.optimize import minimize
from scipy.optimize import minimize_scalar
from scipy.special import inv_boxcox

from statsforecast.arima import (
Expand Down Expand Up @@ -2130,37 +2130,61 @@ def __init__(

# %% ../../nbs/src/core/models.ipynb 129
@njit(nogil=NOGIL, cache=CACHE)
def _ses_fcst_mse(x: np.ndarray, alpha: float) -> Tuple[float, float, np.ndarray]:
r"""Perform simple exponential smoothing on a series.
def _ses_sse(alpha: float, x: np.ndarray) -> float:
r"""Compute the residual sum of squares for a simple exponential smoothing fit.
This function returns the one step ahead prediction
as well as the mean squared error of the fit.
"""
smoothed = x[0]
n = x.size
mse = 0.0
fitted = np.full(n, np.nan, dtype=x.dtype)
Parameters
----------
alpha : float
Smoothing parameter.
x : numpy.array
Clean time series of shape (n, ).
for i in range(1, n):
smoothed = (alpha * x[i - 1] + (1 - alpha) * smoothed).item()
error = x[i] - smoothed
mse += error * error
fitted[i] = smoothed
Returns
-------
sse : float
Residual sum of squares for the fit.
mse /= n
forecast = alpha * x[-1] + (1 - alpha) * smoothed
return forecast, mse, fitted
"""
complement = 1 - alpha
forecast = x[0]
sse = 0.0

for i in range(1, len(x)):
forecast = alpha * x[i - 1] + complement * forecast
sse += (x[i] - forecast) ** 2

def _ses_mse(alpha: float, x: np.ndarray) -> float:
r"""Compute the mean squared error of a simple exponential smoothing fit."""
_, mse, _ = _ses_fcst_mse(x, alpha)
return mse
return sse


@njit(nogil=NOGIL, cache=CACHE)
def _ses_forecast(x: np.ndarray, alpha: float) -> Tuple[float, np.ndarray]:
r"""One step ahead forecast with simple exponential smoothing."""
forecast, _, fitted = _ses_fcst_mse(x, alpha)
r"""Compute the one-step ahead forecast for a simple exponential smoothing fit.
Parameters
----------
x : numpy.array
Clean time series of shape (n, ).
alpha : float
Smoothing parameter.
Returns
-------
tuple of (float, numpy.array)
One-step ahead forecast and in-sample fitted values.
"""
complement = 1 - alpha
fitted = np.empty_like(x)
fitted[0] = x[0]
j = 0

for i in range(1, len(x)):
fitted[i] = alpha * x[j] + complement * fitted[j]
j += 1

forecast = alpha * x[j] + complement * fitted[j]
fitted[0] = np.nan
return forecast, fitted


Expand All @@ -2181,12 +2205,28 @@ def _probability(x: np.ndarray) -> np.ndarray:


def _optimized_ses_forecast(
x: np.ndarray, bounds: Sequence[Tuple[float, float]] = [(0.1, 0.3)]
x: np.ndarray, bounds: Tuple[float, float] = (0.1, 0.3)
) -> Tuple[float, np.ndarray]:
r"""Searches for the optimal alpha and computes SES one step forecast."""
alpha = minimize(
fun=_ses_mse, x0=(0,), args=(x,), bounds=bounds, method="L-BFGS-B"
).x[0]
r"""Compute the one-step ahead forecast for an optimal simple exponential smoothing fit.
Parameters
----------
x : numpy.array
Clean time series of shape (n, ).
bounds : tuple of (float, float)
Lower and upper optimisation bounds for alpha.
Returns
-------
tuple of (float, numpy.array)
One-step ahead forecast and in-sample fitted values.
"""
alpha = minimize_scalar(
fun=_ses_sse,
bounds=bounds,
args=(x,),
).x
forecast, fitted = _ses_forecast(x, alpha)
return forecast, fitted

Expand All @@ -2206,11 +2246,11 @@ def _ses(
fitted: bool, # fitted values
alpha: float, # smoothing parameter
) -> Dict[str, np.ndarray]:
fcst, _, fitted_vals = _ses_fcst_mse(y, alpha)
fcst = {"mean": _repeat_val(val=fcst, h=h)}
fcst, fitted_vals = _ses_forecast(y, alpha)
out = {"mean": _repeat_val(val=fcst, h=h)}
if fitted:
fcst["fitted"] = fitted_vals
return fcst
out["fitted"] = fitted_vals
return out

# %% ../../nbs/src/core/models.ipynb 131
class SimpleExponentialSmoothing(_TS):
Expand Down Expand Up @@ -2380,7 +2420,7 @@ def _ses_optimized(
h: int, # forecasting horizon
fitted: bool, # fitted values
):
fcst_, fitted_vals = _optimized_ses_forecast(y, [(0.01, 0.99)])
fcst_, fitted_vals = _optimized_ses_forecast(y, (0.01, 0.99))
mean = _repeat_val(val=fcst_, h=h)
fcst = {"mean": mean}
if fitted:
Expand Down Expand Up @@ -2759,7 +2799,7 @@ def _seasonal_ses_optimized(
for i in range(season_length):
init_idx = i + n % season_length
season_vals[i], fitted_vals[init_idx::season_length] = _optimized_ses_forecast(
y[init_idx::season_length], [(0.01, 0.99)]
y[init_idx::season_length], (0.01, 0.99)
)
out = _repeat_val_seas(season_vals=season_vals, h=h)
fcst = {"mean": out}
Expand Down

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