Time Series Prediction Model Training (Prophet, NeuralProphet, TimesFM)

Training Time Series Prediction Models (Prophet, NeuralProphet, TimesFM)

Prophet, NeuralProphet and TimesFM — three generations of time series forecasting tools with different tradeoffs between simplicity, flexibility and accuracy. Correct choice depends on data, horizon and interpretability requirements.

Prophet: Decomposition Model

Meta Prophet (2017) — additive model:

y(t) = trend(t) + seasonality(t) + holidays(t) + ε(t)

Trend: piecewise-linear or logistic growth. Changepoints — automatic trend break detection via L1 regularization.

Seasonality: Fourier Series:

• Annual: N=10 (default)
• Weekly: N=3
• Custom: any period

Training and Tuning:

from prophet import Prophet
import pandas as pd

m = Prophet(
    changepoint_prior_scale=0.05,   # trend flexibility
    seasonality_prior_scale=10.0,   # seasonality flexibility
    holidays_prior_scale=10.0,
    seasonality_mode='multiplicative'  # for growing data
)
m.add_country_holidays(country_name='US')
m.add_seasonality(name='monthly', period=30.5, fourier_order=5)
m.fit(df)  # df with columns ds, y

Tuning Parameters:

• changepoint_prior_scale: 0.001-0.5, controls trend overfitting
• seasonality_mode: 'additive' for stationary, 'multiplicative' for growing series
• fourier_order: higher = more flexible seasonality = overfit risk

Prophet Cross-Validation:

from prophet.diagnostics import cross_validation, performance_metrics
df_cv = cross_validation(m, initial='730 days', period='180 days', horizon='365 days')
df_p = performance_metrics(df_cv)

NeuralProphet

NeuralProphet (2021) = Prophet + neural network components:

• Autoregressive component (AR-Net): captures nonlinear lag dependencies
• Lagged regressors: nonlinear impact of external factors
• PyTorch training, much faster than MCMC-Prophet

from neuralprophet import NeuralProphet

m = NeuralProphet(
    n_forecasts=7,        # forecast horizon
    n_lags=14,            # AR lags
    seasonality_mode='auto',
    learning_rate=0.01
)
m = m.add_country_holidays('US')
metrics = m.fit(df, freq='D', validation_df=df_val)

When NeuralProphet Beats Prophet:

• Nonlinear lag dependencies exist
• Need multiple-step ahead forecasts with specific steps
• Lagged external regressors available (delayed weather, competitor sales)

TimesFM: Foundation Model from Google

TimesFM (2024) — pretrained foundation model for zero-shot forecasting:

import timesfm

tfm = timesfm.TimesFm(
    context_len=512,
    horizon_len=128,
    input_patch_len=32,
    output_patch_len=128,
    num_layers=20,
    model_dims=1280,
    backend='gpu'
)
tfm.load_from_checkpoint(repo_id="google/timesfm-1.0-200m")

# Zero-shot inference
forecast_input = [np.array(historical_data)]
frequency_input = [0]  # 0=high freq, 1=low freq
point_forecast, experimental_quantile_forecast = tfm.forecast(
    forecast_input, freq=frequency_input
)

TimesFM Advantages:

• Zero-shot: requires no training on your data
• Fast start: first forecast in minutes
• Strong results on most business tasks out of the box

Limitations:

• Doesn't account for known future covariates (holidays, promos) without fine-tuning
• Limited interpretability
• Requires significant context (> 500 points optimal)

Comparative Selection

Training and Validation Practice

Training Pipeline (Prophet Example):

1. Data prep: resample to target frequency, handle missing (interpolation / forward fill)
2. Analysis: ACF/PACF, decompose, holiday analysis
3. Baseline: Seasonal Naive (forecast = value from year ago)
4. Prophet fit with default params, cross-validation
5. Hyperparameter search: Optuna / grid search on 4-6 params
6. Ensemble with competitor (ETS or NeuralProphet)
7. Productionization: Airflow DAG, MLflow tracking, API endpoint

Comparison Metrics: SMAPE, MASE (Mean Absolute Scaled Error — normalized by Seasonal Naive), Winkler Score for interval forecasts.

Timeline: tuning and training Prophet/NeuralProphet for single series with cross-validation — 1-2 weeks. Production pipeline with monitoring and auto-retraining — 4-6 weeks.