Principle:Sktime Pytorch forecasting Synthetic Data Generation

Knowledge Sources	pytorch-forecasting PyTorch Forecasting Docs
Domains	Time_Series, Data_Engineering, Experimentation
Last Updated	2026-02-08 07:00 GMT

Overview

Technique for generating synthetic autoregressive time series data with controllable trend, seasonality, and noise for model prototyping and testing.

Description

Synthetic Data Generation produces artificial time series that mimic real-world patterns (trend, seasonality, noise) without requiring access to proprietary datasets. This is essential for rapid prototyping, unit testing, benchmarking, and educational demonstrations. The generated series follow a parametric model combining linear and quadratic trends with sinusoidal seasonality and Gaussian noise. By controlling parameters like number of series, timesteps, trend strength, and seasonality frequency, users can create datasets that stress-test specific model capabilities such as long-range dependency learning or seasonal pattern extraction.

Usage

Use this principle when you need reproducible time series data for model development, testing, or demonstration. Particularly useful for univariate models like N-BEATS and DeepAR where simple synthetic patterns allow isolating model behavior. Not suitable for evaluating model performance on real-world forecasting tasks.

Theoretical Basis

The data generation follows a parametric time series model:

$y_{s,t}={\ell }_s\cdot [(a_{s}t+b_s{t}^2)\cdot \tau +c_s\sin \left(\frac{2\pi ft}{T}\right)]\cdot (1+\sigma {ϵ}_{s,t})$

Where:

• $s$ indexes the series, $t$ indexes time
• $a_s,b_s$ are per-series linear and quadratic trend coefficients (drawn from ${𝒩}(0,1)$)
• $\tau$ is the trend multiplier
• $c_s$ is the per-series seasonality amplitude
• $f$ is the seasonality frequency, $T$ is total timesteps
• ${\ell }_s$ is the per-series level
• $\sigma$ is the noise level, ${ϵ}_{s,t}\sim {𝒩}(0,1)$

Pseudo-code:

# Abstract generation logic
for each series s:
    trend = (linear_coeff[s] * t + quadratic_coeff[s] * t^2) * trend_factor
    seasonal = seasonal_coeff[s] * sin(2*pi*freq*t/T)
    noise_term = 1 + noise_level * randn()
    y[s, t] = level[s] * (trend + seasonal) * noise_term

Related Pages

Implemented By

• Implementation:Sktime_Pytorch_forecasting_Generate_Ar_Data