All classes ANFIS Metaheuristics Time Series Forecasting Syllabus · Episode 1 of 6

Class ANFIS Metaheuristics Time Series Forecasting #1: Non-Linear Time Series: Dataset, Stationarity, and Patterns

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Non-Linear Time Series Tutorial with Python: Mackey-Glass, sunspot, ADF test, autocorrelation, embedding. Episode 1 of the ANFIS Metaheuristics Time Series Forecasting Series.

Software: Python (NumPy, statsmodels, PyTorch, Matplotlib)
Level: Intermediate
Duration: ± 10 min
Series total: 59 min · 6 videos
Published: October 25, 2026

Episode 1 of 6 · view syllabus

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Class ANFIS Metaheuristics Time Series Forecasting #1: Non-Linear Time Series: Dataset, Stationarity, and Patterns: Cover: ANFIS Metaheuristics Time Series Forecasting Class #1: Non-Linear Time Series: Dataset, Stationarity, and Patterns

Class ANFIS Metaheuristics Time Series Forecasting #1: Non-Linear Time Series: Dataset, Stationarity, and Patterns: Before you start, steps list, and Step 1

Class ANFIS Metaheuristics Time Series Forecasting #1: Non-Linear Time Series: Dataset, Stationarity, and Patterns: Step 2: Mackey-Glass & sunspot

Class ANFIS Metaheuristics Time Series Forecasting #1: Non-Linear Time Series: Dataset, Stationarity, and Patterns: Step 3: Normalization & case configuration

Class ANFIS Metaheuristics Time Series Forecasting #1: Non-Linear Time Series: Dataset, Stationarity, and Patterns: Step 4: Stationarity & autocorrelation

Class ANFIS Metaheuristics Time Series Forecasting #1: Non-Linear Time Series: Dataset, Stationarity, and Patterns: Step 5: Patterns & chaos attractor

Class ANFIS Metaheuristics Time Series Forecasting #1: Non-Linear Time Series: Dataset, Stationarity, and Patterns: Done: Final Result and Further Practice

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Introduction

Here is the final result, two non-linear time series. The Meki Glass which is chaotic but has a beautiful attractor in the phase map, and the sunspot 300 years with its 11-year cycle. Both of them we prepare as input and target pairs for Anvis. Let's start. Hello, welcome to the tutorial series, metaheuristic model prediction Anvis for non-linear time series forecasting. Many time series in the real world, such as electrical load, rainfall, and prices, are non-linear, making them difficult to predict with linear models. In this 6-part series, we build everything from scratch. Time series analysis, Sugeno phase, Anvis, optimization with PSO and genetic algorithms, comparison with LSTM and ARIMA, up to the Diebold-Mariano test. We open the terminal through the terminal menu,

Step 1: Installing the library

new terminal, then install nampai, pandas, stats models, torque, and metplotlib. Stats models for stationarity testing and ARIMA,

Step 1: library

torque for LSTM comparison.

Step 2: Mackey-Glass & sunspot

Create a file named data_underscore_time_dot_py. The Mackey Glass function integrates a delayed differential equation. Changes in X depend on the value of X 17 time units ago. With tau 17, this series is chaotic, never repeating exactly but still structured, and serves as the classic benchmark for Anvis since the 1993 paper. The Sunspot function reads annual sunspot data from CSV. The embedding function arranges inputs from several past values and the target from future values. The normalization function scales data to the 0 to 1 scale

Step 3: Normalization & case configuration

using only the minimum and maximum of the training data, to prevent leakage from the test data. The case dictionary stores the configuration. Mackey Glass uses lag 18, 12, 6, and 0 to forecast 6 steps ahead. Exactly like the classic study, Sunspot uses lag 9, 2, 1, and 0 to forecast 1 year ahead, with regularization that we will discuss later. The prepare function returns ready-to-use training and test data.

Step 4: Stationarity & autocorrelation

Create the exploration underscore time series file.py and run it. Mackey Glass contains 1,500 points and passes the ADF test with P0, meaning it is stationary, and its autocorrelation peaks again at lag 49. Sunspot contains 309 years, with PADF 0.053 at the boundary, and autocorrelation peaks at lag 10, which corresponds to the solar cycle of about 11 years. Mackey Glass produces 476 training pairs and 600 test pairs, while Sunspot has 210 training pairs and 89 test pairs.

Step 5: Pattern 8 chaotic attractors

Let's look at the graph. The Mackey Glass series looks like a chaotic wave, but the phase plot of X against X 17 steps before forms a neat chaotic attractor, evidence of a deterministic non-linear pattern. Sunspot shows an up-and-down cycle with different peaks, and its autocorrelation oscillates with a period of about 11 years. Non-linear patterns like these will be captured by Anfis.

Done!

Done. We have already generated the Mackey Glass series, loaded the Sunspot data, tested for stationarity, analyzed the autocorrelation and phase plot, and prepared the lag embedding. In the next episode, we will study the Sugeno fuzzy inference system, the foundation of Anfis. Currently working on a thesis, dissertation, or research in the field of forecasting and artificial intelligence? Cerdas Inovasi Digital helps implement forecasting models, from the Sugeno fuzzy system and Anfis, parameter optimization with PSO and genetic algorithms, up to LSTM and ARIMA comparisons and Diebold Mariano tests, as well as opening Python programming courses for engineers. Want to master the entire series, from chaotic time series to statistical evaluation? All 6 episodes, complete with step-by-step PDF guides, dataset, and source code, are available to premium tutorial subscribers. Subscribe starting at Rp69.000 per month, save 28% with the 12-month package, or one-time pay Rp999.000 for lifetime access. Want a single class? Buy the single class with lifetime access. Subscribe now at the premium page cerdasinovasidigital.com Contact our WhatsApp, or visit cerdasinovasidigital.com Thank you for watching, see you in the next episode. Thank you for watching! Thank you for watching!

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Transcript

0:03Introduction

0:57Step 1: Installing the library

1:07Step 1: library

1:13Step 2: Mackey-Glass & sunspot

3:24Step 3: Normalization & case configuration

4:51Step 4: Stationarity & autocorrelation

7:07Step 5: Pattern 8 chaotic attractors

8:57Done!

Ask the class material

My notes

Questions & answers

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▶ Video Lesson

Recommended classes for you

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Transcript

0:03Introduction

0:57Step 1: Installing the library

1:07Step 1: library

1:13Step 2: Mackey-Glass & sunspot

3:24Step 3: Normalization & case configuration

4:51Step 4: Stationarity & autocorrelation

7:07Step 5: Pattern 8 chaotic attractors

8:57Done!

Ask the class material

My notes

Questions & answers

Your instructor

Introduction

Step 1: Installing the library

Step 1: library

Step 2: Mackey-Glass & sunspot

Step 3: Normalization & case configuration

Step 4: Stationarity & autocorrelation

Step 5: Pattern 8 chaotic attractors

Done!

Introduction

Step 1: Installing the library

Step 1: library

Step 2: Mackey-Glass & sunspot

Step 3: Normalization & case configuration

Step 4: Stationarity & autocorrelation

Step 5: Pattern 8 chaotic attractors

Done!