Time Series Analysis with Polynomial Detrending and Fourier Filtering

Overview

This Python script performs time series analysis on financial data (specifically EUR/USD closing prices) using polynomial detrending, Fourier transformation, and forecasting techniques. The code includes methods for removing trends, applying spectral analysis, and making future price predictions.

Features

• Data Loading: Reads EUR/USD price data from CSV files
• Detrending: Implements two detrending methods (difference and linear)
• Polynomial Fitting: Fits polynomial curves to price data for trend extraction
• Fourier Analysis: Applies FFT for frequency domain analysis and filtering
• Forecasting: Generates future price predictions using Fourier components
• Visualization: Creates plots to compare original data, trends, and predictions

Requirements

pandas
numpy
matplotlib
scikit-learn (for LinearRegression - note: currently missing import)

Installation

pip install pandas numpy matplotlib scikit-learn

Usage

Basic Usage

1. Place your EUR/USD price data in a CSV file at the path 'Prices/EURUSD_.csv'
2. Run the script:

python timeseries_analysis.py

Detrending Function

The script includes a detrend() function with two methods:

# Difference method
detrended = detrend(prices, method='difference')

# Linear regression method
detrended = detrend(prices, method='linear')

Key Parameters

• training: Number of data points used for training (default: 226)
• foresight: Number of future points to predict (default: 20)
• deg: Polynomial degree for fitting (default: 10)

Code Structure

Main Components

1. Data Preparation (lines 36-55):

   • Loads and preprocesses EUR/USD price data
   • Sets up training and testing datasets

2. Polynomial Fitting (lines 57-67):

   • Fits a 10th-degree polynomial to training data
   • Calculates percentage error of the fit

3. Residual Analysis (lines 70-75):

   • Computes differences between actual prices and polynomial fit

4. Fourier Analysis (lines 78-112):

   • Applies FFT to residuals
   • Filters frequency components
   • Reconstructs signal using inverse FFT

5. Forecasting (lines 114-138):

   • Extends Fourier components for future predictions
   • Combines polynomial trend and Fourier components
   • Calculates prediction weights

6. Visualization (lines 140-145):

   • Plots original data, polynomial fit, and predictions

Note on Imports

The code currently uses LinearRegression without importing it. Add this import at the top:

from sklearn.linear_model import LinearRegression

Output

1. Console Output:

   • Percentage error of polynomial fit
   • Fourier component values
   • Prediction weight
   • Combined trend and cyclical components

2. Visual Output:

   • Plot 1: Polynomial fit vs. actual closing prices
   • Plot 2: Final predictions vs. original data (training and full dataset)

Example Output Interpretation

Percentage error: 0.XXX %
The prediction weight is: Y.YYY

The prediction weight represents the average of forecasted Fourier components and can be used as an indicator of future price movements.

Important Notes

• The code uses a fixed training size of 226 points
• Fourier filtering thresholds are hard-coded and may need adjustment
• The polynomial degree (10) might lead to overfitting
• Error handling for the detrending function is basic
• File paths are hard-coded and may need modification

Customization

To adapt this script for your needs:

1. Modify df=pd.read_csv('Prices/EURUSD_.csv') to point to your data file
2. Adjust training and foresight parameters based on your data size
3. Change polynomial degree (deg=10) as needed
4. Modify Fourier filtering thresholds for different frequency cutoffs

Limitations

• Missing error handling for file I/O
• LinearRegression import is missing
• Hard-coded parameters may not generalize well
• Limited comments in complex sections
• No validation of forecast accuracy

Future Improvements

• Add cross-validation for parameter selection
• Implement more robust error handling
• Create configuration file for parameters
• Add performance metrics for predictions
• Implement multiple forecasting methods for comparison

Author

Code for time series analysis using polynomial and Fourier methods

#Fourier analysis for Forex predictions https://medium.com/@mnyandenilunga/fourier-analysis-for-forex-predictions-c2313adc6379