Modeling and Forecasting of Non-stationary and Non-linear Time Series Data
Loading...
Date
2025-01-03
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Department of Agricultural Statistics, Bidhan Chandra Krishi Viswavidyalaya, Mohanpur, Nadia – 741252
Abstract
As agricultural commodity prices are non-linear and non-stationary, forecasting them
is considered a difficult undertaking. Due to the strong dependence of agricultural output on
a range of biological and agro-meteorological parameters, conventional smoothing methods
and statistical models sometimes fail to provide a satisfactory model for such series.
Different data-driven and self-adaptive approaches have been developed periodically to
efficiently capture such complicated patterns. With this backdrop, in this study, an empirical
mode decomposition (EMD)-based neural network and support vector regression (SVR)
approaches are proposed for forecasting wholesale prices of five important pulses and spices
Arhar, Chickpea, Chili, Garlic and Onion. Wholesale price data of three prominent markets
for each crop are chosen for modeling and forecasting. As the benchmark models time delay
neural network (TDNN) and SVR models have been employed for the comparative
evaluation. TDNN (Time-Delay Neural Network) models are designed specifically for
modeling sequential data, utilizing fixed-length windows to capture temporal dependencies
and patterns. By processing data through multiple layers with shared weights, TDNNs learn
to extract relevant features from the input sequence. SVR applied to time series forecasting
employs Support Vector Machine (SVM) principles within a regression context to predict
future values based on historical time-series data. SVR seeks to identify a hyperplane that
best suits the training data while minimizing forecast errors. By transforming input data into
a higher-dimensional space and determining the optimal hyperplane with maximum margin
from the data points, SVR effectively addresses nonlinear relationships and highdimensional
datasets. EMD is employed in time series forecasting by breaking down the
original data into Intrinsic Mode Functions (IMFs), representing its inherent oscillatory
modes. Following decomposition, each IMF is analysed independently to discern its unique
characteristics and trends. Forecasting methods are then applied to predict future values for
each IMF. These forecasted values are subsequently amalgamated to generate the overall
forecast for the initial time series. The experimental results clearly reveal the comparative
superiority of the EMD based models over the bench mark models. Ensemble Empirical
Mode Decomposition (EEMD) is utilized in time series forecasting to enhance prediction
accuracy compared to traditional EMD. EEMD introduces randomness into the
decomposition process to address mode mixing issues, resulting in multiple realizations of
Intrinsic Mode Functions (IMFs). By averaging these realizations, EEMD generates more
stable IMFs, leading to improved forecasting performance, especially with noisy or complex
time series data. Therefore, ensemble empirical mode decomposition (EEMD) based models
like EEMD-TDNN, EEMD-SVR models are developed to counter the mode mixing problem
of EMD process. Results indicate that EEMD based models have outperformed other
modeling techniques. Beside this, a new approach is taken to propose an EEMD-SVRTDNN-
ARIMA model for price forecasting. For this, all the IMFs obtained from the EEMD
method are categorized into high frequency, low frequency and trend component by using
Fine to Coarse Reconstruction method. The high frequency components are modelled with
SVR, low frequency components are modelled with TDNN and the trend components are
modelled with ARIMA model. From the results, it is found that this new approach has
performed even better than EEMD-TDNN and EEMD-SVR models in many cases.