Source-linked AI summary
Improving forecasting accuracy of time series data using a new ARIMA-ANN hybrid method and empirical mode decomposition
Ümit Çavuş Büyükşahin, Şeyda Ertekin
TL;DR
Existing models perform differently across domains, with no universal model suitable for all circumstances. The paper proposes a new hybrid ARIMA-ANN forecasting method that outperforms the other examined methods.
Problem
Different model types outperform in different domains, and no universal model suits all circumstances.
Method
The paper proposes a new hybrid ARIMA-ANN forecasting method using multi-scale decomposition and extracting the linear component with an MA filter.
Results
The proposed subseries method gives the best results and outperforms all other remaining and examined methods.
Takeaways & Limitations
The method provides a more general hybrid forecasting approach than methods whose assumptions can degenerate performance in certain circumstances.
Takeaways & Limitations
Assumptions made by other hybrid methods can degenerate their performance in certain circumstances.
Abstract
from arXiv · showhide
Many applications in different domains produce large amount of time series data. Making accurate forecasting is critical for many decision makers. Various time series forecasting methods exist which use linear and nonlinear models separately or combination of both. Studies show that combining of linear and nonlinear models can be effective to improve forecasting performance. However, some assumptions that those existing methods make, might restrict their performance in certain situations. We provide a new Autoregressive Integrated Moving Average (ARIMA)-Artificial Neural Network(ANN) hybrid method that work in a more general framework. Experimental results show that strategies for decomposing the original data and for combining linear and nonlinear models throughout the hybridization process are key factors in the forecasting performance of the methods. By using appropriate strategies, our hybrid method can be an effective way to improve forecasting accuracy obtained by traditional hybrid methods and also either of the individual methods used separately.
1. Introduction and related work
Time-series forecasting methods use linear, nonlinear, or hybrid models, but no single model suits all circumstances. The paper proposes a less assumption-dependent ARIMA-ANN hybrid with decomposition strategies intended to improve forecasting accuracy.
- Motivation and limitations of existing methods: ARIMA provides accurate forecasts for relatively stationary data but assumes linear dependence and no missing observations.Real-world series may contain nonlinear patterns that ARIMA does not model effectively.
- Motivation and limitations of existing methods: ANNs model complex nonlinear functions without requiring stationarity, adapting their structure to time-series characteristics.Their flexibility depends on architecture choices, which can cause overfitting or poor generalization.
- Hybrid forecasting methods: Because linear and nonlinear models perform differently across domains, hybrid methods combine their complementary strengths.Existing hybrids commonly decompose series into linear and nonlinear forms before applying suitable models.
- Hybrid forecasting methods: Existing hybrid methods make strong decomposition or combination assumptions that may degrade performance when datasets exhibit different relationships between components.Some methods infer linear components through ARIMA rather than directly decomposing the original series.
- Proposed method and evaluation: The proposed method uses an MA filter, applies ARIMA to the linear component, and uses ANN to combine model outputs, the nonlinear component, and original data.The study evaluates the method on four datasets and adds EMD to hybrid methods as an improvement.
- Proposed method and evaluation: Accuracy improves with increasing time-series linearity, while EMD creates relatively stationary, simpler-frequency subseries for prediction.The paper reports that the proposed method consistently outperforms the examined linear, nonlinear, and hybrid methods.
2. Time series forecasting methods
The paper reviews ARIMA, ANN, and established ARIMA-ANN hybrids for time-series forecasting. It contrasts their assumptions and processing choices, motivating a hybrid approach that separates components and models them appropriately.
- ARIMA method: ARIMA forecasting expects linear, stationary input and uses differencing or power transformation when trends or heteroscedasticity violate stationarity.Its model orders are represented by (p, d, q) and estimated using correlation analysis tools such as ACF and PACF.
- ARIMA method: ARIMA models future values from past observations and estimated coefficients after identification, parameter estimation, and forecasting steps.The method combines autoregressive and moving-average terms after differencing has established the integration order.
- ANN method: ANNs provide flexible nonlinear forecasting without a prior stationarity assumption, using adjustable layers, hidden nodes, weights, and transfer functions.Excessive complexity can memorize training data, whereas an overly simple network can generalize poorly.
- Zhang’s hybrid method: Zhang’s hybrid applies ARIMA to the series, feeds residual nonlinear information to ANN, and combines the forecasts to improve performance over individual methods.The approach assumes the series is the sum of linear and nonlinear components and that residuals contain only nonlinear relationships.
- Khashei and Bijari’s hybrid method: Khashei and Bijari’s hybrid feeds residuals to ANN with the original data and ARIMA forecast, while learning a functional rather than additive relationship between components.The method addresses the concern that residuals alone may not contain valid nonlinear patterns.
- Babu and Reddy’s hybrid method: Babu and Reddy’s hybrid uses an MA filter selected toward kurtosis approximately 3, separates low- and high-volatility components, and forecasts them with ARIMA and ANN.The resulting forecasts are summed to produce the final forecast.
3. Proposed Method
The proposed hybrid method decomposes a time series into linear and nonlinear components, models them with ARIMA and ANN, and avoids strong assumptions used by traditional hybrids. Its design uses stationarity-guided moving-average decomposition and empirically tuned ANN inputs.
- Motivation: The method addresses two challenges: identifying the data-generating process and the insufficiency of standalone non-hybrid models.These challenges motivate combining linear and nonlinear modeling within a more general forecasting framework.
- Limitations of Existing Hybrids: Traditional hybrid methods may assume additive component relationships or nonlinear residuals, limiting performance when those assumptions do not hold.The paper specifically notes that multiplicative or otherwise complex relationships can be overlooked.
- Decomposition: The proposed method begins by separating the series into linear and nonlinear components with a moving-average filter whose length is adjusted using the ADF stationarity test.The ADF threshold used to adjust the filter is 0.05.
- Hybrid Modeling: ARIMA models the stationary linear component, while ANN models component relationships using past observed values, decomposed linear forecasts, and residuals.The ANN feature lags a and b are empirically tuned according to the time-series characteristics.
- Design Consequence: The proposed model is intended to eliminate three strong assumptions of other hybrid methods and showed competitive performance across varied datasets.The authors report that it exploits individual-model strengths while reducing the risk of low performance in unexpected situations.
4. Empirical Results
The methods were evaluated with one-step-ahead forecasts on four datasets using MAE, MSE, and MASE. Results generally favored hybrid approaches, with the proposed method performing especially strongly on the benchmark series described.
- Experimental Setup: Four datasets were evaluated: Wolf’s sunspot, Canadian lynx, British pound/US dollar exchange rate, and Turkish electricity price.Three are established benchmark datasets, while the electricity-price data are publicly available.
- Evaluation: Forecast accuracy was assessed for one-step-ahead predictions using MAE, MSE, and scale-free MASE.MAE and MSE depend on data scale, whereas MASE supports comparisons across differently scaled series.
- Sunspot Results: On the Sunspot dataset, individual ARIMA and ANN methods had the lowest performance, while hybrid methods performed better.The authors attribute this pattern to standalone models failing to capture all data-series patterns.
- Sunspot Results: On the Sunspot dataset, the proposed hybrid method outperformed the Zhang, Khashei-Bijari, and Babu-Reddy hybrid methods.The paper links this result to eliminating assumptions made by those traditional hybrids.
- Lynx Results: For the Canadian lynx series, ARIMA performed better than ANN among individual methods, while hybrid gains were less easily observed because the data were relatively stationary.The dataset’s ADF result was 0.056, described as almost stationary.
- Exchange-Rate Results: For British pound/US dollar forecasts, the proposed hybrid method captured volatile patterns better and outperformed other methods in all error metrics.ANN and hybrid methods also performed better than individual ARIMA on the highly fluctuating forecast horizon.
5. Discussion and Improvement
The experiments link forecasting error to data regularity and show that EMD-based hybrid methods substantially improve accuracy, especially for non-stationary and highly fluctuating series. The proposed hybrid method avoids strong assumptions and achieves the best reported results among the examined methods.
- ARIMA outperforms ANN on more linear datasets, whereas hybrid methods generally outperform individual methods, particularly on fluctuating datasets.These comparisons motivate combining linear and nonlinear components.
- Proposed method: The proposed hybrid method avoids the strong assumptions of traditional hybrid methods and outperforms the other examined methods.Its EMD-enhanced version achieves the best reported results, while the paper presents the assumption-free design as a more general model.
- More non-stationary datasets produce higher MASE, while the relatively linear Lynx dataset has the lowest errors and Gbp/Usd the highest.The discussion associates regularer data distributions with more accurate forecasts.
- EMD-based improvement: EMD decomposes a series into relatively stationary Intrinsic Mode Functions and a residue, which can be modeled separately before their forecasts are summed.The EMD-based architecture uses decomposition, hybrid forecasting for each IMF, and additive reconstruction.
- EMD-based improvement: EMD-based methods significantly improve accuracy over corresponding methods without EMD, with improvements ranging from 23% to 89% across all error metrics.Average MASE results also indicate less error for methods using EMD.
- EMD-based improvement: EMD improvements are about 30% for Sunspot and 28% for Lynx, but exceed 50% for the highly non-stationary Gbp/Usd and Intraday datasets.The larger gains occur on the more non-stationary datasets.
6. Conclusions
The proposed ARIMA-ANN method addresses assumptions in traditional hybrid models by using broader decomposition and combination strategies. Experiments indicate that EMD decomposition and increased stationarity can improve forecasting accuracy.
- Traditional hybrid ARIMA-ANN methods can suffer from assumptions that produce inconsistent results and lower accuracy when unexpected situations occur.
- The proposed method removes the assumption that ARIMA output is the linear component by extracting that component with a moving-average filter.
- The method does not assume residuals always contain valid nonlinear patterns and avoids restricting how linear and nonlinear components are modeled or combined.
- More stationary time-series data is associated with better forecasting performance, motivating preprocessing that makes the original series more stationary.
- Combining EMD multiscale decomposition with the examined forecasting methods can markedly improve accuracy.
- The proposed hybrid method with EMD achieves remarkably superior accuracy compared with all other examined methods.