IAES Inter national J our nal of Articial Intelligence (IJ-AI) V ol. 15, No. 3, June 2026, pp. 2797 ∼ 2810 ISSN: 2252-8938, DOI: 10.11591/ijai.v15.i3.pp2797-2810 ❒ 2797 Deep h ybrid models f or bitcoin f or ecasting: EMD, CEEMD AN, and LSTM in comparison A y oub Aarabi, Mary em Ait Moulay , Issam Bouganssa, Abdelali Lasfar Laboratory Systems Analysis, Information Processing, and Industrial Management, High School of T echnology Sal ´ e, Mohammed V Uni v ersity in Rabat, Rabat, Morocco Article Inf o Article history: Recei v ed Jul 28, 2025 Re vised Apr 28, 2026 Accepted May 11, 2026 K eyw ords: Bitcoin Complete ensemble empirical mode decomposition with adapti v e noise Deep learning Long short-term memory Machine learning ABSTRA CT In this study , an articial neural netw ork (ANN) w as de v eloped to forecast Bitcoin prices using one of the most successful deep learning architectures for time series analysis: long short-term memory (LSTM) netw orks. This model w as enha nced with a signal processing layer that reduces the impact of the instrument’ s high v olatility on prediction accur ac y by applying tw o signal decomposition techniques: empiri cal mode decomposition (EMD) and complete ensemble empirical mode decomposition with adapti v e noise (CEEMD AN). This study is moti v ated by the major uctuations in Bitcoin prices, which mak e precise forecasting dif cult b ut crucial for e xperts and in v estors. This ndings demonstrate that forecasting performance impro v es when decomposition techniques are used. In particular , compared to the con v entional LSTM and EMD-LSTM models, the CEEMD AN-LSTM model achie v ed the highest a ccurac y , with a mean absolute error (MAE) of 167.837 and a root mean square error (RMSE) of 255.673, outperforming both EMD-LSTM (MAE =168.785, RMSE =256.042) and the standard LSTM (MAE =169.516, RMSE =256.225). The combination of CEEMD AN and LSTM results i n a more reliable model that can accurately capture short-term uctuations i n Bitcoin prices. This is an open access article under the CC BY -SA license . Corresponding A uthor: A youb Aarabi Laboratory Systems Analysis, Information Processing, and Industrial Management High School of T echnology Sal ´ e, Mohammed V Uni v ersity in Rabat Rabat, Morocco Email: ayoub .arb@gmail.com 1. INTR ODUCTION The Ne w Y ork Stock Exchange (NYSE), the w orld’ s lar gest stock e xchange, is currently c o ns idering a transition to w ard e xtended or e v en continuous trading hours. This shift reects broader changes in global nancial mark ets, where cryptocurrencies, led by Bitcoin, ha v e introduced a model of uninterrupted trading. In this conte xt, traditional mark et structures may appear increasingly misaligned with continuously operating digital-asset en vironments. Bitcoin w as introduced by Nakamoto in a seminal white paper published in 2008 [1], with the objecti v e of enabling a decentralized digital payment system without reliance on intermediaries. It is bas ed on blockchain technology , which ensures transparenc y and resistance to tampering through a proof-of-w ork consensus mechanism [2], [3]. Each participant in the netw ork maintains a complete cop y of the transaction ledger , ensuring rob ustness, v eriability , and transparenc y [4]. Initially re g arded with sk epticism, Bitcoin has e xperienced signicant gro wth, with its ma rk et J ournal homepage: http://ijai.iaescor e .com Evaluation Warning : The document was created with Spire.PDF for Python.
2798 ❒ ISSN: 2252-8938 capitalization surpassing $1 trillion in recent years and increasing institutional adoption. It is no w often considered a potential safe-ha v en asset, comparable to gold [5], and a hedge ag ainst inationary pressures and e xpansi onary monetary policies [6]. Some countries, such as El Salv ador and the Central African Republic, ha v e adopted Bitcoin as le g al tender or incorporated it i nto national reserv es [7]. At the same time, major central banks, including the European Central Bank and the People’ s Bank of China, are e xploring the de v elopment of central bank digital currencies (CBDCs) [8], [9]. This gro wing recognition highlights the strate gic importance of cryptocurrencies and moti v ates further in v estig ation into their v olatile dynamics. Unlik e traditional nancial assets, cryptocurrenc y prices are inuenced by a combination of technological, macroeconomic, and beha vioral f actors, which mak es their modeling particular ly challenging [10]. In this conte xt, de v eloping reliable forecasting models, especially those based on deep learning, has become an important scientic and economic issue. 2. RELA TED W ORKS Price prediction of cryptocurrencies is an inherently dif cult task, because it in v olv es fore casting future v alues of a long and highly v olatile nancial time series. This com p l e xity is the result of v ery high v olatility of cryptocurrenc y-based nancial time series, which are inuenced by economic , political, technological, and psychological forces. Such ser ies are typically non-stationary and nonlinear , and are frequently e xposed to e xogenous shocks. T o address the limitations of the classical methods that f ail to capture the dynamics of these series, man y recent studies rely on deep learning approaches. In this re g ard, Derbentse v et al. [11] in v estig ated the short-term dynamics of Bitcoin, Ethereum, and Ripple using sophisticated algorithms including articial neural netw orks (ANNs), random forests (RFs) and binary autore gressi v e trees (B AR Ts). The y found that both ANN and B AR T models substantially outperformed nai v e classication methods (up to 63% accurac y out-of-sample) based on more than 1,500 daily observ ations between 2015 and 2019. Cho wdhury et al. [12] continued with a lar ger number of cryptocurrencies, including the CCI30 inde x, and used more adv anced machine learning models as boosted trees, k-nearest neighbors, and rob ust ensemble models. The authors’ research for the years 2017 to 2019 sho wed that their ensemble models and their boosted tree methods performed v ery well, surpassing e v en se v eral sophisticated models. Ho we v er , multiple studies ha v e since underscored the inherent limitations of deep learning models when the y are applied to this kind of time series. Pintelas et al. [13] sho wed that long short-term memory (LSTM)- or con v olutional neural netw ork (CNN)-based models can be po werful, their performance de grades in the presence of noise and missing data. F or a more rob ust prediction and a prediction with a higher reliability , Li vieris et al. [14] introduced ensemble architectures using bagging, stacking, and a v eraging methods in v olving sets of se v eral LSTM and Con v1D learners on hourly data for Bitcoin, Ethereum, and Ripple. The obtained results suggest that the h ybrid models, though computationally e xpensi v e, e xhibit lar ge mar gins in accurac y . In a similar , more specic manner , P atel et al. [15] proposed a h ybrid LSTM-g ated recurrent unit (GR U) model for Litecoin and Monero price prediction. The results of e xperiments demonstrate that this recurrent model could obtain better results when comparing with the simple LSTM netw orks, especially in terms of root mean squared error (RMSE) and mean absolute percentage error (MAPE). Other studies, such as in [16], [17], emphasized the importance of e xplanatory v ariable selection, emplo ying methods such as the granger causality , mutual information, and gre y relational analysis (GRA) to quantify the inue n c e of macroeconomic v ariables on Bitcoin price. More recent w orks ha v e compared deep h ybrid models to the traditional approaches. Chauhan et al. [18] considered a CNN–GR U model for long horizon prediction in the Bitcoin price and found that deeper netw ork structures do not necessarily lead to better performance without proper pre-processing of signals. Similarly , Qureshi et al. [19] analyzed some classical (e.g., auto-re gressi v e inte grated mo ving a v erage (ARIMA), multi-layer perceptron (MLP), and e xtreme learning machine (ELM)) and h ybrid models, and the y noted that these models are not able to accurately capture the nonlinear dynamics of the cryptocurrenc y price e v olution, especially during the high v olatility periods. Ho we v er , a maj or limitation of all these studies is that the y ha v e generally preferred to impro v e the predicti v e performance by simply e xploiting increasingly comple x architectures, b ut the y ha v e paid less attention to the solid construction of training sets that are full of conte xtual information. Nonetheless, adding appropriate e xogenous v ar iables, such as oil, gold, interest rates, or dollar strength inde x es, can signicantly impro v e the accurac y of forecasts, espec ially in highly v olatile cryptocurrenc y mark ets. This g ap is addressed in the present study by inte grating a ne-grained analysis of basic economic v ariables, where GRA is emplo yed to Int J Artif Intell, V ol. 15, No. 3, June 2026: 2797–2810 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 ❒ 2799 select the most rele v ant e xplanatory features and construct an economically informati v e and coherent input set. 3. METHOD F orecasting Bitcoin prices is a highly challenging task gi v en the high v olatility , non-st ationary , and nonlinear nature of the ass et [20], [21]. T o impro v e forecasting results under such conditions, a data preprocessing, decomposition, and sequential learning approach w as proposed. The general architecture of the proposed methodology is illustrated in Figure 1. Under this methodology v arious input v ariables ha v e been tak en into account including open, high, lo w , close prices, v olume traded, and macroeconomic indicators. GRA is used for the determination of the most inuenti al features that share structural similarities with Bitcoin closing price. At the same time, the tar get v ariable i.e. the closing price series, w ould be decomposed using EMD or its impro v ed v ersion kno wn as complete ensemble empirical mode decomposition with adapti v e noise (CEEMD AN). This process yields a set of intrinsic mode functions (IMF) and a residual term, where each is associated with a particular frequenc y component of the signal. Each IMF and the residue are modeled separately using an LSTM netw ork. These s ub-models capture dif ferent temporal characteristics and help pre v ent o v ert ting to noise. The indi vidual forecasts are subsequently recombined through a reconstruction process to gi v e the nal forecast of closing price of the Bitcoin. In addition to short-term v olatility reduction, such a modular architecture also enhances the interpretability and rob ustness of the predicti v e system. It allo ws a multi-resolution representation of the mark et dynamics which reects the inherent heterogeneity and noisy features of nancial time series. Figure 1. Architecture of our inte grated forecasting model 3.1. Experimental setup and r epr oducibility The dataset (2014 to 2024, daily) is split chronologically into 70% training (2018 to 2021), 15% v alidation (2022), and 15% testing (2023 to 2024) to a v oid data leakage. One-step-ahead forecasting is performed using a sliding input windo w of L = 30 days. All features are normalized using Min–Max scaling tted on the training set. T raining uses the Adam optimizer (learning rate 10 − 3 ) and Huber loss. The LSTM architecture consists of tw o layers (100 and 32 units) with dropout 0.2 and early stopping. Models are trained for up to 100 epochs with batch size 32. All e xperiments are im plemented in Python using K eras/T ensorFlo w with a x ed random seed. Bot h EMD and CEEMD AN decompositions yielded v e IMFs in the e xperiments (with an additional residual component for CEEMD AN). Each component w as modeled by an independent LSTM, and the nal predict ion w as obtained by aggre g ating the forecasts of all components. As summarized in T able 1, the main h yperparameters are reported for reproducibility . In the follo wing, the three forecasting architectures considered in this study are detailed: a benchmark LSTM model, an EMD based h ybrid model, and a CEEMD AN-enhanced v ersion. 3.2. Long short-term memory on nancial time series The LSTM neural netw orks [22] are commonly used for time series predictions tasks, including in nancial mark ets [23], in ener gy [24] and in cryptocurrenci es [25]. The y surpass classic neural netw orks Deep hybrid models for bitcoin for ecasting: EMD, CEEMD AN, and LSTM in comparison (A youb Aar abi) Evaluation Warning : The document was created with Spire.PDF for Python.
2800 ❒ ISSN: 2252-8938 in situations where memory ef fects are important as a consequence of their capacity to learn long-term dependencies in sequential data. The memory cell C t in the LSTM is managed using input i t , for get f t , and output o t g ates that enable the information in the ce ll to be k ept or for gotten o v er time, which mak es it ideal for the unpredictable nature of the cryptocurrenc y mark et. Ho we v er , direct application of LSTM to e xtremely noisy data, e.g., ra w Bitcoin prices, may result in o v ertting to t he noise, causing unstable prediction [26]. At each time step t , gi v en the input x t , pre vious hidden state h t − 1 , and pre vious cell state C t − 1 , the LSTM performs computations as in (1) to (6). f t = σ ( W f · [ h t − 1 , x t ] + b f ) (F or get g ate) (1) i t = σ ( W i · [ h t − 1 , x t ] + b i ) (Input g ate) (2) ˜ C t = tanh( W C · [ h t − 1 , x t ] + b C ) (Candidate cell state) (3) C t = f t ∗ C t − 1 + i t ∗ ˜ C t (Cell state update) (4) o t = σ ( W o · [ h t − 1 , x t ] + b o ) (Output g ate) (5) h t = o t ∗ tanh( C t ) (Hidden state) (6) Here, σ denotes the sigmoid acti v ation function, tanh is the h yperbolic tangent function, and ∗ denotes element-wise multiplication. These mechanisms allo w LSTMs to learn comple x temporal dynamics. T able 1. Main h yperparameters used in the e xperiments Component Setting Look-back windo w L 30 days F orecast horizon 1-step ahead ( t + 1 ) LSTM layers 2 Units per layer 100, 32 Dropout rate 0.2 Optimizer Adam Learning rate 0.001 Batch size 32 Epochs 100 (early stopping enabled) Loss function Huber loss 3.3. EMD-LSTM: fr equency di vision and multiple le v els of r epr esentation T o o v ercome this v olatility , we utilize a h ybrid approach EMD and LSTM. Huang et al. [27] has proposed the EMD, an y time series is decomposed into a number of IMFs, all of which correspond to oscillations ha ving dif ferent characteristi c time scales. Suc h a decomposition is adapti v e and data-dri v en, and is appropriate for nonlinear and nonstationary signals, and mark et prices. Each obtained IMF , c i ( t ) , is presumed to ha v e a higher le v el of re gularity compared to the ra w series and in turn easier for modeling. Therefore, the signal can be written as in (7). x ( t ) = n X i =1 c i ( t ) + r n ( t ) (7) Where r n ( t ) is the non-oscillatory residual. Each such component is modeled as independent LSTM and their output are combined to generate the nal prediction. This frequenc y decoupling w ould mak e the model v ery rob ust in terms of the mark et state [28]. T o capture the subtle frequenc y patterns embedded in the original Bitcoin price signal, we use the EMD, a data-dri v en method that decomposes a non-stationary and non-linear time series into a limited set of IMFs. The decomposition algorithm is gi v en in Algorithm 1. The Algorithm 1 decomposes the original signal adapti v ely into a nite number of IMFs, each representing a specic local oscillation mode of the original signal. In the case of Bitcoin forecasting, EMD enables the short term uctuations to be separated from long term trends, making it possible to learn more stable representations of both using separate LSTM models. Ho we v er , as we will see in the follo wing section, EMD is vulnerable to mode mixing, which dri v es the need for its impro v ed v ersion. Int J Artif Intell, V ol. 15, No. 3, June 2026: 2797–2810 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 ❒ 2801 Algorithm 1 EMD 1: Input: Signal x ( t ) 2: Output: Intrinsic mode functions { c 1 ( t ) , c 2 ( t ) , . . . , c n ( t ) } and residual r n ( t ) 3: Initialize: r 0 ( t ) ← x ( t ) 4: f or i = 1 to n do 5: h 0 ( t ) ← r i − 1 ( t ) 6: while h k ( t ) is not an IMF do 7: Identify local e xtrema of h k ( t ) 8: Interpolate upper and lo wer en v elopes 9: Compute mean en v elope m k ( t ) 10: h k +1 ( t ) ← h k ( t ) − m k ( t ) 11: end while 12: c i ( t ) ← h k ( t ) 13: r i ( t ) ← r i − 1 ( t ) − c i ( t ) 14: end f or 15: r etur n { c 1 ( t ) , . . . , c n ( t ) } and r n ( t ) 3.4. CEEMD AN-LSTM: enhanced r ob ustness and mode mixing a v oided Ho we v er , EMD suf fers from mode mixing, a mixing of frequenc y scales in a single IMF , leading to obstacles to learning. T o resolv e it, the CEEMD AN method [29] is an enhancement performed to stabilize frequenc y separat ion. CEEMD AN introduces white stochastic Gaussian Noise to n copies of the signal in a noise-controlled manner , apply EMD on each n, and a v erages the decompositions to get smooth and stable IMFs. This approach results in impro v ed component orthogonality and true reconstructability while remaining resistant to structural noise. The signal can be written as in (8). x ( t ) = n X i =1 ¯ c i ( t ) + r n ( t ) (8) Where ¯ c i ( t ) is the a v erage of the IMFs e xtracted at each noisy step. CEEMD AN has been applied in v arious elds, such as stock inde x forecasting, biomedical signal processing, and climate analysis, and cryptocurrenc y price modeling [30]. When combined with LSTM, it separates out the high-frequenc y components (noise and micro-oscillations) to enable the training of LSTM to be concentrated on the signals, which are smoother and ha v e more information. Therefore the CEEMD AN-LSTM netw ork i s especially t to the aforementioned v olatile and noisy nancial series. T o o v ercome EMD weaknesses, such as mode mixing, CEEMD AN is utilized t o pro vide rob ust decomposition. The algorithm of the iterati v e ensemble approach to procure noise-rob ust IMFs from the input signal is presented in Algorithm 2. Algorithm 2 Complete ensemble EMD with adapti v e noise (CEEMD AN) 1: Input: Signal x ( t ) , white noise w ( t ) , ensemble size M , noise le v el ε 2: Output: Components { c 1 ( t ) , c 2 ( t ) , . . . , c n ( t ) } and residual r n ( t ) 3: f or m = 1 to M do 4: x m ( t ) ← x ( t ) + ε · w m ( t ) 5: c 1 ,m ( t ) ← EMD( x m ( t )) ▷ Apply EMD to noisy signal 6: end f or 7: c 1 ( t ) ← 1 M P M m =1 c 1 ,m ( t ) ▷ Ensemble a v erage of rst mode 8: r 1 ( t ) ← x ( t ) − c 1 ( t ) 9: f or i = 2 to n do 10: f or m = 1 to M do 11: r i − 1 ,m ( t ) ← r i − 1 ( t ) + ε · w m ( t ) 12: c i,m ( t ) ← EMD( r i − 1 ,m ( t )) 13: end f or 14: c i ( t ) ← 1 M P M m =1 c i,m ( t ) ▷ Ensemble a v erage of i -th mode 15: r i ( t ) ← r i − 1 ( t ) − c i ( t ) 16: end f or 17: r etur n { c 1 ( t ) , . . . , c n ( t ) } and r n ( t ) CEEMD AN generate a series of ensembles with the addition of controlled white noise in the EMD decomposition operation. This helps to reduce the problem of mode m ixing and produces smoother and Deep hybrid models for bitcoin for ecasting: EMD, CEEMD AN, and LSTM in comparison (A youb Aar abi) Evaluation Warning : The document was created with Spire.PDF for Python.
2802 ❒ ISSN: 2252-8938 more interpretable IMFs. Each component obtained by the CEEMD AN decomposition represents independent frequenc y characteristics of the Bitcoin, which enhances the learning capacity of the LSTM and impro v es the rob ustness of prediction. The ensemble-based feature of CEEMD AN also leads to better signal reconstruction and generalization capabilities. In both h ybrid methods, IMF components (obtained from EMD or CEEMD AN) are normalized and fed into separate LSTM netw orks. All LSTMs learn the dynamics of their respecti v e components. Additi v e predictions for all IMFs is then combined to get the nal predicted Bitcoin price. This tw o-step process separates the short-term structures (f ast IMFs) from the long-term structures (slo w IMFs or the residuals), thus impro ving the accurac y of the model. In contrast, CNN architectures such as those used for series or image classication are not good at capturing long temporal dependencies and do not generalize well to v ery noisy one-dimensional signals. Lik e wise, classical approaches namely , ARIMA and GARCH are not able e v en to handle stationary series in such a non-stable and linear re gime as the case of cryptocurrencies [31]–[33]. 3.5. Gr ey r elational analysis In order to e v aluate the importance of the f actors on the tar get, or response v ariable (price of Bitcoin), the so-called GRA introduced in the gre y systems theory w as utilized [34]. This approach allo ws one to estimate the le v el of similarity of time series (including uncertainty , noise, and small amounts of statistical data). The reference series, corresponding to the Bitcoin price, is dened as (9). X 0 = { x 0 (1) , x 0 (2) , ..., x 0 ( n ) } (9) The e xplanatory series is similarly dened in (10). X i = { x i (1) , x i (2) , ..., x i ( n ) } (10) The gre y relational coef cient between x 0 ( k ) and x i ( k ) is e xpressed by (11). ξ i ( k ) = min i min k | x 0 ( k ) − x i ( k ) | + ζ · max i max k | x 0 ( k ) − x i ( k ) | | x 0 ( k ) − x i ( k ) | + ζ · max i max k | x 0 ( k ) − x i ( k ) | (11) Here, ζ ∈ [0 , 1] denotes the distinction coef cient, which is usually set to 0.5. The o v erall gre y relational de gree between X 0 and X i is then computed using (12). γ i = 1 n n X k =1 ξ i ( k ) (12) The closer γ i is to 1, the higher the structural similarity between the e xplanatory v ariabl e X i and the tar get series X 0 . This method is well adapted to non-stationary nancial time-series such as those e xamined in [35] and to the problem of v ariable selection prior to modeling. 3.6. Ev aluation criteria In order to assess the forecasting accurac y of the models for the time series of the Bi tcoin price, tw o typical criteria are emplo yed: the RMSE and the mean absolute error (MAE). These measurements indicate the de viation between predicted and actual v alues. The RMSE metric is dened in (13). R M S E = v u u t 1 n n X t =1 ( y t − ˆ y t ) 2 (13) It represents the square root of the mean squared error and e xpresses the a v erage prediction error in the same unit as the data. The MAE metric is dened in (14). M AE = 1 n n X t =1 | y t − ˆ y t | (14) MAE measures the a v erage absolute prediction error and is generally more rob ust to outliers since it does not e xcessi v ely penalize lar ge de viations. Int J Artif Intell, V ol. 15, No. 3, June 2026: 2797–2810 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 ❒ 2803 4. D A T A COLLECTION AND SOURCES The purpose of this study is to forecast the path of the Bitcoin price by including, be yond its past beha vior , a number of macro-nancial v ariables that can potentially af fect its mo v ement in the short/medium term. Because the cryptocurrenc y mark et is di v erse, as control v ariables were selected a series of indicators standing for the global economy situat ion, the U.S. monetary polic y , the capital o w to w ards safe-ha v en assets, and the dollar dynamics. Data were collected o v er a ten-year period from September 2014 to September 2024, with a daily frequenc y and standardized prior to including to models. 4.1. Crude oil price W est T exas Intermediate The barometer of global economic acti vity that is the oil price w as chosen as the rst e xplanatory v ariable. The demand for oil tends to rise during an economic e xpansion, and f all when the economy is in a recession or is slo wing do wn [36]. Additionally , the v olatility of oil might also af fect the e xpectations of in v estors re g arding ination and monetary polic y , and then speculati v e assets such as Bitcoin [37]. 4.2. Gold price (XA U/USD) Gold has long been considered a refuge in insecure times such as geopolitical turm oil or n a ncial crises [38]. Its dynamics typically embody the anticipation of systemic risk and ination. When the mark et stresses, in v estors will reduce their e xposures to risk y assets, and the risk a v ersion will push up the demand for gold; the latter could dri v e capital ight out of cryptocurrencies into safer assets [39]. Therefore, the beha viour of gold’ s price is a good indicator of the general risk a v ersion. 4.3. 2-y ear United States tr easury bond rates The 2-year T reasury bond yield is strongly related to the mark et’ s beliefs about the monetary polic y of the Fed [40]. So a lo w rate implies an accommodati v e monetary stance (lo wer k e y rates and e xpanding balance sheet), and is good for speculati v e assets and the stock mark et; whereas a high rate speaks of a monetary tightening, which means less liquidity and more stress on risk y assets. In this, the 2Y rate is a k e y dri v er of risk appetite perception and of cross-asset arbitrage [41]. 4.4. United States dollar index The dollar inde x (DXY) is a measure of the v alue of the United States dollar (U.S. dollar) relati v e to a bask et of six foreign currencies (euro, J apanese yen, pound sterling, Canadian dollar , Swedish krona, and Swiss fr anc). The dollar is a reserv e curre nc y for the w orld and is frequentl y seen as a s afe ha v en. A strong U.S. dollar typically means a do wnturn in risk appetite or increased global interest rate tightening, while a weak U.S. dollar can mean a positi v e en vironment for non-U.S. dollar assets [42]. Bitcoin, at times touted as a currenc y-ination hedge, frequently e xperiences a ne g ati v e dynamic with the DXY [43]. 5. RESUL TS AND DISCUSSION 5.1. Results Figure 2 sho ws the output of the GRA for the dif ferent e xplanatory v ariables. Each of the lines is inde x ed to dif ferent time interv als: daily (1d), daily e xcluding week ends (1d b), weekly (1w), monthly (1m), and quarterly (1q) series. From this visualization, it is possible to e v aluate not only the structure of relationship on the basis of all v ariables considered, and their relation to the price of Bitcoin, b ut also the role of the sampling frequenc y on the capacity to e xplain it. The comparison sho ws that the daily data generally ha v e the highest v alues of GRA. Crude oil price, Gold price, US 2Y interest rate, and U.S. dollar inde x ha v e a close GR relationship with Bitcoin, especially in high frequenc y . These ndings indicate that the uctuations of these indicators are highly correlated to daily changes of Bitcoin trading. Accordingly , the model w as designed and trained using only the da ily data, as it is the scale o v er which the information is most rele v ant according to GRA. This option can capture short-term information more precisely and a v oid informati on loss c aused by tem p or al aggre g ation. It also mirrors the short -term horizon upon which crypto mark ets operate, namely their acute sensiti vity to economic data and geopolitical shocks. Figures 3 and 4 sho w the e xtracted IMF components by the EMD method and the CEEMD AN, respecti v ely . It is noticed that the separation of frequenc y presented is ner and less noisy in CEEMD AN, resulting in better -usable signals for the sequential LSTM training. Especially , it can produ c e a bett er separation of high frequenc y components, at the same time, an accurate trend is more distinct. Deep hybrid models for bitcoin for ecasting: EMD, CEEMD AN, and LSTM in comparison (A youb Aar abi) Evaluation Warning : The document was created with Spire.PDF for Python.
2804 ❒ ISSN: 2252-8938 Figure 2. The results of GRA on predictors Figure 3. The IMFs decomposed by EMD Int J Artif Intell, V ol. 15, No. 3, June 2026: 2797–2810 Evaluation Warning : The document was created with Spire.PDF for Python.
Int J Artif Intell ISSN: 2252-8938 ❒ 2805 Figure 4. The IMFs decomposed by CEEMD AN The performances are summarized quantitati v ely in T able 2. The proposed baseline LSTM model pro vides an MAE of 169.516 and an RMSE of 256.225. T olerable performances can be achie v ed by including EMD decomposition (MAE =168.785; RMSE =256.042). Last, the combination of CEEMD AN yi elds the best performance (MAE =167.837; RMSE =255.673) o v erall. Deep hybrid models for bitcoin for ecasting: EMD, CEEMD AN, and LSTM in comparison (A youb Aar abi) Evaluation Warning : The document was created with Spire.PDF for Python.
2806 ❒ ISSN: 2252-8938 T able 2. Performance comparison between LSTM, EMD-LSTM, and CEEMD AN-LSTM models Metric LSTM EMD-LSTM CEEMD AN-LSTM MAE 169.516 168.785 167.837 RMSE 256.225 256.042 255.673 V isual predictions are visualized in Figures 5 to 7. Figure 5 sho ws the forecast of the LSTM model, being capable to recognize the global trend, it misses some quick re v ersals. Figure 6 implemented with the EMD-LSTM model possesses more sensiti vity to local change, which is an immediate consequence of the IMF preprocessing. Figure 7 sho ws that CEEMD AN-LSTM presents the best accurac y both on up and do wn trend is obtained with least error than all other results. The learning curv es de v elopment indicates that the CEEMD AN decomposition is capable of pro viding the LSTM model more solid pattern to grasp the, thus mitig ating the inuence of abnormal uctuations of the Bitcoin price. Figure 5. The forecasting results based on LSTM Figure 6. The forecasting results based on EMD-LSTM Int J Artif Intell, V ol. 15, No. 3, June 2026: 2797–2810 Evaluation Warning : The document was created with Spire.PDF for Python.