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A Comparative Analysis of Forecasting Financial Time Series Using ARIMA, LSTM, and BiLSTM

Sima Siami-Namini, Neda Tavakoli, Akbar Siami Namin

arXiv:1911.09512v1cs.LGcs.CEcs.PFstat.ML

TL;DR

Financial time-series forecasting remains challenging, and prior evidence favored LSTM over ARIMA while leaving the value of additional bidirectional training unresolved. This paper compares ARIMA, LSTM, and BiLSTM through performance and behavioral experiments, finding that BiLSTM forecasts best but reaches equilibrium more slowly.

  • Problem

    Although LSTM has outperformed ARIMA, it remained unclear whether additional bidirectional training would further improve financial time-series forecasting.

  • Method

    The paper experimentally compares ARIMA, unidirectional LSTM, and BiLSTM while analyzing their forecasting performance and training behavior.

  • Results

    BiLSTM models outperform ARIMA and LSTM, achieving a reported 37.78% average reduction in error compared with LSTM.

  • Takeaways & Limitations

    Additional bidirectional training is reported as beneficial for financial time-series forecasting, although BiLSTM reaches equilibrium more slowly than LSTM.

  • Takeaways & Limitations

    RNN training is challenging because vanishing gradients hinder learning long-term dependencies, while exploding gradients can produce very large gradients.

Abstract

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Machine and deep learning-based algorithms are the emerging approaches in addressing prediction problems in time series. These techniques have been shown to produce more accurate results than conventional regression-based modeling. It has been reported that artificial Recurrent Neural Networks (RNN) with memory, such as Long Short-Term Memory (LSTM), are superior compared to Autoregressive Integrated Moving Average (ARIMA) with a large margin. The LSTM-based models incorporate additional "gates" for the purpose of memorizing longer sequences of input data. The major question is that whether the gates incorporated in the LSTM architecture already offers a good prediction and whether additional training of data would be necessary to further improve the prediction. Bidirectional LSTMs (BiLSTMs) enable additional training by traversing the input data twice (i.e., 1) left-to-right, and 2) right-to-left). The research question of interest is then whether BiLSTM, with additional training capability, outperforms regular unidirectional LSTM. This paper reports a behavioral analysis and comparison of BiLSTM and LSTM models. The objective is to explore to what extend additional layers of training of data would be beneficial to tune the involved parameters. The results show that additional training of data and thus BiLSTM-based modeling offers better predictions than regular LSTM-based models. More specifically, it was observed that BiLSTM models provide better predictions compared to ARIMA and LSTM models. It was also observed that BiLSTM models reach the equilibrium much slower than LSTM-based models.

I. INTRODUCTION

The introduction frames financial time-series forecasting as challenging and asks whether bidirectional training can improve LSTM predictions beyond established approaches. It motivates and presents experiments comparing ARIMA, unidirectional LSTM, and BiLSTM models, including their training behavior.

  • I. INTRODUCTION: Forecasting performance depends on data type and context, including seasonality, economic shocks, unexpected events, and organizational changes.These factors make forecasting an essential but challenging component of time-series analysis.
  • I. INTRODUCTION: ARIMA represents conventional forecasting based on linear regression for model fitting followed by moving-average prediction.Its performance is described as reasonable for short-term forecasts but severely deteriorating for long-term predictions.
  • I. INTRODUCTION: LSTM networks model relationships between longer input and output sequences by learning from past data.The introduction contrasts these memory-based recurrent models with conventional approaches and motivates testing whether their performance can be further improved.
  • I. INTRODUCTION: The paper investigates whether additional training layers improve financial time-series prediction and how LSTM and BiLSTM learning behaviors differ.Its research questions cover bidirectional learning, treatment of input data, and the speed at which the architectures reach equilibrium.
  • I. INTRODUCTION: BiLSTM trains by traversing input data twice, first left to right and then right to left.This architecture is examined as an extension of the unidirectional LSTM to test whether opposite-direction training improves prediction.

II. RELATED WORKS

The related-work section contrasts traditional ARIMA-family methods with machine-learning approaches and reviews prior bidirectional LSTM results. It identifies the paper’s contribution as comparing ARIMA, LSTM, and BiLSTM for financial and economic time series, where bidirectional training remained uncertain.

  • II. RELATED WORKS: ARIMA-family methods perform reasonably well but are limited by nonlinear relationships, statistical assumptions, and reduced long-term accuracy.The cited limitations include regression-based modeling, assumptions such as constant standard deviation, and weaker long-term prediction.
  • II. RELATED WORKS: Machine- and deep-learning approaches provide data-driven alternatives to model-driven forecasting, with recurrent networks suited to time-series analysis.The reviewed work also notes that training neural networks and deep-learning algorithms can be difficult.
  • II. RELATED WORKS: Prior work reported that bidirectional LSTM outperformed unidirectional LSTM on multivariate time series, while a stacked architecture outperformed both.These studies motivate further comparison of bidirectional and unidirectional recurrent architectures.
  • II. RELATED WORKS: The paper extends earlier ARIMA-versus-LSTM research by comparing three standards: ARIMA, LSTM, and BiLSTM.Its novelty is framed around testing whether bidirectional learning helps numerical financial time series, not only applications such as scheduling or vulnerability prediction.

III. BACKGROUND

RNNs extend feed-forward networks to variable-length sequences by storing and using prior inputs, but their training can fail over long dependencies because of vanishing or exploding gradients.

  • III. BACKGROUND: RNNs manage variable-length sequential inputs by retaining prior information through memory gates.Unlike feed-forward networks, RNNs use sequential information from previous inputs.
  • III. BACKGROUND: The considered RNNs produce one output sequence representing the probability of each next element given previous inputs.The sequence probability is decomposed into conditional probabilities, with each hidden state calculated recursively.
  • III. BACKGROUND: RNNs can suffer vanishing gradients that erase learning signals across layers, making long-term dependencies difficult to capture.The training algorithm may assign smaller weight values, causing the model to stop learning.
  • III. BACKGROUND: Exploding gradients can instead accumulate into very large gradients, also making RNN training difficult.This problem is described as occurring when information or gradients pass through many layers and grow excessively.

B. Long Short-Term Memory (LSTM) Models

LSTM models extend RNN memory with gated cells that retain long-term dependencies by controlling what information is forgotten, added, and exposed as output.

  • B. Long Short-Term Memory (LSTM) Models: LSTM models address RNN vanishing gradients by extending memory to learn and retain longer-term input dependencies.Their memory supports reading, writing, and deleting information over longer periods.
  • B. Long Short-Term Memory (LSTM) Models: The forget, input, and output gates respectively remove or preserve existing information, add new information, and control cell contributions to the output.Together, the gates regulate memory updates and output generation.
  • B. Long Short-Term Memory (LSTM) Models: The forget gate uses prior state and current input to produce f_t, where 0 discards learned information and 1 preserves it.The gate applies a sigmoid function to make the removal decision; b_f is a constant bias.
  • B. Long Short-Term Memory (LSTM) Models: The input gate combines a sigmoid update decision with tanh-generated candidate values to update LSTM memory.The update forgets part of c_t−1 through the forget gate and adds the new candidate contribution.
  • B. Long Short-Term Memory (LSTM) Models: The output gate selects memory content with a sigmoid layer, applies tanh, and multiplies the result by the sigmoid output.The resulting output value o_t and representation h_t are bounded between −1 and 1 as described.

C. Deep Bidirectional LSTMs (BiLSTM)

Deep BiLSTMs apply LSTM processing in both forward and reverse directions, using two passes over the input sequence to improve long-term-dependency learning.

  • C. Deep Bidirectional LSTMs (BiLSTM): BiLSTMs process the input sequence twice: once left-to-right and once with the reversed sequence.The two passes correspond to forward and backward LSTM layers.
  • C. Deep Bidirectional LSTMs (BiLSTM): The study’s data context is financial time-series prediction, with Table I identifying the time-series data studied.The supplied table passage provides only its title and no cell values.
  • C. Deep Bidirectional LSTMs (BiLSTM): Applying LSTM processing in both directions is described as improving long-term-dependency learning and consequently model accuracy.The paper presents this as the motivation for comparing BiLSTM with regular LSTM architectures.

IV. LSTM VS. BILSTM: AN EXPERIMENTAL STUDY

The paper experimentally compares ARIMA, LSTM, and BiLSTM models for financial time-series forecasting using stock-index and IBM data with a held-out test split.

  • IV. LSTM VS. BILSTM: AN EXPERIMENTAL STUDY: The experiment compares ARIMA, LSTM, and BiLSTM for predicting financial time series.The comparison is explicitly framed as a performance study of these three model families.
  • IV. LSTM VS. BILSTM: AN EXPERIMENTAL STUDY: The datasets include daily, weekly, and monthly series from six stock indices or stocks, with historical periods extending from January 1985 to August 2018.The listed series are N225, IXIC, HSI, GSPC, DJ, and IBM; the IBM daily period begins in July 2009 in the supplied passage.
  • IV. LSTM VS. BILSTM: AN EXPERIMENTAL STUDY: Only the Adjusted Close variable is used as input, and each dataset is split into 70% training and 30% testing observations.The test portion is used to assess model forecasting accuracy.

C. Assessment Metrics

The paper assesses forecasting with loss and RMSE, while contrasting feed-forward, recurrent, LSTM, and bidirectional LSTM architectures. RMSE measures forecast differences and penalizes large errors, and percentage RMSE reduction measures improvement.

  • Assessment metrics: Loss penalizes poor predictions, with training seeking weights and biases that minimize it toward zero.
  • Assessment metrics: RMSE measures differences between actual and predicted values, penalizes large errors, and reports scores in the forecast values’ units.The metric uses N observations, actual values y_i, and predicted values ŷ_i.
  • Assessment metrics: Percentage reduction in RMSE is used to assess forecasting improvement.
  • Neural-network architectures: Feed-forward ANNs process inputs toward outputs without feedback, whereas RNNs preserve information from past inputs through recurrent loops.
  • Neural-network architectures: LSTM networks model long input-output relationships using input, forget, and output gates, while BiLSTMs train the sequence in both directions.BiLSTM processing runs from inputs to outputs and then over the reversed input sequence.

VI. RESULTS

The experiments compare ARIMA, LSTM, and BiLSTM forecasting using rolling evaluation and RMSE. BiLSTM achieves the strongest reported accuracy, substantially reducing error relative to both LSTM and ARIMA.

  • Results: Table II reports RMSE for ARIMA, LSTM, and BiLSTM, with substantial RMSE reduction in most cases except IXIC.weekly.
  • Results: Average RMSE was 20.17 for BiLSTM versus 39.09 for LSTM, a 37.78% reduction, with reductions ranging from 77.60% to 12.93% across series.
  • Results: BiLSTM produced an average 93.11% reduction over ARIMA, compared with an 88.07% reduction for LSTM over ARIMA.
  • Experimental setup: The rolling procedure splits each series into 70% training and 30% testing data, then evaluates one-step forecasts using RMSE.
  • Experimental setup: The implementation switches between LSTM and bidirectional LSTM models, fits them with mean-squared-error loss, and forecasts using the trained model.
  • Forecast illustrations: Figures 2(a)–(c) show IBM forecasts from ARIMA, LSTM, and BiLSTM against the test data.

VII. DISCUSSION

The discussion attributes BiLSTM’s stronger forecasting to traversing inputs in both directions, while noting that its value for numerical financial series was not initially clear. BiLSTM also trains differently and reaches equilibrium more slowly than unidirectional LSTM.

  • Discussion: BiLSTM outperforms unidirectional LSTM in financial time-series forecasting despite uncertainty about whether future-to-past training helps numerical data.
  • Discussion: BiLSTM may capture underlying context better by traversing inputs from left to right and then right to left.

A. Loss vs. Batch Steps (Epoch = 1)

For IBM forecasting, LSTM loss stabilizes earlier than BiLSTM, while the bidirectional model continues adapting across more batches and epochs.

  • A. Loss vs. Batch Steps (Epoch = 1): For Epoch = 1, LSTM loss stabilizes after the third batch and reaches 0.0244 at iteration 42.Its loss remains stable after reaching 0.0256 following the third batch.
  • A. Loss vs. Batch Steps (Epoch = 1): BiLSTM loss starts at 0.0404, peaks at 0.0874 on the third batch round, then decreases without reaching the LSTM value of 0.0256.The authors suggest that BiLSTM requires additional training data to reach equilibrium.
  • A. Loss vs. Batch Steps (Epoch = 1): At Epoch = 1, loss standard deviations are 0.007 for LSTM and 0.012 for BiLSTM, indicating faster equilibrium for LSTM.The reported comparison links the larger BiLSTM variation to its slower stabilization.
  • B. Loss vs. Batch Steps (Epoch = 2): For Epoch = 2 round 1, LSTM stabilizes after 3 batches at 0.019, whereas BiLSTM stabilizes after 8 batches at 0.044.The two models therefore show different batch-level learning behavior under the same epoch setting.
  • B. Loss vs. Batch Steps (Epoch = 2): In Epoch = 2 round 2, LSTM remains near equilibrium at 0.0237, while BiLSTM continues learning and stabilizes after 9 batches at 0.0295.The corresponding standard deviations are 0.004 for LSTM and 0.013 for BiLSTM.

C. Batch Sizes

The same data are divided into larger batches for LSTM and smaller batches for BiLSTM, reflecting the latter model’s two-direction training requirement.

  • C. Batch Sizes: LSTM divides the data into 41–42 batches, whereas BiLSTM divides the same data into 71–75 smaller batches.The authors attribute this difference to the bidirectional network’s need to process inputs from both directions.
  • C. Batch Sizes: Because BiLSTM traverses inputs left-to-right and right-to-left, each batch handles almost half as much training data as a regular LSTM batch.The paper relates this constraint to LSTM limitations in remembering long sequences.
  • C. Batch Sizes: The reported experiment compares ARIMA, LSTM, and BiLSTM performance, accuracy, and behavioral training, with BiLSTM improving forecasting accuracy by 37.78% on average.The study also reports that BiLSTM training is slower and requires additional batches to reach equilibrium.
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