Forecasting Minute-Level Stock Prices with Denoised Data: A Comparative Study of Developed vs. Developing Financial Markets.

4.1 Theoretical framework: Risk premium and market efficiency

The disparate performance of developed and developing equity markets is one of the oldest and most basic theories of economics. At the centre of this distinction is the idea of the Equity Risk Premium (ERP) - the excess return over the risk-free rate that investors expect to be paid to compensate them for the higher level of systematic risk they are taking.^5,11–13 In emerging markets (e.g., USA, Japan, Singapore) the risk will be of a higher nature due to several elements such as political instability, currency fluctuation, and liquidity.^5,11–13 In a more technical manner, while developed markets are characterised by mature institutions and fast information diffusion, developing economies often have persistent inefficiencies and are acutely susceptible to external shocks.^13–16 A prominent study published confirmed this delusion by showing that emerging markets exhibit much higher volatility clustering during global crises than their developed counterparts.

Recent publications further highlight these dynamics. For instance, a recent causality investigation of stock prices and macroeconomic indicators in the Indian stock market reveals a tight relationship between volatility in developing economies and macroeconomics, which, in turn, influences asset pricing.¹⁷ Similarly, research on behavioural biases in the Indian market shows that psychological factors, for instance, overconfidence and disposition effects, amplify under-allocation to developing markets.^3,18 Furthermore, recent work on cointegration in the Indian stock market focuses on spillover effects, in line with the idea that the volatility of developing markets can spread but can also provide unique opportunities for diversification.¹⁹

However, the Adaptive Market Hypothesis (AMH) challenges the traditional Efficient Market Hypothesis (EMH) by positing that market efficiency is a dynamic process rather than an absolute state¹ further suggests that inefficiencies, e.g., time delays in price discovery and volatility clustering, are not only risks but also opportunities for exploitable patterns. This view has empirical support, suggesting that in developing markets, weak-form efficiency is very rare and, as a result, arbitrage opportunities still exist and can be exploited with sophisticated computational models.^20,21 This framework implies that behavioural biases may cause investors to under-allocate capital to developing markets, where informational inefficiencies could be exploited to generate alpha.^2,18

4.2 Deep learning architectures in financial forecasting

Traditional econometric models (e.g., ARIMA, GARCH) have been the standard tools for financial prediction.^22,58 have extensively detailed the use of ARIMA models for stock trend forecasting. However, these linear models can struggle to account for the complex nonlinearities and regime shifts in high-frequency financial data.²³ Consequently, Deep Learning (DL) has emerged as a great alternative, with its adaptive feature learning and its superior generalization on out-of-sample data.

A recent bibliometric review on artificial intelligence and finance, published by,²⁴ charts this evolution, showing a proliferation of neural network applications for predictive modelling and volatility analysis after 2010. This corresponds to our move towards DL for processing noisy & high frequency data for time series forecasting.

4.3 Signal processing and optuna-optimised denoising

Minute-level financial data is almost always noisy, with microstructure effects, such as bid-ask bounces, that obscure fundamental price trends. To perform effective forecasting, rigorous denoising is necessary to improve the Signal-to-Noise Ratio (SNR).

4.4 Overfitting in time series forecasting

Overfitting is a major issue for the prediction of financial time series, as models can learn noise instead of generalizable patterns - a particular danger with volatile developing markets.^10,23 This is especially true of deep learning models for regime shifts. To mitigate this, it is important to implement rigorous validation protocols.

This research follows the standards promoted by,³⁸ using Walk-Forward Validation rather than traditional k-fold cross-validation.⁷⁵ This way, temporal order is preserved without look-ahead bias, and the model is tested on “future” data that does not exist or that it had never seen during training.³⁹ Combined with regularisation techniques inherent in modern architectures (e.g., dropout layers in LSTMs), this validation strategy ensures that the alpha generated is robust and not merely an artefact of overfitting.

4.5 Stock selection and portfolio construction

To ensure a fair and representative comparison across markets, stock selection must account for the varying market structures⁴⁰ demonstrated that K-means clustering based on market capitalisation and beta effectively groups stocks by risk-return profiles, improving prediction accuracy by 10–20% compared to random selection.

For portfolio construction and validation, this study adheres to the rigorous standards advocated by,³⁸ employing Walk-Forward Validation rather than traditional k-fold cross-validation to preserve temporal order and prevent look-ahead bias. We employ Inverse Volatility Weighting for portfolio allocation. In high-frequency regimes, estimating stable covariance matrices is notoriously unstable; inverse volatility weighting prioritises risk control, dynamically allocating capital to lower-volatility assets to minimise drawdowns—a critical feature for short-term strategies.^41,42 Compared to alternatives such as Mean-Variance Optimisation, this method offers greater robustness in volatile, developing markets, though it may underperform in low-volatility environments.

4.6 Gap analysis

Despite extensive literature on financial forecasting (e.g.,⁷⁶), significant gaps remain in the systematic comparison of developed and developing markets using high-frequency data.

Table 1 summarizes the current literature on financial forecasting, pointing out the methodological voids in the literature and indicating how the current paper addresses them by Optuna-tuned denoising pipelines.

A. Data collection and stock selection

We first assemble the dataset by targeting the six equity markets of interest. Using Yahoo Finance, minute-level OHLC and volume data are downloaded for each market’s primary exchange. Within each country, we select the 20 largest companies by market cap and download their latest price series. To ensure representative sampling of market movements, the 30-day rolling beta of each stock relative to its relevant index (e.g., S&P 500, N225, STI) is computed, and stocks with high or low beta are noted. Only large-cap stocks with full data having consistent trading histories are retained for analysis.⁴⁰

Table 2 shows the balanced portfolio of high-liquidity stocks, selected across developing and developed markets (USA, Japan, Singapore, India, Brazil, Malaysia), and provides details of the tickers and their respective market cap ranges in each, which form the basis for the modelling presented later. Retrieve OHLC (Adjusted close) data at the minute level for a selection of stocks through Yahoo Finance and ensure that approx. 30 trading days are gathered for each stock in the market.

Table 3 gives a small glimpse of the raw, minute-level OHLC prices, showing the high-frequency temporal structure before the implementation of our denoising pipeline:

The method generates information for each of the six target markets (developed: US, Japan, Singapore; developing: India, Brazil, Malaysia), shortlists ~20 large-cap stocks by market capitalisation. Compute a 30-day rolling beta against the local benchmark index to ensure broad market representation. Only stocks with complete, high-quality data were retained.⁴⁰ It’s also observed that, for developing countries, selecting companies with strong financial ratios provides a sound basis for effective financial support and portfolio-based prediction.⁴³ An example of a sequential multi-stage denoising pipeline using Discrete Wavelet Transforms, a Variational Autoencoder, and Kalman Filters to produce a clean prediction is shown in Figure 2.

Figure 2. Data preprocessing and denoising flowchart.

A conceptual flowchart of the sequential multi-stage denoising pipeline combining Discrete Wavelet Transforms, Variational Autoencoders, and Kalman Filters.

B. Preprocessing and denoising

Prior to modelling, each raw price series is converted to log-returns and normalised. Minute-level data are notoriously noisy, so we implement a three-stage denoising strategy.

The hyperparameters for each denoising stage (wavelet type, decomposition level, threshold λ; VAE architecture; Kalman noise covariance) are automatically optimised using the TPE sampler in the Optuna library to maximise the signal-to-noise ratio.³⁶

Figure 3 shows how, during the optimisation phase, the specific data transformations are applied, and how Optuna and Wavelet transforms help to filter out microscope noise.

Figure 3. Denoising process of stock price data.

To effectively capture the underlying market dynamics without the distortion caused by microstructure noise, this study extracts the true trend using the Smoothed Sequence approach, following the methodology established by.³² By continuously adjusting to the market, this method filters out transient volatility and isolates the actual price trajectory. Specifically, for a given time series of raw stock prices $\{x_1,x_2,\dots \dots ..,x_{n\}}$ , the smoothed sequence $\{y_1,y_2,\dots \dots .,y_{n\}}$ utilising a window size of $k$ is computed as follows³²:

Where, $y_i$ represents the smoothed value; it moves in the same direction as the market to reflect the true trend. By extracting this smoothed sequence, we ensure that the deep learning models that follow are fed data that reflects true market movements, not erratic movements driven by high-frequency noise.

Figure 4 outlines the structural framework of the six deep learning models utilised in this study, detailing the 30-minute input windows, hidden layers, and evaluation checkpoints.

Figure 4. Model training architecture.

Figure 5 visually illustrates the discrete wavelet transform (DWT) process, showing how the raw signal is split into coarse and detail coefficients.

Figure 5. Real-trend analysis through denoising.

First, a Discrete Wavelet Transform (DWT) using Daubechies wavelets decomposes the return series $x\left(t\right)$ into coarse (approximation) and detail coefficients. Specifically, at the level $j$ , the transform is given by convolutions with a low-pass $h\left[n\right]$ and high-pass $g\left[n\right]$ filters^32,44:

The process essentially classifies the true noise sequence referenced by high-pass g [n] as high-frequency price signals from real low-pass h [n] signals. The methodology trains on real price movements that are repetitive and train-worthy and is intended to be retained in the neural network for real sequence-based price movement applications. Soft-thresholding is then applied to the detail coefficients to suppress high-frequency noise⁴⁵:

Prediction:

Update:

Here, $P_k$ is the error covariance, Q, R are the process/measurement covariances, and $K_k$ is the Kalman gain. This recursive filtering yields a final smooth state estimate ${\widehat{x}}_k$ that forms the clean price signal used for forecasting. Overall, the combination of DWT, VAE and Kalman filtering is an effective approach in amplifying the true signal by absorbing noise sequentially, both high-frequency and model-based noise.

C. Predictive models

In the forecasting stage, we deploy six state-of-the-art deep learning architectures, each designed to capture temporal patterns in the denoised price series. Specifically, we implement:

All denoising hyperparameters (wavelet family, autoencoder bottleneck size, and Kalman covariances) and model hyperparameters (learning rates, layer sizes, and dropout rates) are tuned using Optuna to ensure optimal performance on a held-out validation split. In total, these six architectures encompass both convolutional, recurrent, and attention-based approaches, each expected to capture different aspects of intraday dynamics. We exclude other methods (e.g., technical indicators or simpler ML models) to focus on these well-established deep learning models, which are known to capture nonlinear patterns in financial time series.

D. Model architecture and training

Each forecasting model is trained end-to-end on the Optuna-denoised price series. We use a consistent configuration: two hidden layers (e.g., two LSTM layers or two convolutional stacks), 20% dropout to mitigate overfitting, and the Adam optimiser with mean-squared-error loss (as in²⁵). The input to each model is a fixed-length window of 30 past log-returns, and the output is the predicted next-minute return. Training proceeds on the expanding set of historical data, as in walk-forward validation; no cross-market data leakage is allowed. This uniform architecture facilitates a fair comparison of model performance across markets and ensures that any differences arise from market characteristics rather than model design.

E. Walk-forward validation and performance evaluation

To rigorously assess forecasting accuracy in a simulated real-time setting, we use expanding-window (walk-forward) evaluation. At each validation step (approximately 1 trading day, ≈300 minutes), all models are retrained on the cumulative denoised data up to that point and then tested on the immediately following out-of-sample block. This process is repeated until the end of the sample, yielding an out-of-sample forecast for each step. We record the adjusted $R^2$ of each one-day forecast (typically 78–95%) and monitor overfitting by comparing training vs validation error (overfitting ratio < 10% indicates well-generalised models).

Finally, the last 150-minute forecast (simulating the final day) is used to compute trading performance. In each market, we generate long/short signals based on the predicted returns and form a capital-weighted portfolio. We then compute the risk-adjusted return using the Sharpe ratio, defined as

Market-specific risk-free rates are based on the prevailing 10-year government bond yields (e.g., ~6.65% in India, 13.88% in Brazil, and 3.58% in Malaysia at the end of 2025). All yield estimates are drawn from^5,55 for consistency. A Sharpe ratio above 1 is considered a favourable risk-return tradeoff. The above procedures ensure that our evaluation reflects true out-of-sample performance, free from look-ahead bias.

6.1 Why predicting minute-level price data is difficult

Forecasting on minute-level stock prices is inherently challenging because the raw price series are dominated by short-term noise - for example, in the case of short-term noise due to bid-ask spreads and imbalances in the order book - more so than by stable predictive structures.⁵⁶ Our raw data from Yahoo Finance exhibit erratic behaviour and a high degree of non-stationarity in mean and variance, which limits the ability of standard linear time-series models to a great extent.^57–59 As a result, we utilise nonlinear deep learning architectures and a growing walk-forward retraining strategy to extract weak yet economically relevant signals and maintain forecast validity during rapid regime changes.^2,25,60

6.2 Optuna for denoising and hyperparameter tuning

To explore the complex parameter spaces in our pipeline, we use Optuna, an automated hyperparameter optimisation tool based on Tree-structured Parzen Estimators (TPE).³⁶ Optuna has been used in two separate stages: first, to optimise the signal-to-noise ratio for denoising (optimise the parameters of wavelets, autoencoders and Kalman Filters) and second optimize the prediction error on a dataset not included in the training (optimise the learning rate, the number of layers and the dropout procedure in the Deep Learning models). This automated, define-by-run approach is crucial for managing mutually dependent factors and ensuring resource efficiency when manual grid search would be impractical computationally.

6.3 Denoising processes and their importance

Three complementary denoising techniques are used in order to suppress microstructure noise while retaining economic signals. First, Wavelet transformations (e.g. Daubechies) to deconstruct the series to suppress high frequency coefficients by soft-thresholding (for the purpose of effectively filtering the irregular noise but retaining underlying dynamics.^32,61 Second, denoising autoencoders generate a compressed latent representation because the reconstruction process imposes compression, separating main price signals from random variations.^62,63 Third, Kalman filters are recursive state-space estimators that smooth the series by adapting to changes in volatility without using fixed window lengths.^64,65 Collectively, these methods, tuned with Optuna, improve the signal-to-noise ratio by amplifying meaningful short-term movements that are important for the model’s predictive accuracy.

6.4 Deep learning models for minute-level forecasting

We use deep sequence models (including such models as TCN, GRU, LSTM (both standard and bidirectional), and hybrid architectures of CNN-LSTM/Transformer). Through such modeling we can forecast denoised minute-level movements. By contrast with the traditional linear methods of financial time series analysis (e.g., ARIMA), these nonlinear models account for nonstationary dynamics and complex dependencies, which have long been neglected by old-fashioned statistical tools or shallow neural networks.^25,66

RNN-based models (LSTM, GRU) use gates to learn long-term temporal dependencies while filtering out noise. Hybrid CNN–LSTM architectures are more effective than these: with convolutional layers, they can transform inputs into deeply learned local views before processing them as sequence data.³⁴ Temporal Convolutional Networks (TCN) leverage both dilated causal convolutions for efficient long-range memory (Bai et al., 2018) and Transformers, which utilise self-attention to capture volatility clustering and regime transitions.⁶⁶ Studies have now confirmed that fitting these methods to transient patterns characteristic of intraday markets has significantly improved risk-adjusted returns and reduced RMSE.⁶⁷

7.1 Signal-to-Noise Ratio (SNR) Analysis

To further ensure that the quality of stocks and the strength of exploitable patterns in denoised data were sufficient, we calculated the Signal-to-Noise Ratio (SNR) for selected stocks. In the context of finance, SNR measures the ratio between structured, predictable price movements (signal) against the random microstructure movement (noise), and is borrowed from signal processing. Higher SNR implies cleaner, more reliable forecasting signals - especially important in developing markets where there is typically greater inherent volatility, but also exploitable inefficiencies.

Table 4 compares the initial Signal-to-Noise Ratios (SNR) across the selected assets in developing markets’ imperialistic environments, illustrating the micro-structure noise present in volatile environments.

Table 5 summarises the Signal-to-Noise Ratios (SNR) of large-cap stocks from developed markets as a baseline for clarity, compared with those from developing economies.

We used inverse-volatility weighting to construct portfolios from the best models’ buy/sell signals. In simulated trading, there was a set amount of money to start with (for example, $1,000) over 30 days. The forecasts were for 150 minutes of the day, and the rules were realistic.

Table 6 details the outcomes of the 30-day simulated intraday trading strategy. The results demonstrate that developing markets yielded substantially higher Sharpe ratios and raw profits compared to their developed counterparts.

9.1 Limitations

Although this study provides empirical evidence of the efficacy of deep learning on denoised minute-level data for intraday forecasting in a developing market, there are certain limitations that must be recognised.

First, the analysis is based on a rather limited 30-day trading period. Although the look-ahead bias is reduced by the walk-forward validation method, this limited horizon does not necessarily eliminate regime shifts, structural changes in markets, or exceptional events (e.g., global crises) that may affect the patterns of inefficiencies.^1,69 The data’s robustness would improve by extending it over a multi-year span.

Second, simulated trading portfolios do not account for transaction costs, slippage, or market impact, which are particularly pronounced in high-frequency, minute-level strategies. In less developed financial markets, such as India, Brazil, and Malaysia, lower liquidity and wider bid-ask spreads can severely erode realised returns.⁴¹ In the real world, some portions of the portfolio might not actually generate the Sharpe ratios quoted here.

Third, the denoising pipeline (combination of wavelet transforms, variational autoencoders and Kalman filters), although optimized using Optuna, the risk of over-denoising or removing economically meaningful high frequency signals (e.g. microstructures dynamics critical for intraday alpha)^32,56 are adjusted with proper trend pick up and drop off which is essentially achieved as well but heavy market shocks cannot preserve the require information; Parameter sensitivity and possible signal distortion are still challenges in sequential denoising methods.

Fourth, stock selection targeted the large-cap stocks in the liquid markets and excluded thinner or more volatile segments. This can be an overestimate of exploitable inefficiencies, as the smaller the stock or what is excluded (e.g., from developing regions), the greater the political risk and the lower the predictability.⁵ This process essentially ignores Fama French model, suggest against small market gains are against large-cap stocks in the long run.⁷⁰

Finally, adjusted R² and Sharpe ratios show strong performance; the results are based on historical data from Yahoo Finance, which may include survivorship bias or adjustments that are not 100% indicative of live trading conditions. Overfitting (even with walk-forward validation and reported small gaps (<10%)) is a potential issue for deep learning models trained on noisy financial series.^10,38

These limitations point to directions for future research, including the inclusion of transaction costs, longer horizons, testing in real time for execution, and extending to additional markets or hybrid denoising techniques.