Abstract

Financial time series are nonlinear, non-stationary and highly contaminated with high-frequency noise thus they are difficult to forecast accurately. Although advanced machine learning models have shown a high predictive accuracy, very little has been done on systematic signal conditioning before making a prediction. This paper suggests a systematic multi-lag smoothing model of predicting time-series of stock markets with six moving averages, namely, SMA, EMA, WMA, DEMA, HMA, and AMA. The filter properties of these methods are measured in time and frequency domain with different lag windows (5-100 days). A baseline model that is done using regression is used to isolate the effect of smoothing on predictive accuracy. MSE, MAPE, R2, and Directional Accuracy are used to determine performance. Comparison of performance on benchmark indices (NIFTY 50 and S&P 500) through cross-dataset validation shows that HMA demonstrates consistently lower error in short- and medium-term forecasting, while AMA shows improved performance in long-term trend modeling. Statistical significance is formally validated for HMA versus SMA at the 25-day lag, while other observations are based on comparative empirical results rather than formal hypothesis testing. Paired t-tests are statistically confirmed to be significant (p < 0.05), but moderate effect sizes (Cohen d) (0.42–0.55) are significant. The proposed framework unites the classical FIR filter theory and computational financial modeling, which provides a statistically valid and computationally efficient framework applicable in a real-time financial analytics system.

Keywords

Financial Signal Processing, Finite Impulse Response (FIR) Filters, Moving Average Filtering, Frequency-Domain Analysis, Time-Series Forecasting, Lag Sensitivity Analysis, Multi-Objective Performance Evaluation,

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