Low-frequency Trends Research Articles

TFformer: A time–frequency domain bidirectional sequence-level attention based transformer for interpretable long-term sequence forecasting

Transformer methods have shown strong predictive performance in long-term time series prediction. However, its attention mechanism destroys temporal dependence and has quadratic complexity. This makes prediction processes difficult to interpret, limiting their application in tasks requiring interpretability. To address this issue, this paper proposes a highly interpretable long-term sequence forecasting model, TFformer. TFformer decomposes time series into low frequency trend component and high frequency period component by frequency decomposition, and forecasts them respectively. The periodic information in high-frequency component is enhanced with the sequential frequency attention, and then the temporal patterns of the two components are obtained by feature extraction. According to the period property in time domain, TFformer through periodic extension to predict the future period patterns using sequential periodic matching attention. Finally, the predicted future period pattern and the extracted trend pattern are reconstructed to future series. TFformer provides an interpretable forecasting process with low time complexity, as it retains temporal dependence using sequence-level attentions. TFformer achieves significant prediction performance in both univariate and multivariate forecasting across six datasets. Detailed experimental results and analyses verify the effectiveness and generalization of TFformer.

Open-source synthetic photoplethysmographic signal generator with analog output.

The photoplethysmographic (PPG) signal of the finger is being used to create embedded devices that estimate physiological variables. This project outlines an innovative method for developing a synthetic PPG generator that produces both actual reference digital signals and their equivalent analog signals using open-source technology. A series of PPG profiles is synthesized using three variant Gaussian functions. A low-frequency trend induced by respiratory frequency and background noise are then added. To generate a diverse range of continuously variable PPG profiles within specified boundaries and customizable levels of interference, all parameters undergo random fluctuations on a cycle-by-cycle basis, as per user-defined constraints. The generated signal is then converted into its equivalent analog form through the use of an RC filter that low-frequency filters a Pulse-Width Modulation square wave that is modulated directly by the generated signal. The software returns different PPG profiles and allows the signal comparison before vs after the addition of different-intensity modulated respiratory trends and background noise. The digital signal is faithfully converted into an equivalent analog voltage signal capable of reproducing not only the waveform profile but also the respiratory trend and various levels of noise.

Recalibration of missing low-frequency variability and trends in the North Atlantic Oscillation

Multi-decadal trends in the wintertime North Atlantic Oscillation (NAO) are under-represented by coupled general circulation models (CGCMs), consistent with a lack of autocorrelation in their NAO index series. This study proposes and tests two simple “reddening” approaches for correcting this problem in simulated indices based on simple one parameter short-term (AR; Auto-Regressive order 1) and long-term (FD; Fractional-Difference) time series filters. Using CGCMs from the Coupled Model Intercomparison Project Phase 6 (CMIP6), the FD filter successfully improves the autocorrelation structure of the NAO, and in turn the simulation of extreme trends, while the AR filter is less successful. The 1963–1993 NAO trend is the maximum 31-year trend in the historical period. Raw CGCMs underestimate the likelihood of this trend by a factor of ten but this discrepancy is corrected after reddening. CMIP6 future projections show that long-term (2024–2094) NAO ensemble mean trends systematically increase with the magnitude of radiative forcing: -2.4 to 3.5 hPa/century for low-to-high forcing after reddening (more than double the range using raw output). The related likelihood of future maximum 31year trends comparable to 1963–1993 ranges from 3 to 7% whereas none of these CMIP6 projections simulate this without reddening. Near-term projections of the next 31 years (2024–2054) are less sensitive than long term trends to the future scenario, showing weak-to-no forced trend. However, reddening increases the ensemble range by 74% (to +/-1 standard deviation/decade), which could increase/decrease regional climate change signals in the Northern Hemisphere by magnitudes that are underestimated when using raw CGCM output.

How Maize Farmers in the US Southwest Grew and Prospered Under El Niño but Suffered Under La Niña

Variability in temperature and soil moisture influenced the spread and productive potential of maize. A new low-frequency reconstruction of US Southwest summer temperatures from 3000 BC to present shows generally warmer temperatures until the first century AD. From then until AD 1000, temperatures were generally cooler, though a warming trend continuing to present begins ca. AD 400, interrupted by cooling ca. AD 900 and 1400. Proposing a “ENSO Index” for the US Southwest, we argue that El Niño-like conditions dominated much of the second millennium BC and the first millennium AD, depressing summer temperatures relative to northern hemisphere norms but providing favorable winter moisture for maize. La Niña-like conditions (much less favorable to maize) dominated most of the period from 800 BC – AD 100 and AD 1200 to ca. 1900. We connect these low-frequency trends with tendencies in how and where people lived, emphasizing developments in the ancestral Pueblo area.

Deep factor asset pricing with policy guidance based on multi-source heterogeneous information

We propose a novel latent factor pricing model to extract latent pricing factors and corresponding factor loadings from multi-source heterogeneous information through a deep learning architecture. Notably, we pioneer the extraction of policy pricing factors from China’s national strategies (“Five-Year Plans”, “Government Work Reports”, and “Monetary Policy Reports”) using natural language processing and a dynamic topic model. The proposed mixed-frequency deep factor asset pricing (MIDAS-DF) model learns from mixed-frequency heterogeneous data and captures nonlinear joint patterns between inputs and outputs, providing more nuanced insights into asset pricing. The empirical analyses of the Chinese A-share market from January 1, 2003 to July 31, 2022 show that the MIDAS-DF model outperforms competing models in pricing individual stocks, various test portfolios, and investment portfolios. The results also demonstrate that low-frequency policy information anchors long-term pricing trends, while high-frequency market and sentiment information refine short-term pricing accuracy. They work together to enhance the pricing performance.

Landscape position mediates drought vulnerability in California valley oak (Quercus lobata)

Future climate change will exacerbate drought stress in water-limited ecosystems. However, topography can alter the fine-scale climatic and hydrologic conditions that mediate plant response to meteorological drought. Here, with six new valley oak (Quercus lobata) tree-ring width chronologies, we assess how topography acts as a mediating factor on tree growth and drought sensitivity. Because valley oaks are known to be highly dependent on subsurface water, we predicted that trees growing in riparian sites would be less sensitive to precipitation variability due to greater access to groundwater. Trees were sampled in the Tehachapi Mountains of California across a landscape gradient of sites ranging from 375–1650 m elevation and across upland (55–69 m mean height above nearest drainage) and riparian (2–6 m mean height above the nearest drainage) hillslope positions. Interannual tree growth patterns and drought sensitivity varied substantially in association with hillslope position and elevation. Valley oak radial growth showed a consistently weaker response to precipitation at riparian sites. The influence of hillslope position on drought sensitivity varied with elevation, such that the riparian buffering effect was weakest at sites higher in the watershed and strengthened, progressively, toward the lower elevation sites with greater climatic water deficit. Upland tree growth exhibited a strong response to high-frequency interannual precipitation variability at the high elevation site, whereas trees at lower elevation upland sites responded more to low-frequency decadal trends in precipitation, possibly reflecting hydrogeological processes by which precipitation feeds groundwater lower in the watershed. Our results are consistent with groundwater-dependence of valley oak and indicate that riparian habitats are the most likely refugia for the species during prolonged drought.

Trial- vs. cycle-level detrending in the analysis of cyclical biomechanical data

Biomechanical time series may contain low-frequency trends due to factors like electromechanical drift, attentional drift and fatigue. Existing detrending procedures are predominantly conducted at the trial level, removing trends that exist over finite, adjacent time windows, but this fails to consider what we term ‘cycle-level trends’: trends that occur in cyclical movements like gait and that vary across the movement cycle, for example: positive and negative drifts in early and late gait phases, respectively. The purposes of this study were to describe cycle-level detrending and to investigate the frequencies with which cycle-level trends (i) exist, and (ii) statistically affect results. Anterioposterior ground reaction forces (GRF) from the 41-subject, 8-speed, open treadmill walking dataset of Fukuchi (2018) were analyzed. Of a total of 552 analyzed trials, significant cycle-level trends were found approximately three times more frequently (21.1%) than significant trial-level trends (7.4%). In statistical comparisons of adjacent walking speeds (i.e., speed 1 vs. 2, 2 vs. 3, etc.) just 3.3% of trials exhibited cycle-level trends that changed the null hypothesis rejection decision. However 17.6% of trials exhibited cycle-level trends that qualitatively changed the stance phase regions identified as significant. Although these results are preliminary and derived from just one dataset, results suggest that cycle-level trends can contribute to analysis bias, and therefore that cycle-level trends should be considered and/or removed where possible. Software implementing the proposed cycle-level detrending is available at https://github.com/0todd0000/detrend1d.

A Novel Ensemble Machine Learning Model for Oil Production Prediction with Two-Stage Data Preprocessing

Petroleum production forecasting involves the anticipation of fluid production from wells based on historical data. Compared to traditional empirical, statistical, or reservoir simulation-based models, machine learning techniques leverage inherent relationships among historical dynamic data to predict future production. These methods are characterized by readily available parameters, fast computational speeds, high precision, and time–cost advantages, making them widely applicable in oilfield production. In this study, time series forecast models utilizing robust and efficient machine learning techniques are formulated for the prediction of production. We have fused the two-stage data preprocessing methods and the attention mechanism into the temporal convolutional network-gated recurrent unit (TCN-GRU) model. Firstly, the random forest (RF) algorithm is employed to extract key dynamic production features that influence output, serving to reduce data dimensionality and mitigate overfitting. Next, the mode decomposition algorithm, complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), is introduced. It employs a decomposition–reconstruction approach to segment production data into high-frequency noise components, low-frequency regular components and trend components. These segments are then individually subjected to prediction tasks, facilitating the model’s ability to capture more accurate intrinsic relationships among the data. Finally, the TCN-GRU-MA model, which integrates a multi-head attention (MA) mechanism, is utilized for production forecasting. In this model, the TCN module is employed to capture temporal data features, while the attention mechanism assigns varying weights to highlight the most critical influencing factors. The experimental results indicate that the proposed model achieves outstanding predictive performance. Compared to the best-performing comparative model, it exhibits a reduction in RMSE by 3%, MAE by 1.6%, MAPE by 12.7%, and an increase in R2 by 2.6% in Case 1. Similarly, in Case 2, there is a 7.7% decrease in RMSE, 7.7% in MAE, 11.6% in MAPE, and a 4.7% improvement in R2.

Analyzing the dynamical relationships between meteorological and hydrological drought of Wadi Mina basin, Algeria using a novel multiscale framework

Understanding the relationship between hydrological and meteorological drought in drought-prone regions is critical for proper reservoir management. This study presents a novel multiscale framework for investigating the associations between hydrological and meteorological drought based on the Time-Dependent Intrinsic Correlation (TDIC) method. Firstly, the characteristics of short, medium and long term standardized precipitation index (SPI) and the standardized runoff index (SRI) of the Wadi Mina basin (Algeria) have been analyzed based on data from 6 rainfall and hydrometric stations. Then an Improved Complete Ensemble Empirical Mode Decomposition with adaptive noise (ICEEMDAN) method is used to decompose the most correlated SPI and SRI series to different scales. A stronger association between the two types of droughts is evident in the low-frequency trend component regardless of the station, but their evolution pattern does not remain the same. Subsequently, a TDIC based running correlation analysis is performed between the modes to examine the SPI–SRI associations over the time domain and across the time scales. TDIC analysis has proven the dynamic behavior in the SPI–SRI associations bearing frequent alterations in nature and strength across the process scales and along the time domain. In general, at the intra-annual scales the SPI–SRI correlations are mostly weak positive with localized alterations to negative along the time domain, whereas the relationship is dominantly strong positive and long range at inter-annual scales up to 4 years. This dynamic behavior in the SPI–SRI association and the evolution pattern of trend decipher that the rainfall processes are not directly transferred to streamflow drought, but it also gets controlled by many other local meteorological processes.

Description of multi-periodic signals generated by complex systems: NOCFASS - New possibilities of the Fourier analysis

<p style='text-indent:20px;'>Here, we show how to extend the possibilities of the conventional F-analysis and adapt it for quantitative description of multi-periodic signals recorded from different complex systems. The basic idea lies in filtration property of the Dirichlet function that allows finding the leading frequencies (having the predominant amplitudes) and the shortcut frequency band allows to fit the initial random signal with high accuracy (with the value of the relative error less than 5%). This modification defined as NOCFASS-approach (Non-Orthogonal Combined Fourier Analysis of the Smoothed Signals) can be applied to a wide class of different signals having multi-periodic structure. We want to underline here that the shortcut frequency dispersion has linear dependence <inline-formula><tex-math id="M1">\begin{document}$ \Omega_{k} = c.k+d $\end{document}</tex-math></inline-formula> that differs from the conventional dispersion accepted in the conventional Fourier transformation <inline-formula><tex-math id="M2">\begin{document}$ \omega(k) = \frac{2\pi k}{T} $\end{document}</tex-math></inline-formula>. (<i>T</i> is a period of the initial signal). With the help of integration procedure one can extract a low-frequency trend from trendless sequences that allows to applying the NOCFASS approach for calculation of the desired amplitude-frequency response (AFR) from different "noisy" random sequences. In order to underline the multi-periodic structure of random signals under analysis we consider two nontrivial examples. (a) The peculiarities of the AFR associated with Weierstrass-Mandelbrot function. (b) The random behavior of the voltammograms (VAGs) background measured for an electrochemical cell with one active electrode. We do suppose that the proposed NOCFASS-approach having new attractive properties as the simplicity of realization, agility to the problem formulated will find a wide propagation in the modern signal processing area.</p>

Ultra-high-resolution reflected-light imaging for dendrochronology

Dendroclimatic reconstructions play a key role in contextualizing recent climate change by improving our understanding of past climate variability. The Blue Intensity (BI) measurement technique is gaining prominence as a more accessible alternative to X-ray densitometry for producing climatically highly-sensitive tree-ring predictors. Nevertheless, accurately representing low-frequency trends and high-frequency extremes using scanner-based BI remains a challenge due to color biases and resolution limitations. Herein we introduce several methodological advances in sample surfacing, imaging, and image processing which yield measurement series analogous to BI from ultra-high-resolution (UHR; ∼74 700 dpi) images. Such series capture changes in tree-ring anatomical density by representing wood anatomical structure using binary (i.e., black-white) segmentation of sample images. We refer to this novel technique as Binary Surface Intensity (BSI). By utilizing a UHR system and entirely eliminating color and light intensity as variables, the most substantial drawbacks of scanner BI (i.e., discoloration and resolution biases) are bypassed, resulting in more accurate representations of low-frequency climatic trends and high-frequency extremes. Comparisons of several chronologies developed with the BSI and BI techniques, including a multiparameter dataset from Björklund et al. (2019), showed that BSI datasets outperform BI in terms of common signal (r-bar), but also contain strong climatic signals that can exceed those obtained from BI and X-ray density, and even match density datasets based on quantitative wood anatomy. However, measurement software advancements are still required to unlock the full potential of tree-ring parameters produced using the BSI technique. Ongoing development of this new technique will not only aid the attainment of long unbiased chronologies by overcoming color biases and resolution limitations, but also holds promise for unlocking UHR analyses of surface anatomical (sQWA) parameter datasets from reflected-light images. These advances will lead to more accurate tree-ring-based paleoclimatic reconstructions and could also serve a wider range of dendrochronological applications.

Groundwater Depth Prediction Based on Wavelet Decomposition-LSTM Network

The time series of groundwater depth has the characteristics of trend, abrupt, and non-stationary. Based on the advantages of wavelet decomposition and long short-term memory neural network (LSTM), a new coupling model (wavelet decomposition-LSTM) for groundwater depth prediction is proposed. Firstly, wavelet decomposition is applied to decompose the groundwater data into high-frequency periodic signals and low-frequency trend signals, to reduce the complexity of the time series. Secondly, the decomposed high-frequency and low-frequency signals are taken as inputs to train the model respectively, and then the total prediction value is acquired. The improved model reduces the limitations of LSTM processing complex signals and improves prediction accuracy. Taking the No. 5 well of Lu Wangfen Town and the No. 3 well of Muye Town as the research object, the achieved results from the proposed model were compared with the results of the LSTM model and the back-propagation (BP) neural network model. This comparison shows that the performance of the new model is better than the others, and the average relative errors of the coupling model are 2.11% and 2.49% respectively. The proposed method has high prediction accuracy and generalization ability and is a more effective method for groundwater depth prediction.

Resonance characteristics of tsunami in bay of Japan by the Hunga Tonga-Hunga Ha’apai volcano eruption on 15th January 2022

The massive eruption of the Hunga Tonga-Hunga Ha’apai (HTHH) volcano in Tonga on 15 January 2022 at 04:15 UTC had a global impact and triggered an atmospheric wave and a tsunami. We first analyzed observation data from meteorological stations and tide gauges at 12 locations. Low-frequency trends in the observation data were removed by using a high-pass filter. Fourier and wavelet spectral analyses were applied to determine the frequency characteristics of the filtered data. Modal analysis was developed and used to investigate natural oscillation periods based on bathymetry. The results showed that the Lamb wave generated by the atmospheric pressure wave arrived ~ 7 and ~ 44 h after the eruption. The tsunami arrived ~ 11 and ~ 45 h after the eruption, which corresponded to the arrival time of the Lamb wave. The dominant periods of the Lamb waves were ~ 7.7 and ~ 7.5 min, and for the tsunamis they were ~ 9.9 and ~ 28.7 min. The periods derived from the spectral analysis matched the natural oscillation of the eigenperiod derived from the modal analysis, in eight out of the twelve stations. This study provides valuable insight and information regarding the nonseismic and far-field effects of tsunamis generated by volcanic eruptions.

Saving for retirement in Europe: the long-term risk-return tradeoff

AbstractA comparison of the performances of pension products that ignores long-term trends might significantly overestimate the long-term impact of volatility risks while underestimating the impact of persistent, low-frequency trends. This paper proposes a comparison making use of projection models based on the long-term risk–return tradeoff proposed by Campbell and Viceira (2005) to explicitly take into account slow-moving economic trends. In order to illustrate the approach and its implications, we discuss the capital protection provided by life-cycle target-date fund strategies and minimum guarantee strategies.

QUANTITATIVE INVESTMENT DECISIONS BASED ON MACHINE LEARNING AND INVESTOR ATTENTION ANALYSIS

According to the trading rules and financial data structure of the stock index futures market, and considering the impact of major emergencies, we intend to build a quantitative investment decision-making model based on machine learning. We first adopt the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) signal decomposition technology to separate the short-term noise, cycle transformation and long-term trend from the original series, and use the CSI 500 Baidu index series to reflect the investors’ attention, which provides data support for establishing a more effective forecasting model. Then, the CEEMDANBP neural network model is designed based on the obtained effective information of low-frequency trend series, investor attention index and CSI 500 stock index futures market transaction data. Finally, an Attention-based Dual Thrust quantitative trading strategy is proposed and optimized. The optimized Attention-based Dual Thrust strategy solves the core problem of breakout interval determination, effectively avoids the risk of subjective selection, and can meet investors’ different risk preferences. The quantitative investment decision-making model based on CEEMDAN-BP neural network utilizes the advantages of different algorithms, avoids some defects of a single algorithm, and can make corresponding adjustments according to changes in investors’ attention and the occurrence of emergencies. The results show that considering investor attention can not only improve the predictive ability of the model, but also reduce the cognitive bias of the market, effectively control risks and obtain higher returns.

ALGORITHM FOR ASSESSING THE QUALITY OF MULTIDIMENSIONAL EXPERIMENTAL DATA BASED ON STATISTICAL ANALYSIS OF MARKOV PROCESSES

The article describes a real-time piecewise-stationary vector process with several states stipulated by the appearance of one or more components (research intervals) of the “intense signal” – a low-frequency trend. We have found a separable function equivalent to the process under study in order to determine the state of a random vector process by investigating the character and structure of relationships between the process components, when the finite-dimensional distributions of this process were a priori unknown. This function is represented as a projection of a random process defined in a probability space on a subspace of sample functions located at the smallest distance from the process. Then, according to projection theorem with the account of Markov property, it is possible to construct a H0: Pt(t + h) = Pt(t) statistical hypothesis, assuming that statistical characteristics of (t + h) components interconnection get no significant changes until the detection of an “intense signal” in t + h interval. It is known that the problem of finding the projection corresponds to the problem of finding the mean square regression coefficients. Statistical analysis allowed to find the procedure and get the Bayesian algorithm in order to determine the state of Markov vector process by regression analysis methods. The efficiency of proposed approach is demonstrated on a simple example.

Low frequency ambient noise dynamics and trends in the Indian Ocean, Cape Leeuwin, Australia

Examination of 18 years of nearly continuous low frequency deep ocean ambient noise offshore Cape Leeuwin, Australia, finds evidence of a decreasing nonlinear trend suggestive of long-term cyclic dynamics. The nonlinear trend is found to be consistent with trends in oceanographic sea surface temperature, which are thought to drive changes in Antarctic sea ice extent. Assessment of oscillatory dynamics finds causal covariance between ambient noise levels and Indian Ocean sea surface temperature dipoles. Dynamics of annual ambient noise and Antarctic sea ice extent are examined suggesting a phase-locked relationship revealing nonlinear characteristics of the presumed dependence. Collectively, the hypotheses that deep water ambient noise dynamics in the Indian Ocean are influenced by Antarctic sea ice extent and melt dynamics and that linear models do not fully capture long-term ambient noise trends and dynamics are supported.

Dynamic modeling of experience sampling methodology data reveals large heterogeneity in biopsychosocial factors associated with persistent fatigue in young people living with a chronic condition

ObjectiveTo evaluate associations between self-reported biopsychosocial factors and persistent fatigue with dynamic single-case networks. Methods31 persistently fatigued adolescents and young adults with various chronic conditions (aged 12 to 29 years) completed 28 days of Experience Sampling Methodology (ESM) with five prompts per day. ESM surveys consisted of eight generic and up to seven personalized biopsychosocial factors. Residual Dynamic Structural Equation Modeling (RDSEM) was used to analyze the data and derive dynamic single-case networks, controlling for circadian cycle effects, weekend effects, and low-frequency trends. Networks included contemporaneous and cross-lagged associations between biopsychosocial factors and fatigue. Network associations were selected for evaluation if both significant (α < 0.025) and relevant (β ≥ 0.20). ResultsParticipants chose 42 different biopsychosocial factors as personalized ESM items. In total, 154 fatigue associations with biopsychosocial factors were found. Most associations were contemporaneous (67.5%). Between chronic condition groups, no significant differences were observed in the associations. There were large inter-individual differences in which biopsychosocial factors were associated with fatigue. Contemporaneous and cross-lagged associations with fatigue varied widely in direction and strength. ConclusionsThe heterogeneity found in biopsychosocial factors associated with fatigue underlines that persistent fatigue stems from a complex interplay between biopsychosocial factors. The present findings support the need for personalized treatment of persistent fatigue. Discussing the dynamic networks with the participant can be a promising step towards tailored treatment. Trial registrationNo. NL8789 (http://www.trialregister.nl)

Technical and environmental features of the application of renewable energy for decentralized power supply zones

A feature of the geographical location of the Khanty-Mansiysk Autonomous Okrug - Yugra is the presence of a large number of zones of decentralized power supply. For a comparative environmental assessment of renewable energy installations, it is necessary to take into account the emissions of the entire life cycle. Throughout the presented cycle from mining to the production of power plant structures and then the disposal of the facility, a significant part of CO2 emissions is present. The problem of dismantling and recycling of spent structures of wind power plants is becoming essential. Wind turbines cause the death of birds, violate the conditions of comfortable living for people and animals&#x0D; From a technical point of view, it is necessary to take into account the regime parameters: indicators of the quality of electricity at the point of connection, voltage levels at load nodes, operating modes of energy storage devices. To assess the operating parameters of an isolated power supply system with renewable energy sources, this paper proposes to use the wavelet transform method. The Haar wavelet was used as a basic function in the paper. A mathematical model is presented that makes it possible to obtain a low-frequency (trend) component and a high-frequency component using the wavelet transform. The model allows for the optimal choice of a hybrid energy storage device for a renewable energy source - a battery and a supercapacitor.

Approach to Predict Land Subsidence in Old Goafs considering the Influence of Engineering Noise

Considering that it is easily disturbed by various engineering factors such as weather, hydrology, and construction during engineering monitoring, the collected subsidence data contain various noises. In order to reduce the influence of engineering noise on the accuracy of subsidence prediction, it is proposed to use the Daubechies (DB) wavelet to decompose the original subsidence time series; the items with the low-frequency trend, after decomposition, are predicted using long short-term memory (LSTM) model, items with high-frequency noise used the autoregressive (AR) time series model to make predictions, and the prediction results of the low-frequency trend term and the high-frequency noise term are summed to obtain the total time series predicted value. Combining the actual engineering subsidence monitoring data of the old goaf, compared with the prediction results of the LSTM and RNN models without DB wavelet decomposition and the gray model GM (1,1), the results show that the DB wavelet has an obvious improvement effect in reducing the influence of measurement data noise on prediction error. Compared with the single prediction model LSTM, RNN, and GM (1,1), the proposed prediction model has higher prediction accuracy, smaller error, and better trend. It can be used as a calculation method to improve the prediction accuracy of surface subsidence in old goaf.