Deep Learning vs. Statistical Models for Multi-Horizon Price Forecasting of Second-Hand Electronics: A Systematic Benchmark

Mateusz Buczyński; Michał Woźniak; Konrad Kaczyński; Anna Wróblewska; Sebastian Kuk

q-fin.CPOct 7, 2026

Deep Learning vs. Statistical Models for Multi-Horizon Price Forecasting of Second-Hand Electronics: A Systematic Benchmark

Authors: Mateusz Buczyński, Michał Woźniak, Konrad Kaczyński, Anna Wróblewska, Sebastian Kuk

Organizations: Faculty of Economic Sciences, University of Warsaw, Dluga 44/50, Warsaw, 00-241, PL · WeSub, Branickiego 15, Warsaw, 02-972, PL · Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, Warsaw, 00-662, PL

Abstract

Forecasting resale prices of used electronics is critical for subscription-based platforms where pricing errors translate directly into risk. Unlike structured financial markets, second-hand electronics exhibit high volatility, sparse listing histories, and non-normal price dynamics - yet no systematic time-series benchmark exists for this domain. This paper presents the first multi-horizon benchmark of statistical and deep learning forecasting models for used electronics price prediction. We use a large-scale dataset of daily price listings from Polish online marketplaces (January 2022 to March 2025, 100+ smartphone and laptop models) and evaluate eleven models across six horizons from 1 to 365 days, covering classical methods (ARIMA, ETS, Theta), recurrent and convolutional networks (LSTM, TCN), and modern deep architectures (N-BEATS, N-HiTS, TFT, PatchTST, Informer). Three complementary evaluation protocols assess trajectory fitness, one-shot endpoint accuracy, and cross-horizon transfer. N-BEATS achieves the lowest MAPE beyond 30 days, reaching 8.51% at 365 days versus 14.94% for the best statistical baseline - a 43% reduction. At short horizons (1-7 days), all models converge near 0.72% MAPE and the naive baseline remains competitive. A single N-BEATS model trained at 365 days generalizes to all shorter horizons, eliminating the need for horizon-specific models. N-BEATS and N-HiTS also demonstrate superior hyperparameter stability.

Figures & tables

Reference	Domain	Approach	Task	Gap / Limitation
Hankar et al., 2022b , Ganesh & Venkatasubbu, 2019a , Dutulescu et al.,2023a	Used cars	ML (RF, NN, XGBoost)	Tabular regression	No time dimension; point-in-time price only
Truong et al., 2020a , Wang et al.,2021a	Real estate	ML / DL + images	Tabular regression	Structured market, rich listing attributes
Ghani, 2005a , Raykhel & Ventura,2009a	Used electronics (laptops)	Statistical, KNN	Tabular regression	Small scale; no time-series evaluation
Ali et al.,2018a	Used electronics (Kaggle)	NN	Tabular regression	Single competition dataset; no temporal modelling
Fathalla et al.,2020a	Multi-category e-commerce	Multimodal DL	Tabular regression	Features per listing; no aggregate time-series
Carta et al., 2019a , Fathalla et al.,2023a	Amazon products	ARIMA	Time-series	Single model; no DL comparison; stable market

Table 1: Summary of surveyed studies on used goods price prediction and related time-series forecasting

Figure 1: A schema of the time series preparation system

Abstract item	Predicted price	Market price
apple iphone 13 pro max 512gb grafitowy	4306.70	4250
samsung galaxy a13 128gb	730.45	400
samsung galaxy s22 ultra 256gb	3288.09	3200
acer aspire a515 4gb 128gb	1203.23	1150
apple macbook pro m2 512gb space gray	5416.09	6000

Table 2: Exemplary results of pricing using our matching algorithm with the best prediction per item compared with its business value

Statistic	Value
Date range	January 2022 – March 2025
Number of calendar days (series length)	1,186
Unique abstract items	357
of which smartphones	229
of which laptops	127
of which other	1

Table 3: Quantitative characteristics of the dataset used in this study

Figure 2: Exemplary historical postprocessed time series of used goods analysed in this paper

Figure 3: Illustrative definition of temporal cross-validation utilized in this paper

Metric name	Formula
Mean Absolute Percentage Error (MAPE)	$\frac{1}{n}\sum_{i=1}^{n}\left\|\frac{F_{i}-A_{i}}{A_{i}}\right\|=\frac{1}{n}\sum_{i=1}^{n}\text{APE}_{i}$ (9)
Winsorized MAPE (W-MAPE)	$\frac{1}{n}\sum_{i=1}^{n}\text{winsorize}\!\left(\text{APE},\text{limits}=[0.1,0.1]\right)$ (10)
Symmetric Mean Absolute Percentage Error (SMAPE)	$\frac{1}{n}\sum_{i=1}^{n}\frac{2\|F_{i}-A_{i}\|}{\|A_{i}\|+\|F_{i}\|}$ (11)
Root Mean Squared Error (RMSE)	$\sqrt{\frac{1}{n}\sum_{i=1}^{n}(F_{i}-A_{i})^{2}}$ (12)
Fourth Root Mean Fourth Power Difference (FRMFPD)	$\left(\frac{1}{n}\sum_{i=1}^{n}(F_{i}-A_{i})^{4}\right)^{\frac{1}{4}}$ (13)
Quantile of Absolute Percentage Error ( $Q_{\alpha}(\text{APE})$ )	$\inf\left\{x\in\mathbb{R}:P(\|\text{APE}\|\leq x)\geq\alpha\right\}$ (14)

Table 4: Evaluation metrics utilized in the framework

Horizon	Windows in OOS	No OOS
1	30	30
7	14	9
30	12	9
90	8	3
180	8	3
365	4	3

Table 5: Number of windows in OOS and number of OOS in the experiment

Model	Trials logged	Median (s)	Max (s)
N-BEATS	7,137	14	183
N-HiTS	6,900	15	39
TFT	29,567	9	333
PatchTST	6,902	18	341
Informer	13,350	86	2,447

Table 6: Per-trial training time during hyperparameter search (wall-clock seconds on a single GPU)

Horizon	Model	MAPE	W-MAPE	SMAPE	RMSE	FRMFPD	Q90(APE)	Wasserstein (APE, U[0,5%])
1	NHITS	0.0072	0.0055	0.0072	45.7661	102.7146	0.0191	0.0183
	PatchTST	0.0072	0.0055	0.0072	45.7619	102.7242	0.0191	0.0185
	Naive	0.0072	0.0055	0.0072	45.7619	102.7242	0.0191	0.0194
	TCN	0.0072	0.0055	0.0072	45.7617	102.7242	0.0191	0.0188
	LSTM	0.0072	0.0055	0.0072	45.7615	102.7241	0.0192	0.0182
	NBEATS	0.0072	0.0055	0.0072	45.9056	102.697	0.0186	0.0193

Table 7: Metric results over whole horizon for the tested models with all tested forecast horizons

Figure 4: MAPE and RMSE results for all tested models with all forecast horizons

Figure 5: Forecasts for exemplary items for forecast horizon = 1

Figure 6: Forecasts for exemplary items for forecast horizon = 365

Horizon	Model	MAPE	W-MAPE	SMAPE	RMSE	FRMFPD	Q90(APE)	Wasserstein(APE, U[0,5%])
1	NHITS	0.0072	0.0055	0.0072	45.7661	102.7146	0.0191	0.0188
	PatchTST	0.0072	0.0055	0.0072	45.7619	102.7242	0.0191	0.0173
	Naive	0.0072	0.0055	0.0072	45.7619	102.7242	0.0191	0.0193
	TCN	0.0072	0.0055	0.0072	45.7617	102.7242	0.0191	0.0187
	LSTM	0.0072	0.0055	0.0072	45.7615	102.7241	0.0192	0.0189
	NBEATS	0.0072	0.0055	0.0072	45.9056	102.697	0.0186	0.0176

Table 8: Metric results for point forecast at horizon end for the tested models with all tested forecast horizons

Figure 7: MAPE and RMSE results for all tested models with all forecast horizons for one-shot comparisons

Horizon	Model	MAPE	W-MAPE	SMAPE	RMSE	FRMFPD	Q90(APE)	Wasserstein(APE, U[0,5%])
1	ETS	0.0066	0.0052	0.0067	40.9375	103.7432	0.0164	0.0181
	ARIMA	0.0068	0.0053	0.0068	41.4634	110.2254	0.0157	0.0175
	Theta	0.0071	0.0057	0.0071	41.5503	103.5205	0.0168	0.0174
	TFT	0.0072	0.0058	0.0072	41.5557	102.996	0.017	0.0173
	Naive	0.0072	0.0058	0.0072	41.5559	102.9942	0.017	0.018
	NBEATS	0.0072	0.0059	0.0073	40.2122	105.1397	0.0173	0.0189

Table 9: Metric results for the tested models trained to predict 365-day horizon tested at all horizon lengths horizon end

Horizon	Model	learning_rate	batch_size	max_steps	input_size
1	NBEATS	0.006741	0.000000	630.026454	3.492214
	NHITS	0.015968	0.000000	293.711877	2.366432
	TCN	0.025125	4.800000	250.000000	0.000000
	LSTM	0.030758	5.962848	247.767812	0.000000
	TFT	0.022626	40.209231	625.610813	0.000000
	PatchTST	0.023423	103.395164	2158.703314	8.411896

Table 10: Standard deviation of selected hyperparameters across models and forecast horizons

Horizon	Model	MAPE	Mean MAPE hypertuning	t-test p-value	Wilcoxon test p-value
1	NHITS	0.0072	0.0074	0.347	0.612
	PatchTST	0.0072	0.0283	0.0001	0.0
	TCN	0.0072	0.0283	0.0001	0.0
	LSTM	0.0072	0.0283	0.0001	0.0
	NBEATS	0.0072	0.0282	0.0001	0.0
	TFT	0.0072	0.0283	0.0001	0.0

Table 11: Results of MAPE for final model and during hypertuning for tested deep learning model

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Model	h	Architecture	max_steps	LR
N-BEATS	1	stack=[ identity ], n_blocks=[4], act=SELU	2000	$1.8\!\times\!10^{-4}$
	7	stack=[ trend ], n_blocks=[4], act=SELU	2000	$3.8\!\times\!10^{-3}$
	30	stack=[ trend ], n_blocks=[4], act=SELU	2000	$8.8\!\times\!10^{-5}$
	90	stack=[ trend ], n_blocks=[4], act=SELU	2000	$3.6\!\times\!10^{-4}$
	180	stack=[ identity ], n_blocks=[1], act=ReLU	1500	$3.6\!\times\!10^{-3}$
	365	stack=[ identity ], n_blocks=[1], act=ReLU	1500	$3.6\!\times\!10^{-3}$

Appendix

Table 12: Best hyperparameter configuration per model and forecast horizon, extracted from Ray Tune random search logs (lowest validation MAPE trial across all cross-validation splits); h=180 configurations are used for h=365.

Model	Parameter	Search range / candidates
All DL models	learning_rate	$\mathcal{U}[10^{-5},10^{-1}]$ (log-uniform)
	batch_size	$\{32,64,128,256\}$
	max_steps	Model-specific (see below)
	input_size	Model-specific (see below)
N-BEATS	max_steps	$[100,2000]$
	input_size	$[1,28]$ (multiplier of $h$ )

Appendix

Table 13: Hyperparameter search ranges used in random search tuning (75 trials per model per cross-validation split). Architecture-specific parameters are listed beneath each model’s common parameters. All models had their architecture parameters searched.

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