Competition-Aware CPC Forecasting with Near-Market Coverage

Conference: CVPR 2025
arXiv: 2603.13059
Code: TBD
Area: Time Series / Advertising Forecasting / Graph Neural Networks
Keywords: CPC Forecasting, Competition Proxies, Semantic Graphs, Time Series Foundation Models, Spatio-Temporal GNNs

TL;DR

This work reformulates paid search CPC forecasting as a "forecasting under partially observable competition" problem. It approximates unobservable competitive states using three types of competition proxies: semantic neighborhoods (via Transformer embeddings), behavioral neighborhoods (via DTW alignment), and geographic intent. Evaluations on Google Ads data covering 1,811 keywords over 127 weeks demonstrate that competition-aware enhancements significantly outperform univariate and weak-context baselines in medium- to long-term forecasting (6/12 weeks).

Background & Motivation

Background: In paid search advertising, CPC is a price generated through real-time auctions, jointly determined by competitor bids, platform quality signals, and query conditions. Advertisers can observe their own CPC, clicks, and impressions, but cannot directly observe competitors' bids, budget constraints, and quality scores.

Limitations of Prior Work: (a) Pure autoregressive forecasting methods perform poorly in the medium to long term (6-12 weeks) because latent competitive dynamics (such as competitors adjusting budgets or demand shifts) cannot be captured from historical CPC alone. (b) Prior research on search advertising primarily focuses on auction mechanisms and CTR prediction, offering limited guidance for CPC forecasting. (c) While Graph Neural Networks succeed in domains like transportation and energy, CPC forecasting lacks a natural graph topology—the competitive relationships among keywords must be explicitly constructed.

Key Challenge: CPC is a price generated by competition, yet the competitive state is only partially observable. Advertisers can only observe the "outcome" (CPC) but not the "cause" (the competitive landscape).

Goal - How to construct competition proxies from observable data to approximate unobservable competitive states? - Is it more effective to incorporate these proxies as covariates or as relational priors (graph structures)? - Can time-series foundation models (TSFMs, e.g., Chronos-2, TimeGPT, Moirai) absorb competitive context?

Key Insight: Competition leaves observable footprints along three dimensions: semantic similarity (intent substitution), CPC trajectory synchronization (shared exposure to demand shocks), and geographic intent (spatialized market structures).

Core Idea: Approximate latent competition using semantic, behavioral, and geographic proxies, and inject them into forecasting models through two pathways: covariates and graph structures. This yields consistent performance gains in medium- to long-term forecasting.

Method

Overall Architecture

Two primary pathways are evaluated for incorporating competitive proxies: (1) Covariate pathway: competitive signals serve as exogenous variables input into TSFMs; (2) Relational pathway: a semantic graph serves as an adjacency matrix input into spatio-temporal GNNs. The goal is to forecast weekly CPC for 1,811 keywords across horizons \(h \in \{1, 6, 12\}\) weeks.

Key Designs

1. Semantic Neighborhoods and Semantic Graphs

   • Function: Capture keyword similarity at the intent level using Transformer embeddings.
   • Mechanism: Encode each keyword using all-MiniLM-L6-v2 to obtain \(e_i \in \mathbb{R}^{384}\). Construct a static semantic graph \(A^{sem}\) (with \(k=10\) nearest neighbors) using cosine similarity, row-normalize it for STGNN use, and extract neighborhood-aggregated features as covariates.
   • Design Motivation: Keywords like "car rental lax" and "rent a car los angeles" differ verbatim but compete for the same inventory. Semantic embeddings capture this intent-level substitutability.

2. Behavioral Neighborhoods (DTW Alignment)

   • Function: Identify behaviorally similar keywords through Dynamic Time Warping (DTW) of CPC time series.
   • Mechanism: Calculate the DTW distance between keyword pairs (with a Sakoe-Chiba band constraint) to construct behavioral neighborhoods. Extract leakage-free competitive features from neighborhood historical CPCs as covariates.
   • Design Motivation: Verbatim-dissimilar keywords may exhibit similar CPC dynamics due to shared exposure to demand shocks or competitor adjustments; DTW captures this temporally aligned behavioral similarity.

3. Geographic Intent Covariates

   • Function: Extract geographic information from keyword text as spatialized competitive proxies.
   • Mechanism: Parse geographic names (airports, cities, countries) from keywords and map them hierarchically (continent \(\rightarrow\) country \(\rightarrow\) city) to generate structured location indicators.
   • Design Motivation: Car rental markets are highly localized (with intense competition at airport hubs). Geographic encoding directly reflects localized competitive intensity.

4. Model Architecture Matrix

   • Classical/ML baseline: SARIMAX, XGBoost, LightGBM, LSTM, GRU, TabPFN
   • Covariate-augmented TSFMs: Chronos-2, TimeGPT, Moirai (accepting exogenous covariates)
   • Spatio-Temporal GNNs: DCRNN, GConvLSTM, GraphWaveNet (utilizing semantic graph \(A^{sem}\))

Loss & Training

• All STGNNs are optimized using Mean Absolute Error (MAE), which is more robust to right-skewed CPC distributions.
• A strict chronological split is applied, using the last 20% of observations for testing to prevent temporal data leakage.
• Evaluation metrics: sMAPE (primary) and RMSE (auxiliary).

Key Experimental Results

Main Results (Cross-Horizon Family Comparison)

Model Family	1-week sMAPE (%)	6-week sMAPE (%)	12-week sMAPE (%)
Best Classical/ML baseline	30.42	35.04	40.23
Best Covariate-Augmented TSFM	27.94	27.14	29.14
Best Spatio-Temporal GNN	25.82	30.42	37.46

Detailed Comparison at 6-week Horizon

Model	sMAPE (%)	RMSE
SARIMAX	43.93±23.55	1.660
XGBoost	36.64±17.51	1.301
TabPFN (1-shot)	35.04±17.77	1.250
Moirai	30.14±18.24	1.000
TimeGPT	29.29±17.07	1.002
Chronos-2 + Geographic Covariates	27.14±15.04	0.841
GraphWaveNet + Semantic Graph	30.57±20.57	1.005

Key Findings

• Optimal methods vary by horizon: Spatio-temporal GNNs perform best for 1-week forecasting (capturing short-term dynamics), whereas TSFMs excel at 6/12-week horizons (absorbing competitive covariates to handle regime shifts).
• Competition awareness is most valuable in the medium-to-long term: Short-term forecasting is dominated by temporal inertia, whereas competitive shifts significantly drive long-term price dynamics.
• Geographic intent is the strongest single covariate: Chronos-2 paired with geographic covariates reduces the 6-week horizon sMAPE from a baseline of 35.04% to 27.14% (a 23% reduction).
• Gains are maximized on high-CPC, high-volatility keywords: Keywords located on the "competitive frontier" benefit the most, which corresponds precisely to the highest budget-risk regions.
• Foundation Models effectively absorb competitive signals: Chronos-2 and TimeGPT perform better via the covariate pathway than the graph pathway.

Highlights & Insights

• Problem reformulation under partially observable competition: Reformulating CPC forecasting from a pure time-series task to forecasting under partially observable competition offers a highly inspiring framework applicable to any auction- or market-driven price forecasting.
• Three complementary proxy designs: Semantic (intent substitution), behavioral (dynamic synchronization), and geographic (localized competition) proxies capture distinct facets of competition without relying on proprietary competitor data.
• Competitive Frontier evaluation: Evaluating models on quadrants divided by keyword CPC means and volatilities focuses on high-value, high-risk segments, delivering much higher business utility than simple average error metrics.
• Complementarity of TSFMs vs GNNs: Graph propagation excels in the short term, while covariate enhancement is ideal for the long term, suggesting potential benefits from hybrid approaches.

Limitations & Future Work

• Single-advertiser data restricted to the car rental industry: The external validity of the findings needs to be verified in other industries.
• Static semantic graphs: The actual competitive structure evolves over time; dynamic graphs may offer better performance.
• Excluding the effects of the advertiser's own bidding strategies: CPC is co-determined by external competition and internal bidding decisions.
• Future directions: (1) Constructing dynamic competitive graphs (e.g., updating DTW neighborhoods weekly); (2) Integrating the TSFM covariate pathway with the GNN graph pathway into a unified model; (3) Extending the framework to multi-agent competitive game models.

Related Work & Insights

• vs. Pure ARIMA/Prophet baselines: The proposed method reduces the 6-week sMAPE from 43.93% to 27.14%, demonstrating the crucial value of competitive signals.
• vs. Standard STGNNs (e.g., traffic forecasting): Unlike traffic networks, graphs for CPC forecasting do not exist naturally and must be constructed; semantic graphs present an effective construction strategy.
• vs. Foundation Model zero-shot forecasting: Chronos-2 and TimeGPT perform substantially better when augmented with competitive covariates, indicating that TSFMs still heavily benefit from domain-specific signals.

Rating

• Novelty: ⭐⭐⭐⭐ The problem reformulation (partially observable competition) and the three proxy designs are creative, though the underlying model architectures are existing.
• Experimental Thoroughness: ⭐⭐⭐⭐⭐ Comprehensive evaluation covering 3 horizons, multiple model families, and various proxy combinations.
• Writing Quality: ⭐⭐⭐⭐ Excellent problem definition and framing; the "competitive frontier" concept provides strong business insights.
• Value: ⭐⭐⭐⭐ Direct and high practical value for ad-tech and digital marketing domains.

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