Multivariate Time-Series

Unlike univariate data, a multivariate time-series consists of two or more time-dependent variables that may exhibit complex correlations and causal relationships. In a cellular network, this includes metrics like PRB utilization, Channel Quality Indicator (CQI), RRC connected users, and traffic volume recorded simultaneously. The key insight is that these variables influence one another—a drop in CQI often precedes a spike in PRB usage as the scheduler compensates with more resources. Forecasting models must capture these cross-variable dependencies to make accurate predictions.

Data points in a multivariate time-series are strictly ordered by time, and the sequence itself carries critical information. A fundamental assumption for many classical forecasting models is stationarity—that the statistical properties (mean, variance, autocorrelation) remain constant over time. Real-world RAN telemetry is often non-stationary due to daily commuter patterns, special events, and network upgrades. Techniques like differencing or seasonal decomposition are applied to transform the data before modeling.

At each time step t, the multivariate observation is represented as a feature vector xₜ = [v₁, v₂, ..., vₙ]. For predictive load balancing, a typical feature vector might include:

• PRB utilization (uplink and downlink)
• Average CQI per cell
• Number of active UEs
• PDCP throughput volume
• Handover success rate The model's lookback window defines how many of these historical vectors are concatenated to form a single input sample for forecasting the next time step.

A defining characteristic is the correlation matrix between variables. In RAN data, PRB utilization and the number of active UEs typically exhibit strong positive correlation, while CQI and PRB utilization often show negative correlation (poorer channel quality demands more resource blocks). Advanced models like Transformers use self-attention mechanisms to learn these relationships dynamically, assigning higher weights to variables that are most predictive of future load states. Ignoring these correlations leads to suboptimal forecasts.

Real-world multivariate telemetry is rarely clean. Missing values occur due to network element failures, polling gaps, or transmission errors. Irregular sampling arises when different KPIs are reported at different intervals (e.g., CQI every 2ms, PRB every 1ms). Robust forecasting pipelines must implement imputation strategies—such as forward-filling, linear interpolation, or learned imputation models—and resampling to align all variables to a common time grid before feeding them into the model.

As the number of variables grows, the feature space expands exponentially, a phenomenon known as the curse of dimensionality. A model forecasting 20 correlated KPIs over a 100-step lookback window must process 2,000-dimensional input vectors. This demands careful feature selection to retain only the most predictive variables and the use of dimensionality reduction techniques like Principal Component Analysis (PCA) or attention-based variable selection in modern deep learning architectures to avoid overfitting and computational bloat.

The application of Long Short-Term Memory neural networks to forecast future cellular load states. LSTMs are a type of recurrent neural network specifically designed to learn long-range temporal dependencies while avoiding the vanishing gradient problem. In multivariate time-series, LSTMs can simultaneously process sequences of PRB utilization, CQI reports, and active user counts to predict congestion events. The architecture uses forget gates, input gates, and output gates to selectively retain or discard information across hundreds of time steps.

A modern forecasting approach that uses the self-attention mechanism of Transformer architectures to model complex, non-linear relationships in multivariate network telemetry data. Unlike recurrent models, Transformers process entire sequences in parallel, capturing dependencies between any two time steps regardless of distance. In RAN contexts, attention weights can reveal which historical variables—such as a CQI drop or handover spike—most influence future load. This interpretability is critical for network engineering teams validating model behavior.

The fixed length of historical time-series data used as input for a forecasting model to make a single prediction. This parameter defines the temporal context the model can observe. A window that is too short may miss diurnal patterns or weekly seasonality; a window that is too long introduces noise and increases computational cost. Typical RAN forecasting windows range from 24 hours (capturing daily cycles) to 168 hours (capturing weekly patterns), sampled at 15-minute or 1-hour granularity.

The specific length of time into the future for which a model generates a forecast. This is a critical parameter that balances proactive action with prediction accuracy. Short horizons of 5-15 minutes enable near-real-time load balancing on the Near-RT RIC, while longer horizons of 1-24 hours support energy-saving sleep mode scheduling. Multivariate models typically maintain higher accuracy at extended horizons compared to univariate approaches because they capture leading indicators across correlated variables.

A phenomenon in online learning where the statistical properties of the target variable change over time, rendering the model less accurate. In RAN contexts, concept drift occurs when traffic patterns shift due to new building construction, changes in commuter behavior, or the introduction of new services. Covariate shift affects input distributions; prior probability shift affects target distributions. Multivariate models can be more robust to drift because they learn invariant relationships between variables that persist even as individual distributions change.