Exponentially Weighted Moving Models

ArXiv ID: 2404.08136 “View on arXiv”

Authors: Unknown

Abstract

An exponentially weighted moving model (EWMM) for a vector time series fits a new data model each time period, based on an exponentially fading loss function on past observed data. The well known and widely used exponentially weighted moving average (EWMA) is a special case that estimates the mean using a square loss function. For quadratic loss functions EWMMs can be fit using a simple recursion that updates the parameters of a quadratic function. For other loss functions, the entire past history must be stored, and the fitting problem grows in size as time increases. We propose a general method for computing an approximation of EWMM, which requires storing only a window of a fixed number of past samples, and uses an additional quadratic term to approximate the loss associated with the data before the window. This approximate EWMM relies on convex optimization, and solves problems that do not grow with time. We compare the estimates produced by our approximation with the estimates from the exact EWMM method.

Keywords: Exponentially Weighted Moving Average (EWMA), Time Series Analysis, Convex Optimization, Data Stream Modeling, Equities

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 3.5/10
• Quadrant: Lab Rats
• Why: The paper introduces a convex optimization framework for exponentially weighted moving models, involving advanced concepts like convex duality and quadratic approximations, indicating high mathematical density. While the examples discuss practical applications like covariance estimation and quantile regression, the paper lacks backtests, specific datasets, or implementation details for quantitative finance, resulting in lower empirical rigor.

  flowchart TD
    A["Research Goal: EWMM Approximation"] --> B["Methodology: Window + Quadratic Approx"]
    B --> C["Data: Vector Time Series"]
    C --> D["Process: Solve Convex Opt"]
    D --> E["Exact EWMM"]
    D --> F["Approximate EWMM"]
    E --> G["High Compute + Storage"]
    F --> H["Fixed Storage + Efficient Compute"]
    G & H --> I["Outcome: Validated Approximation"]