Stochastic coherency in forecast reconciliation

• Hierarchical forecasting has been receiving increasing attention in the literature. The notion of coherency is central to this, which implies that the hierarchical time series follows some linear aggregation constraints. This notion, however, does not take several modelling uncertainties into account. We propose to redefine coherency as stochastic. This allows to accommodate overlooked uncertainties in forecast reconciliation. We show analytically that there are two potential sources of uncertainty in forecast reconciliation. We use simulated data to demonstrate how these uncertainties propagate to the covariance matrix estimation, introducing uncertainty in the reconciliation weights matrix. This then increases the uncertainty of the reconciled forecasts. We apply our understanding to modelling accident and emergency admissions in a UK hospital. Our analysis confirms the insights from stochastic coherency in forecast reconciliation. It shows that we gain accuracy improvement from forecast reconciliation, on average, at the cost of the variability of the forecast error distribution. Users may opt to prefer less volatile error distributions to assist decision making. 

Subject headings

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Keyword

Coherency

Covariance estimation

Forecast combination

Forecasting

Model uncertainty

Covariance matrix

Decision making

Stochastic models

Stochastic systems

Uncertainty analysis

Forecast combinations

Linear aggregation

Model uncertainties

Potential sources

Sources of uncertainty

Stochastics

Times series

Uncertainty

Skövde Artificial Intelligence Lab (SAIL)

Skövde Artificial Intelligence Lab (SAIL)

Publication and Content Type

ref (subject category)

art (subject category)