Wind Forecast Mspe Eval

wind-forecast-mspe-eval

Gaussian linear state-space model for wind fields in the North-East Atlantic — Bessac et al. (2013) (arXiv:1312.5530, 2013)

What this evaluates

Evaluates the ability of a Gaussian linear state-space model to accurately forecast short-term wind speeds in the North-East Atlantic using historical observations. It also assesses the model's capacity to reproduce realistic spatiotemporal wind statistics and compares parameter estimation methods (GMM vs ML).

Datasets

• ERA Interim reanalysis data (North-East Atlantic) — total ?; splits: train (-1), test (-1)

Metrics

• MSPE (primary) — range: percent
  • Mean Square Percentage Error at location i: MSPE(i) = var(Y_t(i) - E[Y_t(i) | Y_0, ..., Y_{t-1}]) / var(Y_t(i)). It measures the variance of the one-step ahead forecast error normalized by the variance of the original wind field at each location.

Input / output format

Input: Historical 6-hourly wind speed observations at K spatial locations up to time t-1.

Output: One-step ahead predicted wind speed at each location i, computed via Kalman recursions.

Scoring recipe

# For each location i in 1..K:
forecast_error_var = variance(Y_t(i) - E[Y_t(i) | Y_0...Y_{t-1}])
original_var = variance(Y_t(i))
mspe_i = forecast_error_var / original_var
# Average across locations
average_mspe = mean(mspe_i over all locations)
# Compare against baselines: persistence, site-wise ARMA(2,1), VAR(1)

Common pitfalls

• GMM estimation matches short-term autocorrelations well but introduces bias in second-order structure, while ML better captures longer-term dynamics.
• Model performance degrades near domain boundaries because the scalar latent process oversimplifies complex space-time structures.
• MSPE is computed per location and then averaged; baselines include persistence and site-wise ARMA models, not just VAR(1).

Evidence (verbatim from paper)

The forecast skill of the model at location $i \in {1, \dots, K}$ is evaluated by computing the natural empirical estimate of the Mean Square Percentage Error (MSPE) defined as $$ \mathrm {M S P E} (i) = \frac {\operatorname {v a r} (Y _ {t} (i) - \operatorname {E} [ Y _ {t} (i) | Y _ {0} , \dots , Y _ {t - 1} ])}{\operatorname {v a r} (Y _ {t} (i))} $$ where the MSE of the forecast error (the numerator) is normalized by the variance of the field at the individual locations, with $Y_{t}$ the original non-transformed wind.

Citation

@misc{bessac2013gaussian,
  title={Gaussian linear state-space model for wind fields in the North-East Atlantic},
  author={Bessac et al. (2013)},
  year={2013},
  note={arXiv:1312.5530}
}

• arXiv: 1312.5530