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* Time-series forecast evaluation metrics.
*
* Pure functions operating on Float32Array — zero dependencies,
* zero allocations beyond the return value.
*
* Reference sources:
* - scikit-learn sklearn.metrics (BSD License)
* - Hyndman & Koehler (2006) "Another look at measures of forecast accuracy"
* - Google TimesFM evaluation harness
*/
/**
* Mean Absolute Error.
*
* MAE = (1/n) * Σ|actual_i - predicted_i|
*/
export function mae(actual: Float32Array, predicted: Float32Array): number {
if (actual.length !== predicted.length) {
throw new RangeError(`Length mismatch: actual=${actual.length}, predicted=${predicted.length}`);
}
if (actual.length === 0) return 0;
let sum = 0;
let count = 0;
for (let i = 0; i < actual.length; i++) {
if (Number.isFinite(actual[i]) && Number.isFinite(predicted[i])) {
sum += Math.abs(actual[i] - predicted[i]);
count++;
}
}
return count > 0 ? sum / count : 0;
}
/**
* Root Mean Square Error.
*
* RMSE = sqrt((1/n) * Σ(actual_i - predicted_i)²)
*/
export function rmse(actual: Float32Array, predicted: Float32Array): number {
if (actual.length !== predicted.length) {
throw new RangeError(`Length mismatch: actual=${actual.length}, predicted=${predicted.length}`);
}
if (actual.length === 0) return 0;
let sumSq = 0;
let count = 0;
for (let i = 0; i < actual.length; i++) {
if (Number.isFinite(actual[i]) && Number.isFinite(predicted[i])) {
const diff = actual[i] - predicted[i];
sumSq += diff * diff;
count++;
}
}
return count > 0 ? Math.sqrt(sumSq / count) : 0;
}
/**
* Mean Absolute Percentage Error.
*
* MAPE = (100/n) * Σ|(actual_i - predicted_i) / actual_i|
*
* Points where |actual_i| < 1e-10 are skipped to avoid division by zero.
*/
export function mape(actual: Float32Array, predicted: Float32Array): number {
if (actual.length !== predicted.length) {
throw new RangeError(`Length mismatch: actual=${actual.length}, predicted=${predicted.length}`);
}
if (actual.length === 0) return 0;
let sum = 0;
let count = 0;
for (let i = 0; i < actual.length; i++) {
if (
Number.isFinite(actual[i]) &&
Number.isFinite(predicted[i]) &&
Math.abs(actual[i]) > 1e-10
) {
sum += Math.abs((actual[i] - predicted[i]) / actual[i]);
count++;
}
}
return count > 0 ? (sum / count) * 100 : 0;
}
/**
* Symmetric Mean Absolute Percentage Error.
*
* SMAPE = (100/n) * Σ 2 * |actual_i - predicted_i| / (|actual_i| + |predicted_i|)
*
* Range: [0, 200]. Symmetric — swapping actual and predicted yields
* the same result.
*/
export function smape(actual: Float32Array, predicted: Float32Array): number {
if (actual.length !== predicted.length) {
throw new RangeError(`Length mismatch: actual=${actual.length}, predicted=${predicted.length}`);
}
if (actual.length === 0) return 0;
let sum = 0;
let count = 0;
for (let i = 0; i < actual.length; i++) {
if (Number.isFinite(actual[i]) && Number.isFinite(predicted[i])) {
const denominator = Math.abs(actual[i]) + Math.abs(predicted[i]);
if (denominator > 1e-10) {
sum += (2 * Math.abs(actual[i] - predicted[i])) / denominator;
count++;
}
}
}
return count > 0 ? (sum / count) * 100 : 0;
}
/**
* Mean Absolute Scaled Error.
*
* MASE = MAE(model) / MAE(naive)
*
* Values < 1 indicate the model outperforms the naive (no-change) forecast.
*/
export function mase(
actual: Float32Array,
predicted: Float32Array,
naiveForecast: Float32Array,
): number {
const modelMAE = mae(actual, predicted);
const naiveMAE = mae(actual, naiveForecast);
if (naiveMAE < 1e-10) return modelMAE < 1e-10 ? 1 : Infinity;
return modelMAE / naiveMAE;
}
/**
* R² coefficient of determination.
*
* R² = 1 - SS_res / SS_tot
*
* Range: (-∞, 1]. 1 = perfect fit, 0 = mean-predictor baseline,
* negative = worse than the mean baseline.
*/
export function r2Score(actual: Float32Array, predicted: Float32Array): number {
if (actual.length !== predicted.length) {
throw new RangeError(`Length mismatch: actual=${actual.length}, predicted=${predicted.length}`);
}
if (actual.length === 0) return 0;
let sumActual = 0;
let n = 0;
for (let i = 0; i < actual.length; i++) {
if (Number.isFinite(actual[i])) {
sumActual += actual[i];
n++;
}
}
if (n === 0) return 0;
const meanActual = sumActual / n;
let ssRes = 0;
let ssTot = 0;
for (let i = 0; i < actual.length; i++) {
if (Number.isFinite(actual[i]) && Number.isFinite(predicted[i])) {
const diffRes = actual[i] - predicted[i];
const diffTot = actual[i] - meanActual;
ssRes += diffRes * diffRes;
ssTot += diffTot * diffTot;
}
}
if (ssTot < 1e-10) return 1;
return 1 - ssRes / ssTot;
}
/**
* Prediction Interval Coverage.
*
* The fraction of actual values that fall within [lower, upper].
*
* Range: [0, 1]. 1 = all values covered, 0 = none covered.
*/
export function picCoverage(
actual: Float32Array,
lower: Float32Array,
upper: Float32Array,
): number {
if (actual.length !== lower.length || actual.length !== upper.length) {
throw new RangeError('Length mismatch between actual, lower, and upper arrays');
}
if (actual.length === 0) return 0;
let covered = 0;
let total = 0;
for (let i = 0; i < actual.length; i++) {
if (Number.isFinite(actual[i]) && Number.isFinite(lower[i]) && Number.isFinite(upper[i])) {
if (actual[i] >= lower[i] && actual[i] <= upper[i]) covered++;
total++;
}
}
return total > 0 ? covered / total : 0;
}
/**
* Average Prediction Interval Width.
*
* The mean width of the prediction interval across all time steps.
*/
export function piWidth(lower: Float32Array, upper: Float32Array): number {
if (lower.length !== upper.length) {
throw new RangeError(`Length mismatch: lower=${lower.length}, upper=${upper.length}`);
}
if (lower.length === 0) return 0;
let sum = 0;
let count = 0;
for (let i = 0; i < lower.length; i++) {
if (Number.isFinite(lower[i]) && Number.isFinite(upper[i])) {
sum += upper[i] - lower[i];
count++;
}
}
return count > 0 ? sum / count : 0;
}
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