timeseriesmetrics 0.1.0

This package is a set of metrics commonly used to analyze the performance of predictive models for time series, such as MAPE, Theil's U, ARV, ID (Index of Disagreement), wpocid.

Timeseries Metrics

This package provides several metrics used to evaluate the performance of predictive models in time series.

Installation

You can install the package using pip:

pip install timeseriesmetrics

Usage

The package can be used as follows:

from timeseriesmetrics import *

y_true = [1, 2, 3, 4, 5]
y_pred = [3, 4, 3, 4, 5]

theil(y_true, y_pred)

Where y_true represents the real values ​​and y_pred the predicted values.

Definitions

• $ N $: number of observations.
• $ u_{t} $: real values.
• $ \widehat{u}_{t} $: predicted values.
• $ \overline{u}_{t} $: mean of the real values.

Available Metrics

MAPE

MAPE (Mean Absolute Percentage Error) measures the accuracy of the model, presenting a relative value:

$$ MAPE = \frac{100}{N} \sum_{t=1}^{N} \left| \frac{u_{t} - \widehat{u}{t}}{u{t}} \right| $$

ARV

ARV (Average Relative Variance) compares the predictor's performance with the simple average of past values ​​in the series:

$$ ARV = \frac{\sum_{t=1}^{N} \left( u_{t} - \widehat{u}{t} \right)^{2}}{\sum{t=1}^{N} \left( \widehat{u}{t} - \overline{u}{t} \right)^{2}} $$

ID

ID (Index of Disagreement) disregards the unit of measurement, presenting values ​​in the interval [0, 1]:

$$ ID = \frac{\sum_{t=1}^{N} \left( \widehat{u}{t} - u{t} \right)^{2}}{\sum_{t=1}^{N} \left( \left| \widehat{u}{t} - \overline{u}{t} \right| + \left| u_{t} - \overline{u}_{t} \right| \right)^{2}} $$

Theil'U

Theil'U compares prediction performance to the Random Walk model (in which $ u_{t} $ is inferred by $ u_{t-1} $), where Theil< 1 indicates a better prediction than the Random Walk model:

$$ Theil = \frac{\sum_{t=2}^{N} \left( u_{t} - \widehat{u}{t} \right)^{2}}{\sum{t=2}^{N} \left( u_{t} - u_{t-1} \right)^{2}} $$

WPOCID

WPOCID measures how well the model predicts the trend of the target time series:

$$ \left.\begin{aligned} & WPOCID = 1 - \frac{\sum_{t=2}^{N} D_{t}}{N-1}, \ & D_{t} = \left{ \begin{array}{l} 1, \text{ se } \left( u_{t} - u_{t-1} \right) \left( \widehat{u}{t} - \widehat{u}{t-1} \right) \geq 0 \ 0, \text{ se } \left( u_{t} - u_{t-1} \right) \left( \widehat{u}{t} - \widehat{u}{t-1} \right) < 0 \end{array} \right. \end{aligned}\right. $$

References

More details on the metrics discussed can be found in the article A non-central beta model to forecast and evaluate pandemics time series.