How can i define and plot Prediction interval for non-parametric distribution?

I want to do probabilistic forecast from point forecast. I do have error distribution (non parametric) from point forecast. I want to define and plot prediction interval within which the deand data may lie, with a certain probability.

Answer 1

[Shubham]

Hi israt,

To create a probabilistic forecast from a point forecast using a non-parametric error distribution, you can follow these steps:

1. Point Forecast: Have your point forecast ready for the period you are interested in.
2. Error Distribution: Have the historical forecast errors (actual - forecast) at hand.
3. Determine the Confidence Level: Choose the confidence level for your prediction interval (e.g., 90%, 95%, 99%).
4. Calculate the Prediction Interval: Use the empirical percentiles from the error distribution to find the bounds of the prediction interval.
5. Plot the Prediction Interval: Visualize the point forecast and the prediction interval.

Here is a MATLAB script that demonstrates these steps:

% Point forecast for a certain period
point_forecast = 100;

% Historical forecast errors (actual - forecast)
errors = [-5, -3, -1, 0, 1, 2, 4, 5];

% Confidence level for the prediction interval
confidence_level = 0.95;

% Calculate the empirical percentiles of the error distribution
lower_percentile = (1 - confidence_level) / 2 * 100;  % e.g., 2.5 for 95% confidence
upper_percentile = (1 + confidence_level) / 2 * 100;  % e.g., 97.5 for 95% confidence

% Calculate the prediction interval bounds
lower_bound = point_forecast + prctile(errors, lower_percentile);
upper_bound = point_forecast + prctile(errors, upper_percentile);

% Plotting the point forecast and prediction interval
figure;

% Plot the point forecast
line([0, 1], [point_forecast, point_forecast], 'Color', 'blue', 'LineStyle', '-', 'LineWidth', 2);
hold on;

% Plot the prediction interval as a shaded area
fill([0, 1, 1, 0], [lower_bound, lower_bound, upper_bound, upper_bound], 'k', 'FaceAlpha', 0.1, 'EdgeColor', 'none');

% Set the plot labels and title
xlabel('Time');
ylabel('Forecast Value');
title('Point Forecast with Prediction Interval');
legend('Point Forecast', 'Prediction Interval', 'Location', 'Best');

% Adjust the limits of the x-axis
xlim([0, 1]);

hold off;

This MATLAB script will plot your point forecast as a horizontal line and shade the area between the lower and upper bounds of the prediction interval. Adjust the point_forecast and errors variables to match your actual data. If you have multiple point forecasts for different periods, you can extend the script to include those in the visualization.