my forecasted wind speed doesn't align with the fitted ARIMA model

1)will MATLAB ARIMA model be able to forecast data of this nature

2) 1440 points of rolling window forecast has not followed the pattern of the data

3) is it that the ARIMA is not suited for the model or that ARIMA GARCH is most appropriate to be applied

refer below script thus:

% Ensure P_w is correctly defined

head(P_w)

t =(0:15:(length(P_w)-1)*15)';

wind_speed = [t, P_w];

% Create datetime array starting from a specific point in time

startTime = datetime('2019-08-23 00:00:00'); % Adjust as needed

timeVector = startTime + minutes(t);

% Create timetable

wind_speed = timetable(timeVector, P_w, 'VariableNames', {'WindSpeed'});

% Number of future points to forecast

numForecasts = 1440;

% Generate future time points correctly

futureTimes = wind_speed.Properties.RowTimes(end) + minutes(15) * (1:numForecasts)';

% Forecast future wind speeds

[forecastedValues, forecastedMSE] = forecast(ARIMA_P_w1, numForecasts, 'Y0', wind_speed.WindSpeed);

% Create timetable for forecasted data with the same variable name as wind_speed

forecastedWindSpeed = forecastedValues; % Rename to match wind_speed

forecastedData = timetable(futureTimes, forecastedWindSpeed, forecastedMSE, ...

'VariableNames', {'WindSpeed', 'ForecastedMSE'}); % Ensure 'WindSpeed' matches

% Ensure both tables have the same variables before concatenation

forecastedData.ForecastedMSE = []; % Remove extra column if necessary

% Combine original and forecasted data

combinedData = [wind_speed; forecastedData]; % Now both have 'WindSpeed' column

% Plot the results

figure;

plot(combinedData.timeVector, combinedData.WindSpeed, 'b', 'DisplayName', 'Observed & Forecasted Wind Speed');

hold on;

plot(forecastedData.futureTimes, forecastedData.WindSpeed, 'r--', 'DisplayName', 'Forecasted Wind Speed');

hold off;

legend;

title('Wind Speed Forecast');

xlabel('Time');

ylabel('Wind Speed');

Any help will be appreciated for young researcher as the research continues to have forecasted windspeed that doesnt align wih the original data layout.

Answer 1

[Akanksha]

Hey Walter,

Following’s a breakdown of queries along with the recommended actions :

MATLAB's ARIMA model cannot entirely handle this kind of wind speed data.From the plots, it’s clear that the forecasted values are too smooth and don’t reflect the actual fluctuations in wind speed. This usually means the ARIMA model isn’t capturing the changing variance in the data, which is a common limitation when using ARIMA on data like wind speed, which often shows non-stationary behavior and volatility.

The forecast not match the actual pattern since ARIMA models only the mean of the time series, not the variance. Also, forecasting 1440 points is quite a long horizon, and ARIMA’s accuracy tends to drop over such extended forecasts. The model simply isn’t equipped to handle the dynamic nature of your data over that range.

Yes, you should switch to ARIMA-GARCH since :

• The current ARIMA model doesn’t capture the volatility structure of the wind speed data.
• ARIMA-GARCH combines: ARIMA for modeling the mean and GARCH for modeling the variance (volatility).
• This combination is much beneficial for data like wind speed, where the variability changes over time and will give more realistic and responsive forecasts.

Here are some official MathWorks links and the specific sections you should check out:

• https://www.mathworks.com/help/econ/arima.html : “Composite Conditional Mean and Conditional Variance Model”
• https://www.mathworks.com/help/econ/arima.html : Refer to: “[Y,YMSE,V] = forecast(Mdl,numperiods,Y0)”, this shows how to forecast both the mean and variance.
• https://www.mathworks.com/help/econ/arima.forecast.html : This example walks through estimating ARIMA, fitting GARCH, and forecasting both mean and volatility,relevant to your case.

Hope this helps!