forecast one step ahead an arma model in matlab

To forecast one step ahead using an ARMA model in MATLAB, you can use the forecast function from the Econometrics Toolbox. Here is an example code:

main.m
% Load data
data = load('myData.mat');
Y = data.Y;

% Split data into estimation and validation sets
numObs = length(Y);
numEst = floor(numObs*0.8);
Yest = Y(1:numEst);
Yval = Y(numEst+1:end);

% Estimate ARMA model
Mdl = arima(2,1,2);
EstMdl = estimate(Mdl, Yest);

% Perform one-step ahead forecasting
numVal = length(Yval);
Yfcst = zeros(numVal,1);
for i = 1:numVal
    [Yfcst(i,:), YMSE] = forecast(EstMdl, 1, 'Y0', Yest(end+i-EstMdl.Offset), 'MSE', true);
end

% Plot the results
figure;
plot(Yval, 'b');
hold on;
plot(Yfcst, 'r--');
legend('Validation', 'Forecast');
title('ARMA Model Forecasting');
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In this code, we first load the time series data and split it into estimation and validation sets (80%/20% split). Next, we estimate an ARMA(2,1,2) model using the estimation set. Then, we perform one-step ahead forecasting for the validation set using a loop that iterates through each observation in the validation set. Finally, we plot the validation set and the one-step ahead forecasts.

Note that the forecast function outputs the forecasted value and its mean squared error, which can be useful for constructing prediction intervals.