compare vs forecast with models

I'm using ARMA-models to predict a signal. My signal is a timeseries with n points;

input = iddata(signal,[],Ts);

My model is an ARMA-model with p=10 and q=10;

model = armax(input,[10 10]);

After I build my model, I use the compare command to check the performance of my model for 1-step-ahead predictions

[y,fit,xo] = compare(model,input,1);

I also use the forecast command to check the performance of my model

for k = 1:length(input.y)-10
    x(k,1) = forecast(model,input.y(k:k+9),1);
end

Both commands check 1-step-ahead forecast, if I'm not mistaken. But when I compare the results from both, they are not equal.

plot(y.y(11:end));
hold on
plot(x);

So here is my question: How come that compare and forecast give two different answers.

Answer 1

[Fei Deng]

Hi, It is my understanding that you built a ARMA model based on the signal you have and you used function 'compare' and 'forecast' to evaluate the ARAM model. You want the predicted/evaluated output value at time t to be predicted using values in measured output data (input.y) up to time t-1. In order to do that, in the loop you have, change

x(k,1) = forecast(model,input.y(k:k+9),1);

to

x(k,1) = forecast(model,input.y(1:k+9),1);

otherwise, the predicted value at time t will be obtained based on each 10 values in input.y before time t.

If you still don’t get equal results that you expected, here are two suggestions:

1) Check the differences and consider if they are reasonable error by white-noise disturbance value in the model.

2) Consider if the sampling rate is enough for your data.

[s.p4m]

Thank you for your input. You a right my loop is there so I make prediction based on the last 10 values in input.y. But since my ARMA-model only consider the last 10 values, why should I consider more. The parameter of the model are set in:

model = armax(input,[10 10]);

and won't change after that.

For your 2 suggestions:

2) Doesn't matter, because right now I'm not interested in a good forecast but rather want to understand why the outputs are different.

1) This could be the reason. I will check it and come back

[s.p4m]

I just checked if the white noise process could be the reason but the difference is far to big.

But I also checked your Input about using all past data instead of only the last 10 and you're right. When changing

x(k,1) = forecast(model,input.y(k:k+9),1);

to

x(k,1) = forecast(model,input.y(1:k+9),1);

the output from forecast and compare are the same. Could you explain the reason for this, because I thought the model only consider the last 10 entries and the parameter were fix.