Why is my armax model converging to 0?

I have Matlab R2008b installed. I have self-acquired time-series data for blood pressure variation with a sampling time of 0.05s. My aim is to establish an arma model in order to forecast next(unacquired) values. Thanks to AIC i found that orders [4 2] would better fit my data.

I first extracted 10sec of data to create a training set, established my model on the training set and used the forecast function posted by Rajiv Singh.

I expected to have forecasted data that i would have compared to my real data (validation set). Unfortunately, the forecasted data quickly converge towards 0 after a few oscillations.

I also plotted the fitting percentage vs step ahead prediction to see how fast it decreases.

    trainiddata = iddata(trainy,[],Ts); %Create time-series iddata obj
    mod=armax(trainiddata,[4 2]); %create arma model
    yf=forecast(mod,trainiddata,10*Fs); %Forecast for 10 secs

    FITV=[];%Empty vector
    for(i=1:100)
    [YH, FIT, X0] = compare(mod,trainiddata,i); %Retrieve fitting for i-step ahead prediction
    FITV=[FITM;FIT];
    end

    subplot(211)
    plot(trainiddata)
    hold on
    plot(yf,'r.');

    subplot(212)
    plot(FITV);

How comes that my model's forecasting power is limited to such a short future ? Am I doing something wrong ?

I also tried an arma[100 10] model, which gives a slightly better result but still cannot predict a peak.

Answer 1

[Roger Wohlwend]

I think your expectations are too high. I doubt that an arma model is the appropriate model for a time series such as the one you present in the first picture. The time series is too dynamic for an arma model. You can check that by computing the goodness of fit. Look at the R-square, or compare the actual values to the estimated values. In my opinion you're doing nothing wrong. You just have the wrong model for your problem. That is why your forecasts are bad. And by the way ... arma model forecasts always converge to 0 when using stationary data.

Answer 2

[Romeo]

Thank you very much for your fast answer. Indeed my goodness of fit decreases very fast. Roméo.