time series prediction

Thank you for reading and commenting I present my problem with a simple example. consider an ARX or ARMAX model. the goal is predicting the output k-step ahead. current time is t = 5. i have the following data. output : y = [1 2 3 4 5] input : u = [10 20 30 40 50] consider a simple arx model y(t) + ay(t-1) = bU(t-1) + cU(t-2) + e(t) want to predict y(10), that is 5 step ahead prediction for output. i do not have the input nor output for t = 6,7,8,9,10. do i have to have the input for prediction ? what can i do if i do not. I know how to do k-step prediction with AR models. the input part (X) makes this confusing. I am also familiar with predict function in matlab. it requires input up to the prediction time (10) minus the delay (nk = 1). Thanks

[Chia Woon Wang]

hi, :). can i know how u do the k-step prediction with AR model?

Answer 1

[Rajiv Singh]

If your regression equation suggests that output at a time t is a function of input at time t-1, then you do need that input value. There is no way to "simulate" the input values (unlike the past output values which a model may also require; for those, simulated values replace the measured ones).

Consider an example; the speed of a car is a function of how much you press on the gas pedal. Now if you are asked to predict what the speed of the car will be 10 minutes into future, how would you do it? You will need to make some assumption about what you are going to do with your gas pedal between now and 10 min in future (like releasing it, holding it constant or some other prescription). If instead you say that the gas pedal will be manipulated arbitrarily (or you have no idea what it will do), there is no way to say what the speed will be.

[pemfir]

Thank you !

Answer 2

[Gurudatha Pai]

To continue on what Rajiv said above, the X in ARX or ARMAX stands for eXogenous input. An AR (ARMA) model is noise driven but an ARX (ARMAX) model is driven by both signal and noise. So, if you don't have an input signal, you are probably better off choosing an AR or ARMA model; only then would you be able to do a k-step prediction (in least square sense typically).

So in short, like Rajiv said, answer to your question is, no you cannot simulate or predict the output of an ARX (ARMAX) model with an input signal.

[pemfir]

Thank you !