# Predicting time t given time t-n

..Hi, Everyone!

I'm having a bit of trouble with a statistics/forecasting problem and I could use some help. I have temperature measurements for each hour of each day for the past 10 years. Given the temperature at time t, which represents an hour of a given day, I need to be able to predict the temperature at time t+n (any subsequent hour).

For example, with this model, I might want to use today's 12pm temperature to predict the temperature for all subsequent hours of the day (1pm, 2pm, 3pm, etc . . ..).

At first, I thought of using an autoregression model, but I'm not really sure if that solves my problem (I'm not terrifically familiar with autoregression models). In any case, I don't have the requisite toolbox in MATLAB and I don't know how to do it in SPSS. Also, I'm not sure if it's a viable solution to my problem. Is it?

Any help would be greatly appreciated. Thanks!!!!!

• Autoregressive models allow you to predict $t$ given $t-1, t-2, t-3, \ldots, t-p$ (for a model of order $p$). Based on what I have read, you are trying to predict $t+1, t+2, t+3, \ldots$ given $t$. Based on that, an autoregressive model is unsuitable. Commented Jul 5, 2013 at 23:26

To me, autoregression seems like a viable option, but you might want to consider a seasonal model of some sort. For example, a $SAR_{24}(1, 1)$ could probably be a decent starting point (though I know absolutely nothing about temperature). Such a model can be expressed as: $$Y_t=\alpha + \phi Y_{t-1}+ \gamma Y_{t-24}+ u_t$$