# How to model time series with unevenly spaced observations?

I have three time series of the following form:

$$T = T_{2000}, T_{2004}, T_{2008}, …$$

$$U = U_{1998}, U_{1999}, U_{2000}, U_{2001}, U_{2002}, U_{2003}, …$$

$$V = V_{1998}, V_{1999}, V_{2000}, V_{2001}, V_{2002}, V_{2003}, …$$

I would like to predict $$T$$ from $$U + V$$, but since the time series have unequal numbers of observations ($$T$$ has four times less data points: the series 'coincide' only every four years), I am unsure of how to go with it.

Any help (and software recommendations, preferably with R) would be very much appreciated!

## 1 Answer

If you want to use U & V as features what you can do is have rows equal to the number of T observations and since T has a frequency of 4 years hence have 8 features equal to the last 4 years (compared to the year you are predicting) observation of U & V each.

As an example to predict T(2004) use U(2000-2003) & V(2000-2003) as features.

This is just one such way. It might also be that your prediction of U(2008) is dependant on V(1998 ~ 2007). In such case, you might want to model using the past value of T as well since it might capture well the previous values of U & V ( for years >4 )

• So I should just use lags of (T, U, V)? What kind of model is that? AR(x)? – fullwheel Mar 26 at 8:53
• You will have to check which model works, but Arima etc should work nicely. But I was talking about creating a dataset/features. It makes sense that to predict T(2004) you can only use U < 2004 & V < 2004. – Axelius Mar 26 at 8:57
• Alright. I'll wait a bit for additional suggestions, but will start looking into ARIMA straight away. – fullwheel Mar 26 at 9:14