# how to model this multivariate time series?

Say I have a dataset as follows.

|Time     | Unemployment_rate | GDP_growth | Customer_defaults |
-------------------------------------------------------------
| 2000 Q1 |               4% |         2% |         5%         |

| 2000 Q2 |               6% |         2% |         6%         |


forecasting the defaults rate (but I already have the forecasts for the factors)

| 2000 Q3 |              5% |          3% |               ??? |


I have timeseries data for some macroeconomic factors which drives the customer defaults for home loans. The important point here is that I ALREADY HAVE the forecasts for the factors and want to use those to forecast the defaults.

I know this is like a multivariate time series modelling problem. But from what I have read those models would forecast my factors as well which I don't want (as I already have forecasts received from experts).

So my question is what kind of techniques I could use to solve this?

• it is unclear what you want to do, you want to forecast the customer default rates, but you already have other forecasts for the customer default rates? – hakanc Mar 26 at 8:46
• @hakanc yes correct. For eg., I have historical data for customer defaults (as well for other economic factors) until 2000Q2 and want to forecast defaults starting from 2000Q3. But I already have the values of the eco factors for the horizon starting from 2000Q3. Thus I DO NOT want to use the model predictions for the eco factors for my forecasts starting from 2000Q3. Does that make sense now? – samsamara Mar 27 at 0:39
• ok, so if $y_{cdr}[n]$ is customer default rate, $y_{eco}[n]$ are other economic factors, both at time $n$. You have measured values of $y_{cdr}[n]$ when $n = 2000Q2$ and backwards. For $y_{eco}[n]$ you have measured values when $n = 2000Q2$ and backwards. Additionally, you seem to have both measured values of $y_{eco}[n]$ and estimates $\hat{y}_{eco}[n]$ when $n = 2000Q3$ and forward. Is this correct? – hakanc Mar 27 at 7:22
• @hakanc Yes exactly. I have the estimates for eco data for n = 2000Q3 and forward. – samsamara Mar 29 at 2:27
• ok, if you already have measured values of $y_{eco}[n]$, why should you use the estimates, $\hat{y}_{eco}[n]$, of the same variable? – hakanc Mar 29 at 9:52

FYI take a look at the following question Forecasting a time series $(x_t,{\bf Y_t})$ where all we care about is forecasting $x_t$ as to how to convolute the uncertainties when your predictor variables have to be incorporated i.e. self-predicted (not your stated problem BUT a more common problem ).