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?

  • $\begingroup$ 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? $\endgroup$ – hakanc Mar 26 at 8:46
  • $\begingroup$ @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? $\endgroup$ – samsamara Mar 27 at 0:39
  • $\begingroup$ 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? $\endgroup$ – hakanc Mar 27 at 7:22
  • $\begingroup$ @hakanc Yes exactly. I have the estimates for eco data for n = 2000Q3 and forward. $\endgroup$ – samsamara Mar 29 at 2:27
  • $\begingroup$ 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? $\endgroup$ – hakanc Mar 29 at 9:52

VAR models predict ALL variables . A SARIMAX model https://autobox.com/pdfs/SARMAX.pdf only predicts 1 series i.e. customer default rates . Future values of all known X's can either be pre-specified or user-specified. If you have future values pre-specified then simply use them . If your software of choice doesn't allow pre-specification of the future values for your causals find one that that does.

Now the "cheat" that is normally in play is to assume that you have perfect knowledge (no uncertainty ) of the predictors . Optionally I would want to have a probability distribution of future values for each of the pre-specified exogenous predictors for each forecast period and incorporate these uncertainties via monte-carlo methods thus in my opinion providing a more honest assessment of the prediction intervals for the output series.

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 ).

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