Forecasting over a different dataset

The parameters of a model are estimated over a certain dataset. For instance, in the case a rolling window are the last n datapoints used to estimate the parameters of a model. In this paper is investigated, whether the dataset to estimate the parameters could be chosen in such a way that the parameter estimates improve and subsequently provide better forecasts. It is researched in the context of timeseries, such that two choices for the dataset could be made. The parameters in a model could be estimated over the same dataset, or each parameter could be estimated over a different dataset. Secondly, every parameter in a model could for every time t be estimated over, for instance, the last n datapoints, or it could differ per time t how many datapoints are used to estimate the parameters. Choosing the right option could significantly reduce the forecast error, because there could be a different impact over time of some variables on the dependent variable or there could be for some variables a long-term and for others a short-term relation with the dependent variable. In this paper is a chain of formulas developed, to get the best dataset and subsequently better parameter estimates. A real-life example was used, namely forecasting the Dutch GDP, to determine whether this approach improves the forecasts. Only estimating the parameters for every time t over a different dataset has some implications to be better than a simple rolling window.