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Neural Networks (NN) have demonstrated remarkable time series fitting and prediction abilities, outperforming in several applications other methods and particularly linear models, such as dynamic linear regression. However, due to their nature, NNs are not easy to interpret and are often considered as black box models. The importance of each independent variable is hard to estimate and therefore test whether they have significant explanatory power and hence be included in the model or not. This task is very important for several applications, where the effect of each variable has to be identified, such as marketing modelling and analysis, where the effectiveness of different marketing instruments has to be estimated, commonly modelled as impulse interventions. Statistical inference in these cases is sought, hindering the use of NNs. This paper proposes a framework to allow statistical inference of impulse interventions modelled with NNs. The effects of interventions are estimated and tested for statistical significance. Using a Monte Carlo simulation the power of the proposed test is compared with dynamic linear regression models. The power is found to be higher and the estimation of the simulated effects is more accurate. Based on this framework strategies to code multiple impulses with NNs are discussed.

Neural Networks (NN) have demonstrated remarkable time series fitting and prediction abilities, outperforming in several applications other methods and particularly linear models, such as dynamic linear regression. However, due to their nature, NNs are not easy to interpret and are often considered as black box models. The importance of each independent variable is hard to estimate and therefore test whether they have significant explanatory power and hence be included in the model or not. This task is very important for several applications, where the effect of each variable has to be identified, such as marketing modelling and analysis, where the effectiveness of different marketing instruments has to be estimated, commonly modelled as impulse interventions. Statistical inference in these cases is sought, hindering the use of NNs. This paper proposes a framework to allow statistical inference of impulse interventions modelled with NNs. The effects of interventions are estimated and tested for statistical significance. Using a Monte Carlo simulation the power of the proposed test is compared with dynamic linear regression models. The power is found to be higher and the estimation of the simulated effects is more accurate. Based on this framework strategies to code multiple impulses with NNs are discussed.