# Specific description of the signal decomposition issue in time series forecasting

While we forecast the time series with various deep learning models, signal decomposition like EMD (Empirical Mode Decomposition) and ITD (Intrinsic time-scale decomposition) is widely used to decompose the target series before feed them into the deep learning model to improve the forecasting performance.

However, EMD or ITD has a deadly edge effect, which in my humble opinion, is wrong if you use it before feeding them into the model. I don't know why people keep using it, maybe I am wrong

Take ITD for example, assume the target series is $$X_t$$, the formulation of ITD is: $$X_t =L_t +H_t$$ $$L_{t}=L_{k}+\left(\frac{L_{k+1}-L_{k}}{X_{k+1}-X_{k}}\right)\left(S_{t}-X_{k}\right), \quad t \in\left(\tau_{k}, \tau_{k+1}\right]$$

$$L_{k+1}=\alpha\left[X_{k}+\left(\frac{\tau_{k+1}-\tau_{k}}{\tau_{k+2}-\tau_{k}}\right)\left(X_{k+2}-X_{k}\right)\right]+(1-\alpha) X_{k+1}$$

In this way, we can decompose the $$X_t$$ into $$L_t$$ and $$H_t$$ for independent forecast, and we can sum up the forecasting results of them as the final forecasts of $$X_t$$.

Among them, $$τ_k$$ represents the time-abscissa corresponding to the $$k^{th}$$ extreme value. Then, if you want to decompose the signal whose time is between $$(τ_k, τ_{k+1})$$, the information of $$τ_{k+2}$$, that is, the future information, must be used.

As shown in Figure in this link, where solid line denotes the target series $$X_t$$ and dashed one denotes the decomposed one. When the value of the point $$τ_{j+1}$$ (solid line) is available, $$τ_j$$ and the decomposed data before it (dotted line) can be decomposed, which means you need a future data point for decomposition before forecasting. However, we do not know the future value when we forecast. So I briefly assume signal decomposition like ITD is not available for pre-process of time series forecasting. Wanted to know if it's right.

• On a slightly off-topic note, I noticed that people feed anything to neural networks and if it works out, it works out, regardless of theoretical considerations.
– Snoop
Jan 9, 2022 at 17:25
• Thanks for your answers. I agree that many people use signal decomposition before feeding into neural networks and it works out. But this is only work out in experiments but it is not applicable, i.e., we cannot transform it to fit real-life applications.
– Jasonmils
Jan 9, 2022 at 17:33