## 3 Methods  
### Two-Stage Decomposition  
First stage decomposition method: Smoothing the sequence \(y\) by STL decomposition [40], adjusting the robustness weights of Loess in the inner loop using the outer loop, and the complete detrending and cycling of sequences in inner loops is performed to obtain the trend component \(Y_{t}\) and the period component \(Y_{c}\), while the residual component \(Y_{r}\) consists of the remaining values of the original sequence. The expression is as follows:  
\[y=f(Y_{t},Y_{c},Y_{r}) \tag{1}\]  
STL can break down practically any data with periodicity, is less impacted by missing and aberrant data, and has higher robustness when compared to decomposition techniques like X-11 and SEATS. It is usually considered that the time series can be decomposed into three components: a deterministic component, a periodic component, and a volatile component [41]. The urban traffic flow is a time series with stable changes and accompanied by some random disturbances [42], due to the inherent characteristics of the traffic flow, such as road attributes and the geographical location where the road is located, which makes the traffic flow have a long-term trend; the travel plans of traffic participants, such as going out plans, such as going out to work and going to school on working days, make the traffic flow have a relatively fixed periodicity; changes in the traffic environment, such as adverse weather conditions and traffic anomalies, lead to sudden changes in the traffic flow state. STL is used to decompose the traffic flow data and then extract the trend and periodic features in the traffic flow. Two common decomposition models of STL are the additive model and multiplicative model; for the inherent trend component and the fluctuation of the periodic component, which do not follow the change of time, choose the additive model; when the trend component follows the change of time with fluctuation changes, choose the multiplicative model, and considering the trend of the traffic flow determined by its intrinsic characteristics, the additive model should be selected. Second stage decomposition method: The EMD interpolates the extreme points found from the sequence into the upper and lower envelopes, then subtracts the original sequence from the mean of the envelope to obtain a new sequence, and keeps updating it continuously when the difference between the number of extreme points and the number of over zero points is less than one or the mean of the envelope is zero, which indicates that intrinsic mode function (IMF) components are smooth, and stops the above operation. VMD greatly reduces the probability of such problems and makes it adaptive and more fault tolerant, so VMD is chosen for the secondary decomposition of traffic flow. VMD decomposes a non-smooth time series by setting the number \(k\) of band-limited intrinsic mode functions (BIMF) and the quadratic penalty factor \(\alpha\). The principle is to transform the variational constrained problem into an unconstrained variational problem; the transformation process needs to satisfy that the sum of the bandwidths of each BIMF is minimum, and the summed sequence is equal to the original sequence; based on Wiener filtering, the original sequence is decomposed into \(k\) BIMFs to ensure that the estimated broadband sum of each component is at a minimum, and the specific derivation process of the VMD algorithm is described in Reference [43]. After the traffic flow sequence is decomposed by STL, the residual components with high frequency are obtained. Considering that there are still potential features that are not smooth, and thus interfere with the prediction effect of the model, VMD is used to decompose the residual components twice to fully exploit the useful information in them. The steps regarding the decomposition of the traffic flow by VMD are as follows. (1) Construct the variational constraint problem. \[\left\{