Wavelet Packet‐Autocorrelation Function Method for Traffic Flow Pattern Analysis

Accurate, timely forecasting of traffic flow is of key importance in effective management of traffic congestion in intelligent transportation systems. A detailed understanding of properties of traffic flow is essential for building a reliable forecasting model. The discrete wavelet packet transform (DWPT) provides more coefficients than the conventional discrete wavelet transform (DWT), representing additional subtle details of a signal. In wavelet multiresolution analysis, an important decision is the selection of the decomposition level. This paper proposes a statistical autocorrelation function (ACF) for the selection of the decomposition level in wavelet multiresolution analysis of traffic flow time series. A hybrid wavelet packet-ACF method is proposed for analysis of traffic flow time series and determining its self-similar, singular, and fractal properties. A DWPT-based approach combined with a wavelet coefficients penalization scheme and soft thresholding is presented for denoising the traffic flow. The proposed methodology provides a powerful tool in removing the noise and identifying singularities in the traffic flow. The methods created in this work are of value in developing accurate traffic-forecasting models.