We explore the performance of two dimensional (2-D) prediction based LSF quantization method for both wide-band and telephone-band (narrow-band) speech. The 2-D prediction based method exploits both the inter-frame and intra-frame correlations of LSF parameters. We show that a 4th order 2-D predictor provides optimum prediction gain as well as improved quantization performance at various choices of frame shift for both wide-band and telephone-band speech. Existing one dimensional (1-D) predictive method, exploiting only inter-frame correlation, results in poor performance at larger frame shifts; whereas proposed 2-D predictor provides lower spectral distortion as well as lower number of outliers compared to existing memory-based and memory-less methods.