It is known that in longitudinal studies, repeated measurements might be highly skewed and thus the violation of Gaussian assumption may be expected. Although positive skewness could be reduced by a variance stabilizing transformation such as the logarithmic transformation, difficulties may arise in the interpretation of parameters with respect to the original scale of the data. We propose partial antecorrelation models with independent asymmetric laplace (ALD) innovations for modeling skewed longitudinal data. We derive the distribution of a linear combination of independent standard ALD variables by an induction method and give the explicit forms for its probability density function, cumulative distribution function and moments. These give us a convenient way to investigate the proper-ties for the marginals of the model such as mean, variance, skewness and so on.Furthermore, we give an iterative algorithm for maximum likelihood estimation.Method of moments estimates are used as initial values for the algorithm. The simulation results and experiments with a real longitudinal data set are reported to illustrate the model and evaluate the accuracy of the estimation method.