We present the results of the Fermi-Large Area Telescope (LAT) light curve (LC) modelling of selected blazars: six flat spectrum radio quasars (FSRQs) and five BL Lacertae (BL Lacs). All objects have densely sampled and long-term LCs, over 10 years. For each blazar we generated three LCs with 7, 10, and 14 days binning, using the latest LAT 8-year source catalog and binned analysis provided within the fermipy package. The LCs were modelled with several tools: the Fourier transform, the Lomb-Scargle periodogram (LSP), the autoregressive moving average (ARMA), the fractional autoregressive integrated moving average, the continuous-time autoregressive moving average (CARMA) processes, the Hurst exponents ($H$), the $\mathcal{A}-\mathcal{T}$ plane, and the wavelet scalogram. The power law indices $\beta$ calculated from the Fourier and LSP modelling are consistent with each other. Many objects yield $\beta\simeq 1$, with PKS 2155$-$304 even flatter, but some are significantly steeper, e.g. Mrk 501 and B2 1520+31. The power law PSD is indicative of a self-affine stochastic process characterised by $H$, underlying the observed variability. Several algorithms for the $H$ estimations are employed. For some objects we found $H>0.5$, indicating long-term memory. We confirm a quasi-periodic oscillation (QPO) in the PKS 2155$-$304 data with the period of $612\pm 42$ days at a $3\sigma$ significance level, but do not detect any QPOs in other objects. The ARMA results give in general higher orders for 7 days binned LCs and lower orders for 10 and 14 days binned LCs, implying temporal variations in the LCs are consistently captured by the fitted models. CARMA modelling leads to featureless PSDs. The recently introduced $\mathcal{A}-\mathcal{T}$ plane allows to successfully classify the PSDs based on the LCs alone and clearly separates the FSRQ and BL Lac types of blazars.