Air　pollution　is　a　major　global　problem,　closely　related　to　economic　and　social　development　and　ecological　environment　construction.　Air　pollution　data　for　most　regions　of　China　have　a　close　correlation　with　time　and　seasons　and　are　affected　by　multidimensional　factors　such　as　meteorology　and　air　quality.　In　contrast　with　classical　peaks-over-threshold　modeling　approaches,　we　use　a　deep　learning　technique　and　three　new　dynamic　conditional　generalized　Pareto　distribution　(DCP)　models　with　weather　and　air　quality　factors　for　fitting　the　time-dependence　of　the　air　pollutant　concentration　and　make　statistical　inferences　about　their　application　in　air　quality　analysis.　Specifically,　in　the　proposed　three　DCP　models,　a　dynamic　autoregressive　exponential　function　mechanism　is　applied　for　the　time-varying　scale　parameter　and　tail　index　of　the　conditional　generalized　Pareto　distribution,　and　a　sufficiently　high　threshold　is　chosen　using　two　threshold　selection　procedures.　The　probabilistic　properties　of　the　DCP　model　and　the　statistical　properties　of　the　maximum　likelihood　estimation　(MLE)　are　investigated,　simulating　and　showing　the　stability　and　sensitivity　of　the　MLE　estimations.　The　three　proposed　models　are　applied　to　fit　the　PM　2.5　time　series　in　Beijing　from　2015　to　2021.　Real　data　are　used　to　illustrate　the　advantages　of　the　DCP,　especially　compared　to　the　estimation　volatility　of　GARCH　and　AIC　or　BIC　criteria.　The　DCP　model　involving　both　the　mixed　weather　and　air　quality　factors　performs　better　than　the　other　two　models　with　weather　factors　or　air　quality　factors　alone.　Finally,　a　prediction　model　based　on　long　short-term　memory　(LSTM)　is　used　to　predict　PM　2.5　concentration,　achieving　ideal　results.