Date of Graduation

Fall 2019


Master of Science in Mathematics



Committee Chair

Yingcai Su


This work studies seasonal time series models with application to lake level and weather data. The thesis includes related time series concepts, integrated autoregressive moving average models (abbreviated as ARIMA), parameter estimation, model diagnostics, and forecasting. The studied time series models are applied to the data of daily lake level in Beaver Lake (1988-2017) and the data of daily maximum temperature in New York Central Park (1870-2017). Due to seasonality of the data, three different approaches are proposed to the modeling: regression method, functional ARIMA method and multiplicative seasonal ARIMA method. The forecasted values of the year 2018 are compared with observations; regression method is better to forecast daily values, and multiplicative ARIMA method is a better choice owing to higher accuracy for a short term and shorter period.


seasonal time series, AR model, MA model, ARMA model, ARIMA model, multiplicative seasonal ARIMA, forecast

Subject Categories

Longitudinal Data Analysis and Time Series | Statistical Models


© Mengqing Qin

Open Access