Application of the Mixed Autoregressive Moving Average Time Series Model to Temperature Pattern in Lagos, Nigeria

Abstract

Background: There is the need to take some precautions that will help to reduce the rates at which temperature increases which usually leads to global warming, that is the gradual rise in the mean temperature of the earth and its oceans. Objectives: The study examines temperature pattern in Lagos state using monthly data for 114 years (1901-2014). Methods: The univariate Box-Jenkins Autoregressive Moving Average (ARMA) model methodology and the maximum likelihood estimation method were used to obtain the parameters of the Mixed ARMA (MARMA) model of order (P,Q). This was derived from two independent ARMA models of order (p_1,q₁) and (p₂, q₂); where p=p₁+p₂  and. The Lagrange multiplier was used to test for linearity and Augmented Dickey Fuller test for stationarity. Forecast values from the optimum model were compared with the original rainfall series using the Mean Absolute Error (MAE). Results: The results showed that the data is linear, stationary and non-seasonal. ARMA models (5, 1) and (5, 2) emerged as the best models among others and are then used to obtain the fitted MARMA model (10, 7). Monte Carlo simulation was carried out using the MARMA model at different sample sizes n=250, n=500 and n=1000, each replicated 50 times. Each forecast value gave close estimates to the real temperature values with MAE=1.41535. Conclusions: The fitted MARMA model performed more excellently than the independent ARMA models in studying the behavior of temperature data and forecasting its future values.

Keywords: Temperature, Monte Carlo, independent ARMA, Mixed ARMA, Fitted MARMA