Using ARIMA Models in Time Series Analysis of Air Temperature in Portuguese Metropolitan Areas, 1950-2010

Air temperature, a temporal series, can be modeled using various techniques; including autoregressive integrated moving average (ARIMA) models [1]. The aim of this approach is to express current time series values as a linear function of past time series values (the autoregressive component) and current and lagged values of a white noise process (moving average component) [2].This research will analyse the characteristics of temperature series (Tmax-maximum , Tmin-minimum and Tm-mean) in the Lisbon Metropolitan Area (LMA), and a statistical model will be proposed using Box & Jenkins methodology. To the temperature series the used data were the month average, from January 1950 to December 2010. For modeling by autocorrelation function (ACF) and partial autocorrelation (PACF) methods, examination of values relative to auto regression and moving average were made and at last, an appropriate model for estimate of temperature values were found. To introduce objectivity in the numerical error analysis, the performance of the models were evaluated by certain statistical evaluation indices. Thus, seven indicators are used to calculate the predictive skill of the models developed in this study. The Index of Agreement (ID), Mean Absolute Percentage Error (MAPE), Root Mean Squared Error (RMSE), average absolute percentage error (AAPE), Akaike Information Criterion (AIC), Bayesian Information Criteria (BIC) and Hannon-Quinn Information Criterion (HIC) were calculated between predicted and observed admissions to evaluate the predictability of the model. The models evaluation statistics suggest that considerably satisfactory real-time forecasts of air temperature in Lisbon Portuguese Area can be generated using the Box–Jenkins approach. The model proposed will be useful for future decisions.

References [1] FC McMichael, JS Hunter. Stochastic modeling of temperature and flow in rivers, Water Resources Research. (1), 87-98.

[2] Box G., Jenkins G.M. (1994) Time series analysis: forecasting and control (3rd Edn). Englewood Cliffs, NJ: Prentice Hall.