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" Global warming is a topic of considerable importance and has attracted much attention in recent years. If a rise in global temperature continues, it will have a major impact on the global economy. We analyzed the monthly global temperature anomalies from January 1880 to August 2010. The time plot and ACF of the original sequence, ACF and PACF of the difference sequence are in Fig.1: (a) Describe the empirical characters of the global temperature anomalies based on Fig.1; (b) Briey describe the modelling procedure for this data set, including model speeilication1 estimation and diagnostic checking. (c) Assume we nally established the following two models: Model 1 : {1 le)(1 L)yt = (1 81L12)et, Model 2 : {1 AlLyt a t) 2 {1 11'1L12je3, Do the next 3-steps ahead forecasts according to Models 1 and 2 respec- tively. (Write down forecasting values and their uncertainty.) Series diff(Gt$V3) temperature C ACF -0.4 -0.2 0.0 02 04 0.6 0.B OBBL 1900 1920 1940 1960 1980 2000 0 10 15 20 25 30 year Lag Series Gt$V3 Series diff(Gt$V3) 1.0 0.0 -0.1 ACF Partial ACF 0.0 02 0.4 0.6 0.8 -0.2 -0.3 D 5 10 15 20 25 30 0 5 10 15 20 25 30