The table shows monthly time-series data for short-term visits to the United Kingdom and its territories by Australian residents.

(a) Explore trends in these data by using linear and quadratic trend models. Comment on the performance of these models.

(b) Use a 10-month MA to forecast values for January 2014 to May 2020.

(c) Use simple exponential smoothing to forecast values for January 2014 to May 2020. Let ? = 0.3 and then = 0.7. Which weight produces better forecasts?

(d) Compute the MAD for the forecasts obtained in parts (b) and (c) and compare the results.

(e) Determine seasonal effects using decomposition on these data. Let the seasonal effects have four periods. After determining the seasonal indices, deseasonalise the data.

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Period Number Number Period Oct. 16 Nov. 16 Jan. 13 19000 27 100 Feb. 13 16400 23 500 Mar. 13 25400 Dec. 16 43 200 Apr. 13 May 13 32 700 Jan. 17 17 400 52 700 Feb. 17 16 500 June 13 58 900 Mar. 17 27 500 July 13 Aug. 13 Sep. 13 Oct. 13 Nov. 13 44700 Apr. 17 May 17 June 17 July 17 Aug. 17 Sept. 17 Oct. 17 Nov. 17 46 100 62 100 46300 52 200 75 500 53 700 27 100 22 400 57 600 Dec. 13 45 000 57 700 25 600 Jan. 14 20100 16300 Feb. 14 24 100 Mar. 14 46 900 28300 Dec. 17 Apr. 14 May 14 June 14 37 300 52 500 Jan. 18 18 500 16 900 Feb. 18 Mar. 18 55 200 33 100 July 14 Aug. 14 Sept. 14 44 100 Apr. 18 May 18 June 18 July 18 Aug. 18 Sept. 18 Oct. 18 Nov. 18 43 700 62 200 50300 50300 68 700 Oct. 14 24900 47 000 Nov. 14 20300 42 700 18500 51 300 Dec. 14 59 100 Jan. 15 28 900 Feb. 15 15700 24 700 56 700 Mar. 15 26600 Dec. 18 Apr. 15 May 15 June 15 July 15 Aug. 15 Sept. 15 35 000 Jan. 19 18 200 15 700 32 900 47 000 69 000 Feb. 19 53 500 57 300 Mar. 19 Apr. 19 May 19 52 300 52 100 52 000 June 19 80 300 July 19 Aug. 19 Sept. 19 Oct. 19 Nov. 19 Oct. 15 27 000 64 900 Nov. 15 24500 58 800 45300 18600 Dec. 15 64 300 Jan. 16 26 900 15100 Feb. 16 25 500 Mar. 16 Apr. 16 May 16 29400 Dec. 19 58 800 33 100 Jan. 20 18 800 57 200 70 800 Feb. 20 15 600 June 16 Mar. 20 28 500 Apr. 20 May 20 July 16 Aug. 16 Sept. 16 51500 46 200 54 100 56 200 60 600