ECO2012 Tutorial 4b 2012 PDF

ECO2012 TUTORIAL 4b QUESTION 1 The Economic Statistics Bureau located in Gauteng, South Africa, has recorded the number of company liquidations over 27 consecutive time periods as follows: Period Liquidations Period Liquidations Period...

ECO2012 TUTORIAL 4b QUESTION 1 The Economic Statistics Bureau located in Gauteng, South Africa, has recorded the number of company liquidations over 27 consecutive time periods as follows: Period Liquidations Period Liquidations Period Liquidations 1 246 10 273 19 234 2 243 11 284 20 162 3 269 12 305 21 240 4 357 13 293 22 298 5 163 14 348 23 264 6 154 15 423 24 253 7 109 16 291 25 293 8 162 17 320 26 302 9 222 18 253 27 188 (a) Calculate a three-period moving average for the time series data of company liquidations. (b) Calculate a five-period moving average for the time series data of company liquidations. QUESTION 2 The number of insurance claims per quarter on household policies submitted to the Port Elizabeth branch of a well-known insurance company is given as follows: Year Q1 Q2 Q3 Q4 2008 84 53 60 75 2009 81 57 51 73 2010 69 37 40 77 2011 73 46 39 63 (a) Plot the time series of household policy claims on a line graph. 1 (b) Isolate the trend effect by calculating a least squares trend line. Describe the trend in claims. (c) Calculate the quarterly seasonal indexes for household policy claims. Interpret the seasonal impact. (d) Calculate the seasonally adjusted trend estimate of the number of claims on household policies for the first and second quarters of 2012. QUESTION 3 The Department of Marine Resources reported the number of tonnes of pelagic fish caught off the Southern Coast of South Africa during each four-month period for the years from 2007 to 2010 as follows: Period 2007 2008 2009 2010 Jan-Apr 44 45 38 40 May-Aug 36 42 32 31 Sept - Dec 34 34 27 28 (a) Calculate the three-period moving average trend of pelagic fish caught off the southern coast. (b) Plot the actual catches of pelagic fish and the moving average trend on the same graph. Comment on the pattern of pelagic fish catches over the past four years. (c) Calculate the seasonal indexes for each of the four-month periods. Give an interpretation of the seasonal index for the four-month period from September to December. (d) Find the least squares trend line for pelagic fish caught off the southern South African coast for the past four years. (e) Estimate the seasonally adjusted expected number of tonnes of pelagic fish to be caught off the South Coast of South Africa for each four-month period of 2011. 2