The following data refers to a realization {x} of a time series {X,} observed over 4 time periods of magnitude 3 seasons.
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- Which of the time series forecasting methods would not be used to forecast seasonal data?Period Value Jan-2005 441 Feb-2005 446 Mar-2005 445 Apr-2005 445 May-2005 450 Jun-2005 455 Jul-2005 464 Aug-2005 476 Sep-2005 487 Oct-2005 490 Nov-2005 502 Dec-2005 511 Jan-2006 523 Feb-2006 539 Mar-2006 552 Apr-2006 565 May-2006 565 Jun-2006 566 Jul-2006 572 Aug-2006 566 Sep-2006 559 Oct-2006 554 Nov-2006 543 Dec-2006 536 Jan-2007 538 Feb-2007 544 Mar-2007 545 Apr-2007 548 May-2007 545 Jun-2007 542 Jul-2007 537 Aug-2007 533 Sep-2007 527 Oct-2007 514 Nov-2007 503 Dec-2007 497 Jan-2008 487 Feb-2008 477 Mar-2008 470 Apr-2008 458 May-2008 451 Jun-2008 435 Jul-2008 419 Aug-2008 409 Sep-2008 395 Oct-2008 381 Nov-2008 371 Dec-2008 353 Jan-2009 341 Feb-2009 326 Mar-2009 311 Apr-2009 300 May-2009 291 Jun-2009 280 Jul-2009 270 Aug-2009 261 Sep-2009 252 Oct-2009 243 Nov-2009 237 Dec-2009 234 Jan-2010 233 Feb-2010 231 Mar-2010 227 Apr-2010 217 May-2010 216 Jun-2010…The data for the energy production was recorded over the period from January 2014 to December 2022. This data has been averaged to quarterly data and the time series plot is give below in the Exhibit 14. a) Discuss the time series components evident in this data series shown in Exhibit 14. b) We carried out an estimated model of the household quarterly electricity demand from Qtr1 2014 to Qtr4 2022 as a function of time and quarter dummy variables. The variables are defined as: Y variable: total_energy: = is the total energy production of different sources (GWh) X variables: Time: = number of quarters since Qtr1 2014 to Qtr4 2022. Qtr 1: = 1 if the quarter is from January to March and 0 otherwise. Qtr 2: = 1 if the quarter is from April to June and 0 otherwise. Qtr 3: = 1 if the quarter is from July to September and 0 otherwise. Qtr 4: = 1 if the quarter is from September to December and 0 otherwise. Quarter 4 was used as the base quarter.
- The sales (in $'000) of CBO by a large department store for each period of three months are as follows. Quarter 20X4 First Second Third Fourth Required (a) Using an additive model, find the centred moving average trend. (b) Find the average seasonal variation for each quarter. (c) Predict sales for the last quarter of 20X7 and the first quarter of 20X8, stating any assumptions Show your workings more so in part b 20X5 20X6 20X7 8 30 60 20 20 50 80 40 40 62 92 24A time series trend equation is 23 + 73x. What is your forecast for period 20?(On inequal time interval) Obtain the straightline trend equation for the following data by the method of least square. Year : 1989 1991 1992 1993 1994 1995 1998 Sales (in '000 Rs.) : 140 144 160 152 168 176 180 Also, estimate the sales for 1996
- Calculate trend values by the method of least square from the data given below and estimate the sales for 1983 : Year 1976 1977 1978 1979 1980 : Sales of Co. ('000,000) : 70 74 80 86 90For this question, create a new column in the dataset where total rainfall is just the sum of our three separate rainfall variables. (Solve this question by Excel and econmetrics knowlege like time series) (a) plot crop yield vs. time. Does yield appear to be stationary? Why or why not? (b) plot total rainfall vs. time. Does total rainfall appear to be stationary? Why or why not? (c) plot the first-difference of crop yield vs. time. Does this series appear to be stationary? Why or why not? (d) formally test whether crop yield, rainfall and the first-difference of crop yield are stationary using the appropriate test. Be sure to do all parts of the hypothesis tests. After these tests, what can you say the order of integration is for each of the variables?(e) estimate a model where yield is a function of rainfall and time. You do not have to worry about the time variable being stationary or not, but the other two must be stationary (you might need to difference one or both of them to…Briefly outline Autoregressive Integrated Moving Average (ARIMA) models and illustrate their application for time-series modelling.
- Table 6 shows the year and the number ofpeople unemployed in a particular city for several years. Determine whether the trend appears linear. If so, and assuming the trend continues, in what year will the number of unemployed reach 5 people?The US. import of wine (in hectoliters) for several years is given in Table 5. Determine whether the trend appearslinear. Ifso, and assuming the trend continues, in what year will imports exceed 12,000 hectoliters?An economist at Nedbank ran a study of the relationship between FTSE/JSE All Shares index return (JALSH) and consumer price index (CPI) from 2006 to 2017, the data collected is shown in the Table 1 below. FTSE/JSE All Shares index return (JALSH) and consumer price index (CPI) from 2006 to 2017. Year JALSH (Y) CPI (X) 2006 0.41 4.7 2007 0.19 7.1 2008 -0.23 11.5 2009 0.32 7.1 2010 0.19 4.3 2011 0.03 5.0 2012 0.27 5.6 2013 0.21 5.7 2014 0.11 6.1 2015 0.05 4.6 2016 0.00 6.4 2017 0.21 5.3 The estimated regression…
