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- Q.13 Describe models of a time series. CS Scanned with CamScannerQuestion 7 The following plots have been obtained for a time series. a) Suggest an appropriate ARIMA model based on the below plots. 120- 90- 60- 30- acf ## 1980 Jan 0.2- 0.1- 0.0 -0.1- 1990 Jan lag [1M] ## 1 arima011 ## 2 arima110 ## 3 auto 2000 Jan Month pact 0.2- 0.1- 0.0 -0.1- 2010 Jan lag [1M] .model sigma2 log_lik AIC AICC BIC ar roots b) The following ARIMA output has been obtained from R. Based on this output, explain which model would you recommend for forecasting? 2020 Jan poat ma_roots 17.1 -1393. 2787. 2787. 2806. 17.1 -1399. 2780. 2780, 2815, 17.4 -1392. 2788. 2788. 2807. c) If your selected model in part b) above has a p-value of 0.900 in the Ljung-Box test, would you recommend using this model? Explain why or why not.Companies are devoting time and energy to promote recycling. A major recycling company found some old documents that present the recorded amount of cell phone collected over a span of eight years. Year Cellular Telephones Collected (in millions) 2009 2.2 2010 2.6 2011 2.9 2012 3.4 2013 3.1 2014 4.2 2015 4.9 2016 5.3 Part a) Develop a time series plot with Year on the X axis and Cellular Telephones Collected on the Y axis. Part b) Does there appear to be a relationship between time and cellular telephones collected?
- An article in Quality Engineering presents viscosity data from a batch chemical process. A sample of these data is in the table. Reading left to right and up to down, draw a time series plot of all the data and comment on any features of the data that are revealed by this plot. Consider that the first 40 observations (the first 4 columns) were generated from a specific process, whereas the last 40 observations were generated from a different process. Does the plot indicate that the two processes generate similar results? Calculate the sample mean and sample variance of the first 40 and the second 40 observations.Determine the trend regression function for this data set. In order to obtain full marks for this question, you must complete the relevant table (template provided below) and then apply the appropriate time series formulae in the formulae sheet.Consider the time series data in the table below (a-c all count as one problem) a. Construct a time series plot. What type of pattern exists in the data?b. Develop a three-week moving average for this time series. Compute MSEand a forecast for week 8. c. Use α = 0.2 to compute the exponential smoothing value for the time series.Compute MSE and a forecast for week 8.
- Table 7 shows the seasonal factors for a monthly time series: Table 7 Month Seasonal Month Factor January -358.1 May February -196.3 June March 12.5 July April 187.4 August Describe the seasonal variation in this time series. Seasonal Factor 487.2 276.1 -27.9 -124.6 Month September October November December Seasonal Factor -136.7 92.6 70.4 -282.6Demand for haircut at PogiPoints Barber Shop has increased steadily for the past few months as seen in the following time series data. Do the necessary computations and choose the best answer that would complete each statement. With alpha = 0.8, the ES forecast for Month 6 would be: * A. 565 haircuts B. 574 haircuts C. 578 haircuts D. 584 haircutsPeriod 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…
- Question 2 For each of the below ACF plots which are obtained for a time series data of 4 different variables of interest:a) Explain the ACF plot. b) Describe what the raw data is likely to look like over time. c) What kind of variable is this plot likely to characterise (e.g., stock prices, exchange rates, temperature, etc.)?The component of a time series attached to long term variations is termed as O a. Secular trend O b. Seasonal trend O c. Cyclic variation O d. Random variationThe elevation of a lake surface (feet above sea level) varies according to the annual flow of a river that feeds it. A geological survey provided the following data from equally spaced intervals of time over a 15 year period. Time Period Elevation 1 4817 2 4819 3 4824 4 4822 5 4826 6 4831 7 4836 8 4837 9 4839 10 4837 11 4832 12 4827 13 4823 14 4818 15 4817 Make a time-series graph displaying the data.