Exam 22: Time Series Analysis

A large automobile parts supplier keeps track of the demand for a particular part needed by its customers, automobile manufacturers. The time series plot below shows monthly demand for this part (in thousands) for a five-year period. The dominant component(s) in this time series is(are)

Consider the following to answer the question(s) below: Quarterly sales data (in $10,000) for a small company specializing in green cleaning products are shown in the time series graph below. A seasonal regression model was fit to these data and the results are shown below. The regression equation is Sales = 89.06 + 1.37t - 23.37Q2 - 23.91Q3 + 27.88Q4. -The regression coefficients in the seasonal regression model indicate that

Daily closing stock prices for Kyopera Corporation were obtained from August 3, 2016 through August 23, 2016 and appear in the time series graph below. a. Identify the dominant time series component(s) in the data. b. The method of moving averages was applied to these data. Below are time series graphs showing moving average results using two different values of L. In which application is a larger value of L used? i. ii. c. Suppose that the single exponential smoothing (SES) model was applied to these data. Below are time series graphs showing SES results using two different smoothing constants (α = 0.2 and α = 0.8). In which application is a larger value of α used? i. ii.

Consider the following to answer the question(s) below: A third-order autoregressive model, AR (3) was fit to monthly closing stock prices, adjusted for dividends, of Boeing Corporation from January 2006 through August 2008 (closing price on the first trading day of the month). The results are as follows: -Which of the following statements is true?

Consider the following to answer the question(s) below: A third-order autoregressive model, AR (3) was fit to monthly closing stock prices, adjusted for dividends, of Boeing Corporation from January 2006 through August 2008 (closing price on the first trading day of the month). The results are as follows: -Assume that the year 2000 is used as the index base period and that sales were $12 million in the year 2000. If sales were $18 million in the year 2006, the simple index number for the year 2006 is

A company has recorded annual sales (in $thousands) for the past 14 years and found the following linear trend model: = 5.23 + 144.60 t. This means that

Annual estimates of the population in the age group 65+ in a mid-sized city from 2005 (t = 1) onward are shown in the time series graph below. a. Identify the dominant time series component(s) in the data. b. Below are the results from fitting a linear trend model to the data. Use this model to estimate the 65+ population in this city for 2014 (t = 10). Fitted Trend Equation , = 145,703 + 801t c. Below are the results from fitting a quadratic trend model to the data. Use this model to estimate the 65+ population in this city for 2014 (t = 10). Fitted Trend Equation , = 148,187 - 554t + 135.5t2 d. The actual population estimate for 2014 is 157,218. Which model does better? Why?

Annual estimates of the population in a certain city from 2004 (t = 1) onward are shown in the time series graph below. a. Identify the dominant time series component(s) in the data. b. Below are the results from fitting a linear trend model to the data. Use this model to estimate the population in this city for 2014 (t = 11). Fitted Trend Equation , = 57,206 + 528t c. Below are the results from fitting a quadratic trend model to the data. Use this model to estimate the population in this city for 2014 (t = 11). Fitted Trend Equation , = 58,159 + 52t + 43.3t2 d. The actual population estimate for 2014 is 63,828. Which model does better? Why?

Consider the following to answer the question(s) below: The quarterly sales of all types of bicycles sold at a small sporting goods store in Charlottetown for the 16 quarters from January 2012 to December 2015 are depicted in the time series graph below. -Which of the following statements do not describe this data and model?

Consider the following to answer the question(s) below: A company has developed a linear trend model to forecast monthly sales. The following data show the actual sales and the "fitted" sales for months 1-12. -Based on these data, what is the mean absolute percentage error (MAPE) for the linear trend model?

Monthly closing stock prices, adjusted for dividends, were obtained for Boeing Corporation from January 2006 through August 2008 (closing price on the first trading day of the month). The time series graph of these data is shown below. a. Below are the results of fitting a third-order autoregressive model, AR (3). Write out the model. Are the second and third lagged values significant? Explain. Final Estimates of Parameters Type Coef SE Coef T P Lag 1 0.9247 0.1898 4.87 0.000 Lag 2 0.0429 0.2603 0.16 0.870 Lag 3 -0.0764 0.1959 -0.39 0.699 Constant 8.362 1.223 6.84 0.000 b. Below are the results of fitting a first-order autoregressive model, AR (1). Write out the model. Is this model typical for stock price data? Explain. Final Estimates of Parameters Type Coef SE Coef T P Lag 1 0.9098 0.0969 9.39 0.000 Constant 6.835 1.207 5.67 0.000

Consider the following to answer the question(s) below: The following table shows actual sales values and forecasts. -The MAD for the forecasting method used is

The MSE for the forecasting method used is

A large automobile parts supplier keeps track of the demand for a particular part needed by its customers, automobile manufacturers. The time series plot below shows monthly demand for this part (in thousands) for a five year period. a. Identify the dominant time series component(s) in the data. b. Suppose that the single exponential smoothing (SES) model was applied to these data. Below are time series graphs showing SES results using two different smoothing constants (α = 0.2 and α = 0.8). In which application is a larger value of α used? i. ii. c. What forecasting method may be a better choice than SES for these data? Explain.

Quarterly sales data (in $10,000) for a small company specializing in green cleaning products are shown in the time series graph below. A seasonal regression model was fit to these data and the results are shown below. The regression equation is Sales = 89.06 + 1.37t - 23.37Q2 - 23.91Q3 + 27.88Q4. a. Is the seasonal regression model significant overall? Explain. b. Interpret the regression coefficients in this model. c. Use this model to provide forecasts for each of the four quarters of the next year.

Consider the following to answer the question(s) below: Annual estimates of the population in a certain city from 2005 (t = 1) onward are shown in the time series graph below. -The forecasting method that will most likely be best for this time series is

Consider the following to answer the question(s) below: Quarterly sales data (in $10,000) for a small company specializing in green cleaning products are shown in the time series graph below. A seasonal regression model was fit to these data and the results are shown below. The regression equation is Sales = 89.06 + 1.37t - 23.37Q2 - 23.91Q3 + 27.88Q4. -Which of the following is not true?

Consider the following to answer the question(s) below: A third-order autoregressive model, AR (3) was fit to monthly closing stock prices, adjusted for dividends, of Boeing Corporation from January 2006 through August 2008 (closing price on the first trading day of the month). The results are as follows: -Let Boeing stock price be dependent variable y. The estimated model is

Which of the following statement is true about statistical measures used to estimate and report forecast error?

The following table shows actual sales values and forecasts provided by two different methods. a. Calculate the MAD for each method. b. Calculate the MSE for each method. c. Which method forecasts better?