Exam 20: Time-Series Analysis and Forecasting

Seasonal variation is one of the four different components of a time series.These are cycles that occur over short repetitive calendar periods and,by definition,have duration of less than one year.

Daily Sandwich Sales The daily sales figures shown below have been recorded in a sandwich shop. week Day 1 2 3 4 Manday 38 46 35 59 Tuesday 40 36 52 53 Wednesday 17 32 25 28 Thursday 20 17 28 33 Friday 26 20 32 20 -{Daily Sandwich Sales Narrative} Does there appear to be a seasonal (weekly)pattern?

The quarterly earnings of a large microcomputer company have been recorded for the years 2011-2014.These data (in millions of dollars)are shown in the accompanying table. Year Quarter 2011 2012 2013 2014 1 60 65 68 74 2 75 83 85 90 3 93 98 102 106 4 62 69 71 75 Use an appropriate moving average to measure the quarterly variation by computing the seasonal (quarterly)indexes.

Which of the following statements about moving averages is not true?

Coffee Imports The coffee imports (in millions of dollars)from a Latin American country for 10 years are shown below. Year t Exports 2011 1 96 2012 2 110 2013 3 125 2014 4 141 2015 5 132 2016 6 126 2017 7 118 2018 8 125 2019 9 133 2020 10 148 -{Coffee Imports Narrative} Calculate the percentage of trend.

The term b₁ in the equation $\tilde { y } _ { t }$ = b₀ + b₁t + b₂Q₁ + b₃Q₂ +b₄Q₃,where $\tilde { y } _ { t }$ represents the predicted value of y at time t,is:

An estimated second-order autoregressive model for average mortgage rate is: $\hat { \gamma } _ { t } = - 2.5 + 1.8 y _ { t - 1 } - .5 y _ { t - 2 }$ .If the average mortgage rate in 2003 was 7.0,and in 2002 was 6.5,the forecast for 2004 is ____________________,and for 2005 is ____________________.

Given a data set with 15 yearly observations,a 3-year moving average will have fewer observations than a 5-year moving average.

Coffee Imports The coffee imports (in millions of dollars)from a Latin American country for 10 years are shown below. Year t Exports 2011 1 96 2012 2 110 2013 3 125 2014 4 141 2015 5 132 2016 6 126 2017 7 118 2018 8 125 2019 9 133 2020 10 148 -{The Pyramids of Giza Narrative} Use the seasonal indexes computed in the previous question to deseasonalize the original time series data,and plot the deseasonalized time series.

If a time series does not exhibit a long-term trend,the method of exponential smoothing may be used to obtain short-term predictions about the future.

The time series component that reflects a long-term,relatively smooth pattern or direction exhibited by a time series over a long time period (more than one year)is called:

Smoothing time series data by the moving average method or exponential smoothing method is an attempt to remove the effect of the:

To assess the adequacy of a forecasting model,one measure that is often used is the

The trend equation for annual sales data (in millions of dollars)is $\tilde { y } _ { t }$ = 65 + 2.5t,where t = 1 for 2011.The monthly seasonal index for December is 0.97.The forecasted sales' value for December of 2020 is:

In general,it is easy to identify the trend component of a time series by using:

The most commonly used measures of forecast accuracy are the:

Daily Sandwich Sales The daily sales figures shown below have been recorded in a sandwich shop. week Day 1 2 3 4 Manday 38 46 35 59 Tuesday 40 36 52 53 Wednesday 17 32 25 28 Thursday 20 17 28 33 Friday 26 20 32 20 -{Daily Sandwich Sales Narrative} Plot the series and the moving averages on the same graph.

Suppose that we calculate the four-period moving average of the following time series 1 2 3 4 5 6 16 28 21 15 26 12 The centered moving average for period 3 is:

Carpet Outlet A carpet outlet has been keeping daily sales records over the past four weeks as shown below. Weat Day 1 2 3 4 Manday 22 27 24 25 Tuesday 25 29 25 27 Wednesday 27 28 28 25 Thursday 32 30 32 29 Friday 35 32 34 33 -{Carpet Outlet Narrative} What do the daily indexes tell us?

Biodiesel Sales Biodiesel (a vegetable oil or animal fat based diesel fuel)sales in Nebraska have been recorded over the past 10 months as shown below. Month Jan. Feb. March April May June July Aug. Sept. Oct. Sales 75 72 81 92 90 105 112 107 110 93 -{Biodiesel Sales Narrative} Compute the exponentially smoothed sales with w = 0.4 and w = 0.8.