Exam 20: Time-Series Analysis and Forecasting

The trend line $\tilde { y } _ { t }$ = 125 + 2t and seasonal indexes shown in the table below were computed from 10 years of quarterly data.Forecast the values for the next four quarters. Quarter 1 0.6 2 1.3 3 1.6 4 0.5

The linear model for long-term trend is: y = $\beta$ ₀ + $\beta$ ₁t + $\varepsilon$ ,where t is the time period.The trend is indicated by:

If the time series displays a gradual or no trend and no evidence of seasonal variation,exponential smoothing is not an effective as a forecasting method.

The easiest way of measuring the long-term trend is by ____________________ analysis,where time is the independent variable.

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} Calculate the four-month moving average,and four-month centered moving average.

The model y_t = T_t + C_t + S_t + R_t + $\varepsilon$ _t that assumes the time series value at time t is the sum of the four time series components T_t,C_t,S_t,and R_t is referred to as:

The most commonly used measures of forecast accuracy are mean absolute deviation (MAD)and the ____________________.

Weekly iPhones sales (in $1,000s)in an Apple store for the past three months are shown in the table below.Compute the four-week centered moving averages. Manth Week Sales 1 1 14 2 22 3 20 4 16 2 1 18 2 20 3 24 4 20 3 1 22 2 26 3 24 4 18

Use exponential smoothing,with w = 0.4,to forecast the next value of the time series that follows. 1 20 2 16 3 24 4 25 5 22 6 21

Which method would you recommend to your statistics professor in selecting the appropriate forecasting model if avoiding large errors is extremely important to him or her?

An estimated second-order autoregressive model for average mortgage rate is: $\tilde { y } _ { z } = - 3 + 2.0 y _ { t - 1 } - .75 y _ { t - 2 }$ .If the average mortgage rate in 2004 was 6.5 and in 2011 was 6.0,the forecast for 2013 is ____________________.

The linear trend $\hat { T } _ { 2 }$ = 115.8 + 2.5t was estimated using a time series with 25 time periods.The forecasted value for time period 26 is:

Photo Equipment Store Earnings The quarterly earnings of a chain of Photo Equipment stores 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 65 70 73 79 2 80 88 90 95 3 98 103 107 111 4 67 74 76 80 -Regression analysis was used to develop the following equation from 60 observations of quarterly data: $\tilde { y } _ { t }$ = 2500 - 3t - 3Q₁ + 2Q₂ + 5Q₃,where $Q _ { i } = \left\{ \begin{array} { l } 1 \text { if quarter } i \quad ( i = 1,2,3 ) \\0 \text { otherwise }\end{array} \right.$ Forecast the next four quarters.

In forecasting,we use data from the past in predicting the future value of the variable of interest.

The time series component that reflects a wavelike pattern describing a long-term trend that is generally apparent over a number of years is called cyclical.

Which of the following terms describes the overall long-term tendency of a time series?

Photo Equipment Store Earnings The quarterly earnings of a chain of Photo Equipment stores 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 65 70 73 79 2 80 88 90 95 3 98 103 107 111 4 67 74 76 80 -Regression analysis with t = 1 to 80 was used to develop the following forecast equation: $\tilde { y } _ { t }$ = 250 + 7.8t + 1.4Q₁ - 1.7Q₂ -1.4Q₃,where $Q _ { i } = \left\{ \begin{array} { l } 1 \text { if quarter } i \quad ( i = 1,2,3 ) \\0 \text { otherwise }\end{array} \right.$ Forecast the next four values.