Exam 20: Time-Series Analysis and Forecasting

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 regression analysis to develop the trend line.

The overall upward or downward pattern of the data in an annual time series will be contained in which component of the time series?

Given a data set with 15 yearly observations,there are only seven 9-year moving averages.

Any variable that is measured over time in sequential order is called a time series.

Two forecasting models were used to predict the future values of a time series.These are shown in the accompanying table,together with the actual values. Forecast Value $F_{t}$ $\quad$ $\quad$ $\quad$ $\quad$ Actual Value $y_{t}$ Model 1 Model 2 9.0 7.7 7.6 7.8 8.1 8.2 7.0 8.5 8.9 9.6 9.0 11.0 Compute the mean absolute deviation (MAD)and sum of squares for forecast (SSE)for each model to determine which was more accurate.

If summer 2011 sales were $12,600 and the summer seasonal index was 1.20,then the deseasonalized 2011 summer sales value would be:

The time series component that reflects a long-term,relatively smooth pattern or direction exhibited by a time series over a long time period is called seasonal.

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

An estimated first-order autoregressive model for stock sales is: $\tilde { y } _ { t } = 1,000 + 1.3 y _ { t - 1 }$ .If sales in 2011 were 12,000,the forecast of sales for 2012 is ____________________.

Quarterly Sales The quarterly sales (in millions of dollars)of a Motorcycle Dealership were recorded for the years 2011-2014.They are listed below. Year Quarter Sales 2011 1 21 2 36 3 28 4 44 2012 1 25 2 23 3 39 4 36 2013 1 30 2 41 3 47 4 55 2014 1 34 2 29 3 32 4 48 -{Quarterly Sales Narrative} Calculate the four-quarter centered moving averages.

If summer 2011 sales were $16,800 and the summer seasonal index was 1.20,then the deseasonalized 2011 summer sales value was $20,160.

Hotel Occupancy A small hotel has recorded the number of rooms occupied during weekdays over a period of four weeks as is shown in the table below: Weat Day 1 2 3 4 Manday 16 15 18 21 Tue5day 22 21 20 25 Wednesday 20 23 20 24 Thursday 29 28 32 28 Friday 35 31 29 36 -{Hotel Occupancy Narrative} What do the daily indexes tell us?

{Hotel Occupancy Narrative} Calculate the seasonal indexes,based on the regression trend line developed in the previous question.

In determining weekly seasonal indexes for gas consumption,the sum of the 52 means for gas consumption as a percentage of the moving average is 5050.To get the seasonal indexes,each weekly mean is to be multiplied by:

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} Plot the percentage of trend.

Random variation is one of the four different components of a time series.It is caused by irregular and unpredictable changes in a time series that are not caused by any other component.It tends to mask the existence of the other more predictable components.

Which of the following methods is appropriate for forecasting a time series when the trend,cyclical,and seasonal components of the series are not significant?

Cyclical variation,one of the four different components of a time series,is more likely to exhibit business cycles that record periods of economic recession and inflation.

The formula S_t = wy_t + (1 - w)S_t-1 is used in time-series forecasting with exponential smoothing,where S_t is the exponentially smoothed time series at time t,y_t is the value of the time series at time t,and w is the smoothing constant.The forecasted value at time t + 1 where w = .4 is given by:

The purpose of using the moving average is to take away the short-term seasonal and random variation,leaving behind a combined trend and cyclical movement.