Exam 17: Time-Series Analysis and Forecasting

Which of the following are examples of seasons when measuring the seasonal component of a time series?

A time series is shown in the table below: Time period 1 48 2 50 3 46 4 42 5 40 6 32 7 34 8 26 9 21 10 13 a. Plot the time series to determine which of the trend models appears to fit better. b. Use the regression technique to calculate the linear trend line and the quadratic trend line. Which line fits better? Use the best model to forecast the value of y for time period 7.

The model that assumes the time-series value at time t is the sum of the four time-series components is referred to as the:

A retailing outlet has been keeping daily sales records over the past four weeks, as shown below. Week Day 1 2 3 4 Monday 20 25 22 27 Tuesday 26 30 26 28 Wednesday 28 29 29 26 Thursday 34 32 34 31 Friday 38 35 37 36 a. Use the regression technique to calculate the linear trend line. b. Calculate the daily indexes based on the regression trend line in part (a). c. What do the daily indexes tell us?

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.

Share prices at the end of trading for 10 selected stocks is an example of a time series.

Which of the following will be reflected by a deseasonalised time series?

A trend is one of the four different components of a time series. It is a long-term, relatively smooth pattern or direction exhibited by a series, and its duration is more than one year.

Smoothing time-series data by the moving average method or exponential smoothing method is an attempt to remove the effect of the random variation component.

A company selling swimming goggles wants to analyze the company's Australian sales time figures. Time series forecasting with regression was used to generate Excel output to estimate trend of the time series of Swimming goggle sales (in thousands of dollars) where the origin is the March Quarter 2000. SUMMARY OUTPUT Regression Statistics Muttiple R 0.37281 R Square 0.13899 Adjusted R Square 0.12243 Standard Error 10.3925 Observations 54 $\text { ANOYA }$ df SS MS F Significance F Regression 906.5867925 906.59 8.39406 0.005497292 Residual 52 5616.172467 108 Total 53 6522.759259 Coefficients StandardError tStat P-value Lover 95\% Upper 35\% Intercept 12.237 2.789633876 4.3866 5.6-05 6.639227133 17.8348469 0.26289 0.090738795 2.8973 0.0055 0.080812368 0.4449738 Interpret the 95% confidence interval for time t.

Petrol sales in Newcastle have been recorded over the past 10 months as shown below. Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Sales 75 72 81 92 90 105 112 107 110 93 a. Compute the five-month moving average. b. Calculate the four-month moving average, and four-month centred moving average. c. Compute the exponentially smoothed sales with w = 0.4 and w = 0.8. d. Draw the time series and the two sets of exponentially smoothed values. Does there appear to be a trend component in the time series?

A time series regression equation for a surfboard manufacturing company in Australia is given below: Y = 35 + 4Q₁ + 0.5Q₃ + 8Q₄ + 3t With t in quarters and the origin is December 2010 and Q₁ is the indicator variable for March, Q₃ is the indicator variable for September and Q₄ is the indicator variable for December. Which of the following statements is correct regarding the coefficient of Q₄?

The following trend line was calculated from quarterly data for 2006-2010: ŷ = 2.35 + 0.12t, where t = 1 for the first quarter of 2006. The seasonal indexes computed from the trend line for the four quarters of the year 2011 are 0.88, 0.93, 1.04, and 1.17, respectively. The seasonalised forecast for the third quarter of the year 2011 is:

To calculate the five-period moving average of a time series for a given time period, we average the value in that time period and the values in the four preceding periods.

Monthly sales (in $1000s) of a computer store are shown below. Month Jan Feb Mar Apr May Jun Sales 73 65 72 82 86 90 a. Compute the three-month and five-month moving averages. b. Compute the exponentially smoothed sales with w = 0.3 and w = 0.5 c. Calculate the four-month moving average, and four-month centred moving average.

The term 'seasonal variation' may refer to the four traditional seasons, or to systematic patterns that occur during a quarter, a week, or even one day, but within 12 months.

The daily sales figures below have been recorded in a medium-sized insurance company. Week Day 1 2 3 4 Monday 38 46 35 59 Tuesday 40 36 52 53 Wednesday 17 32 25 28 Thursday 20 17 28 33 Friday 26 20 32 20 a. Compute the three-day and five-day moving averages. b. Plot the series and the moving averages on the same graph. c. Does there appear to be a seasonal (weekly) pattern?

The number of four-period centred moving averages of a time series with 28 time periods is:

The following are the values of a time series for the first four time periods: t 1 2 3 4 23 25 28 24 Using exponential smoothing, with w = 0.25, the forecast value for time period 5 is:

A company selling swimming goggles wants to analyze its Australian sales figures. Time series forecasting with regression was used to generate Excel output to estimate trend and seasonal effects of the time series of Swimming goggle sales (in thousands of dollars) where the origin is the March Quarter 2000 and Q1 denotes sales in the March quarter, Q3 denotes sales in the September quarter and Q4 denotes sales in the December quarter. SUMMARY OUTPUT Regression Statistios Multiple R 0.9460 R Square 0.8950 Adjusted R Square 0.8864 Standard Error 3.7394 Obserwations 54 $\text { ANOYA }$ df SS MS F Significance F Regression 4 5837.596003 1459.4 104.3701 2.41949-23 Residual 49 685.1632564 13.9829 Total 53 6522.759259 Coeffients Standard Error tStat P-value Lower 95\% Upper 95\% Intercept 3.0588 1.3331 2.2944 0.0261 0.3797 5.7378 0.2518 0.0327 7.7052 0.0000 0.1861 0.3175 1 12.4604 1.3897 89664 0.0000 9.6677 15.2530 3 1.1458 1.4721 0.7784 0.4401 -1.8124 4.1041 4 23.9121 1.4403 16.6025 0.0000 21.0177 26.8064 (a) Forecast swimming goggle sales for all four quarters of 2016. (b) Are these good forecasts? Explain. (c) Separate the difference in your forecasts for June 2016 and December 2016 between seasonal and trend.