Exam 17: Time-Series Analysis and Forecasting

A time series is shown in the table below: Week Day 1 2 3 4 Monday 16 15 18 21 Tuesday 22 21 20 25 Wednesday 20 23 20 24 Thursday 29 28 32 28 Friday 35 31 29 36 a. Compute the five-day moving averages to remove the seasonal and random variation. b. Calculate the seasonal (daily) indexes. c. What do the daily indexes tell us? d. Find the regression trend line. e. Calculate the seasonal indexes, based on the regression trend line developed in (d).

Which of the following is the time-series component that reflects the irregular changes in a time series?

Which of the following smoothing constants causes the most rapid reaction to a change in the current time-series value?

Quarterly sales revenue (in $million) for a particular company has been modelled using linear regression with indicator variables: Y = 132 + 2Q1 + 3Q2 - 5Q4 + 2t Where t is time in quarters, with origin March 2006 and Q1, Q2 and Q4 are the indicator variables for March, June and December quarters, respectively. Describe the trend and seasonal effects.

Which of the following statements is not correct?

We compute the five-period moving averages for all time periods except the first two and the last two.

In an exponentially smoothed time series, the smoothing constant w is chosen on the basis of how much smoothing is required. In general:

Consider the time series shown in the following table. Time period y Time period y 1 35 9 46 2 32 10 43 3 29 11 48 4 26 12 41 5 28 13 34 6 32 14 29 7 38 15 25 8 43 16 23 a. Calculate the percentage of trend for each time period. b. Plot the percentage of trend. c. Describe the cyclical effect (if there is one).

A time series regression equation measuring the number of surfboards sold by 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 trend component?

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 trend value for the third quarter of the year 2011 is:

Time-series forecasting with exponential smoothing uses the following formula:` $S _ { t } = w Y _ { t } + ( 1 - w ) S _ { t - 1 }$ . 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 forecast value at time t + 1, where w = 0.3, is given by:

The mean absolute deviation (MAD) and the sum of squares for forecast error (SSE) are the most commonly used measures of forecast accuracy. The model that forecasts the data best will usually have the:

We compute the three-period moving averages for all time periods except the first and last.

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 seasonal.

The actual and forecast values of a time series are shown below. Actual values Forecast values 2325 2330 2555 2595 2835 2860 3185 3125 3510 3390 a. Calculate the mean absolute deviation (MAD). b. Calculate the sum of squares for forecast error (SSE).

One of the simplest ways to reduce random variation is to smooth the time series via moving averages and exponential smoothing.

The mean absolute deviation averages the absolute differences between the actual values of the time series at time t and the forecast values at time:

The trend equation for quarterly sales data (in millions of dollars) for 2001-2005 is $\ddot{\mathbf{p}}_{t} = 6.8 + 1.2 t$ , where t = 1 for the first quarter of 2001. The seasonal index for the third quarter of 2006 is 1.25. The forecast sales for the third quarter of 2006 is:

Which of the following best describes what may be used when measuring the seasonal and random variation of a time series with no cyclical effect?

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) Using p-values test the significance of the independent variables. (b) Test the significance of the overall regression equation.