Exam 17: Time Series Forecasting and Index Numbers

The linear regression trend model was applied to a time series sales data set based on the last 24 months' sales. The following partial computer output was obtained. Test the significance of the time term at α =.05. State the critical t value and make your decision using a two-sided alternative.

The demand for a product for the last six years has been 15, 15, 17, 18, 20, and 19. The manager wants to predict the demand for this time series using the following simple linear trend equation: tr_t = 12 + 2t. Use this equation to forecast the demand for this product, and then calculate the MAD.

The linear trend equation for the following data is = 1.4286 + 2.5(t) . Find the residual value (error) for period 7.

A time series decomposition method would not be used to forecast seasonal data.

Given the following data, compute the mean squared deviation (error).

The price and quantity of several food items are listed below for the years 1990 and 2000. Compute the Paasche index, using 1990 as the base year.

The simple moving average method is primarily useful in determining the impact of trend on a time series.

Two forecasting models were used to predict the future values of a time series. The forecasts are shown below with the actual values. Calculate the mean absolute deviation (MAD) for Model 2.

Consider the following data and calculations. Calculate the estimated value of b₁ and b₀, and state the linear trend regression prediction equation. = 28 = 140 = 80 = 1,090 = 390

When there is first-order autocorrelation, the error term in period t is related to the error term in period ________.

Removing the seasonal effect by dividing the actual time series observation by the estimated seasonal factor associated with the time series observation is called deseasonalization.

Consider a time series with 15 quarterly sales observations. Using the quadratic trend model, the following partial computer output was obtained. Write the prediction equation.

Causal variables can be used in forecasting models.

Based on the following data, a forecaster used simple exponential smoothing and determined the following: S₀ = 19, S₁ = 18.6, S₂ = 19.08, S₃ = 19.064, S₄ = 19.851, and S₅ = 19.481. Calculate the Mean Absolute Deviation (MAD).

Consider the quarterly production data (in thousands of units) for the XYZ manufacturing company below. Calculate the 4-period (quarter) centered moving average for the entire time series.

Two forecasting models were used to predict the future values of a time series. The forecasts are shown below with the actual values. Calculate the mean squared deviation (MSD) for Model 2.

Based on the following data, a forecaster used simple exponential smoothing and determined the following: S₀ = 19, S₁ = 18.6, S₂ = 19.08, S₃ = 19.064, S₄ = 19.851, and S₅ = 19.481. Calculate the average forecast error.

When using simple exponential smoothing, the more recent the time series observation, the ________ its corresponding weight.

A simple index is computed by using the values of one time series, while a(n) ________ index is based on a "market basket" consisting of more than one time series.

Consider the quarterly production data (in thousands of units) for the XYZ manufacturing company below. The normalized (adjusted) seasonal factors are winter = .9982, spring = .9263, summer = 1.139, and fall = .9365. Based on the following deseasonalized observations (d_t), a trend line was estimated. The linear regression trend equation is tr_t = 10.1 + 1.91(t). Based on this trend equation, the following trend values are calculated for each period in the time series. Year 1998 Year 1999 Year 2000 Isolate the cyclical and irregular components by calculating the estimate of CL_t × IR_t for the first four quarters in the time series.