Exam 18: Time Series and Forecasting

Based on quarterly data collected over the last four years, the following regression equation was found to forecast the quarterly demand for the number of new copies of an economics textbook: _t = 3,305 - 665Qtr1 - 1,335Qtr2 + 305Qtr3, where Qtr1, Qtr2, and Qtr3 are dummy variables corresponding to Quarters 1, 2, and 3. Which of the following is not true?

The model y_t = β₀ + β₁y_{t - 1} + ε_t is known as a(n) ________.

The ________ method is a smoothing technique based on computing the average from a fixed number of the most recent observations.

The following table includes the information about a monthly time series. What is the forecast for May when the three-month moving average method is applied?

The following table includes the information about a monthly time series. When the exponential smoothing method with α = 0.5 is applied, what is the MSE?

The following table shows the annual revenues (in millions of dollars) of a pharmaceutical company over the period 1990-2011. The scatterplot indicates that the annual revenues have an increasing trend. Linear, exponential, quadratic, and cubic models were fit to the data starting with t = 1, and the following output was generated. Which of the following is a revenue forecast for 2012 found by the polynomial trend equation with the best fit?

Smoothing techniques are suitable for use when forecasts need to be updated frequently due to new observations that become available.

The following table includes the information about a monthly time series. What is the forecast for May using the exponential smoothing method with α = 0.5?

With the method of seasonal dummy variables, we estimate a trend forecasting model that includes ________ variables to capture seasonal variations.

Quantitative forecasting procedures are based on the judgment of the forecaster, who uses prior experience and expertise to make forecasts.

The following table shows the annual revenues (in millions of dollars) of a pharmaceutical company over the period 1990-2011. The autoregressive models of order 1 and 2, y_t = β₀ + β₁y_{t - 1} + ε_t, and y_t = β₀ + β₁y_{t - 1} + β₂y_{t - 2} + ε_t, were applied on the time series to make revenue forecasts. The relevant parts of Excel regression outputs are given below. Model AR(1): Model AR(2): Using the AR(1) model, find the company revenue forecast for 2012.

The following table shows the annual revenues (in millions of dollars) of a pharmaceutical company over the period 1990-2011. The scatterplot indicates that the annual revenues have an increasing trend. Linear, exponential, quadratic, and cubic models were fit to the data starting with t = 1, and the following output was generated. Which of the following is a linear trend equation?

When a time series is analyzed by the model y_t = T_t × S_t × I_t and the trend component T_t is set to be the centered moving average _t, which of the following remains to be estimated?

If there are T observations to estimate the lagged regression model y_t = β₀ + β₁x_{t - 1} + ε_t, what is the actual number of observations used to make the forecast for time period T?

A seasonal component differs from a cyclical component in that the seasonal component ________.

Which of the following is not true of seasonal dummy variables?

In the decomposition method, which of the following time series is used to estimate the trend?

If T denotes the number of observations, which of the following equations represents the one-step-ahead forecast for the model y_t = β₀ + β₁x_t + ε_t?

The following table includes the information about a monthly time series. When a forecast is made by the three-month moving average method, all three monthly observations used to make this forecast are treated equally in the sense that each of them has the same weight of 1/3. What is the forecast for May when the three-month weighted moving average method is applied with the weights: 1/6, 2/6, and 3/6? Assign the smallest weight to the oldest data and the largest weight to the most recent data.

Based on quarterly data collected over the last five years, the following regression equation was found to forecast the quarterly demand for the number of new copies of a business statistics textbook: _t = 2,298 - 6635Qtr1 - 1,446Qtr2 + 303Qtr3 + 26t, where Qtr1, Qtr2, and Qtr3 are dummy variables corresponding to Quarters 1, 2, and 3, and t = time period starting with t = 1. The demand forecast for the second quarter of the next year is ________.