Exam 14: Time Series Analysis

Mary collected data on women's summer Olympic 100 meter winning times and performed the trend analysis shown below. Describe the data and discuss her fitted trend's adequacy for making a 2008 forecast. What trend alternative(s), if any, might be preferred? Explain your reasoning.

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Question 1

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The linear trend may give forecasts that are too low since times seem to have leveled out. The linear model predicts that times will continue to decline by .07 second every four years, but this did not happen in the last three Olympics. The fit is reasonably good, but historical fit is only one criterion. Linear trend (the simplest model) is a reasonable choice by Occam's Razor only if it gives adequate forecasts, which it doesn't in this case. As an alternative, Mary might try an exponential trend, which is also a simple two-parameter model.

If a fitted trend equation is y_t = 816e^0.065^t, then the forecast for period 7 is:

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Question 2

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If y_t = 50e^0.07^t, then the forecast for period 10 is approximately:

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Question 3

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Which trend would you choose to forecast the 2013 value of Bob's beer can collection?

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Question 4

To initialize the forecasts in an exponential smoothing process, it is acceptable to:

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Question 5

Which data would be measured over an interval of time as opposed to at a point in time?

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Question 6

The quadratic model's R² is always at least as high as the linear model fitted to the same data.

(True/False)

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Question 7

Consider the following linear trend equation of an industry's sales: y_t = 120 + 12t, where t is measured in years and sales are measured in millions of dollars. Which is the most reasonable conclusion?

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Question 8

Which of the following is the least useful time-series forecasting model when there is a strong upward trend in the data?

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Question 9

The fitted annual sales trend is y_t = 227e^.037^t. The values of y_t are:

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Question 10

Monthly seasonal factors should be adjusted so they sum to 12.

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Question 11

The quadratic model can never have more than one turning point (peaks or troughs).

(True/False)

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Question 12

The shape of the fitted quadratic model y_t = 544 + 62t - 3.2t² is declining, then rising.

(True/False)

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Question 13

For the fitted time-series trend model y_t = 9.23e^-0.0867^t, it is correct to say that:

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Question 14

If the trend model y_t = a + bt + ct² is fitted to a time series, we would get:

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Question 15

Moving average models are causal models (as opposed to time-series models).

(True/False)

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Question 16

Concerning a seasonal index for monthly data, which statement is incorrect?

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Question 17

Bob analyzed the trend in the value of his investment portfolio over the last 16 quarters. (1) Translate each trend into plain English that a business person could understand. (2) Use each fitted trend to make a mathematical prediction for Bob's investment portfolio's value in period 20. (3) Which trend model seems most reasonable (or more than one)? What would Occam's Razor say?

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Question 18

In exponential smoothing, using α = .20 will give a smoother series than using α = .05.

(True/False)

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Question 19

Quarterly seasonal factors will sum to 4.

(True/False)

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Question 20

Showing 1 - 20 of 114

Mary collected data on women's summer Olympic 100 meter winning times and performed the trend analysis shown below. Describe the data and discuss her fitted trend's adequacy for making a 2008 forecast. What trend alternative(s), if any, might be preferred? Explain your reasoning.

If a fitted trend equation is y_t = 816e^0.065^t, then the forecast for period 7 is:

If y_t = 50e^0.07^t, then the forecast for period 10 is approximately:

Which trend would you choose to forecast the 2013 value of Bob's beer can collection?

To initialize the forecasts in an exponential smoothing process, it is acceptable to:

Which data would be measured over an interval of time as opposed to at a point in time?

The quadratic model's R² is always at least as high as the linear model fitted to the same data.

Consider the following linear trend equation of an industry's sales: y_t = 120 + 12t, where t is measured in years and sales are measured in millions of dollars. Which is the most reasonable conclusion?

Which of the following is the least useful time-series forecasting model when there is a strong upward trend in the data?

The fitted annual sales trend is y_t = 227e^.037^t. The values of y_t are:

Monthly seasonal factors should be adjusted so they sum to 12.

The quadratic model can never have more than one turning point (peaks or troughs).

The shape of the fitted quadratic model y_t = 544 + 62t - 3.2t² is declining, then rising.

For the fitted time-series trend model y_t = 9.23e^-0.0867^t, it is correct to say that:

If the trend model y_t = a + bt + ct² is fitted to a time series, we would get:

Moving average models are causal models (as opposed to time-series models).

Concerning a seasonal index for monthly data, which statement is incorrect?

In exponential smoothing, using α = .20 will give a smoother series than using α = .05.

Quarterly seasonal factors will sum to 4.

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Describing Data Visually

Descriptive Statistics

Probability

Discrete Probability Distributions

Continuous Probability Distributions

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One-Sample Hypothesis Tests

Two-Sample Hypothesis Tests

Analysis of Variance

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Exam 14: Time Series Analysis

Mary collected data on women's summer Olympic 100 meter winning times and performed the trend analysis shown below. Describe the data and discuss her fitted trend's adequacy for making a 2008 forecast. What trend alternative(s), if any, might be preferred? Explain your reasoning.

If a fitted trend equation is yt = 816e0.065t, then the forecast for period 7 is:

If yt = 50e0.07t, then the forecast for period 10 is approximately:

Which trend would you choose to forecast the 2013 value of Bob's beer can collection?

To initialize the forecasts in an exponential smoothing process, it is acceptable to:

Which data would be measured over an interval of time as opposed to at a point in time?

The quadratic model's R2 is always at least as high as the linear model fitted to the same data.

Consider the following linear trend equation of an industry's sales: yt = 120 + 12t, where t is measured in years and sales are measured in millions of dollars. Which is the most reasonable conclusion?

Which of the following is the least useful time-series forecasting model when there is a strong upward trend in the data?

The fitted annual sales trend is yt = 227e.037t. The values of yt are:

Monthly seasonal factors should be adjusted so they sum to 12.

The quadratic model can never have more than one turning point (peaks or troughs).

The shape of the fitted quadratic model yt = 544 + 62t - 3.2t2 is declining, then rising.

For the fitted time-series trend model yt = 9.23e-0.0867t, it is correct to say that:

If the trend model yt = a + bt + ct² is fitted to a time series, we would get:

Moving average models are causal models (as opposed to time-series models).

Concerning a seasonal index for monthly data, which statement is incorrect?

In exponential smoothing, using α = .20 will give a smoother series than using α = .05.

Quarterly seasonal factors will sum to 4.

Overview of Statistics

Data Collection

Describing Data Visually

Descriptive Statistics

Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions and Estimation

One-Sample Hypothesis Tests

Two-Sample Hypothesis Tests

Analysis of Variance

Simple Regression

Multiple Regression

Chi-Square Tests

Nonparametric Tests

Quality Management

Filters

If a fitted trend equation is y_t = 816e^0.065^t, then the forecast for period 7 is:

If y_t = 50e^0.07^t, then the forecast for period 10 is approximately:

The quadratic model's R² is always at least as high as the linear model fitted to the same data.

Consider the following linear trend equation of an industry's sales: y_t = 120 + 12t, where t is measured in years and sales are measured in millions of dollars. Which is the most reasonable conclusion?

The fitted annual sales trend is y_t = 227e^.037^t. The values of y_t are:

The shape of the fitted quadratic model y_t = 544 + 62t - 3.2t² is declining, then rising.

For the fitted time-series trend model y_t = 9.23e^-0.0867^t, it is correct to say that:

If the trend model y_t = a + bt + ct² is fitted to a time series, we would get: