Question 121
A model that performs well in one period but poorly in another may suffer from:
A. Stable relationships
B. Structural change
C. Zero residuals
D. Perfect fit
Check answer
Select an option first.
Correct answer: B — Structural change
Explanation: Changing relationships → structural break. A/C/D: Incorrect.
Question 122
Text data is considered:
A. Structured
B. Unstructured
C. Numeric
D. Stationary
Check answer
Select an option first.
Correct answer: B — Unstructured
Explanation: Text lacks fixed structure. A/C/D: Incorrect.
Question 123
A linear trend model assumes that a variable increases by a constant amount each period. This implies the variable grows at:
A. A constant percentage rate
B. A constant dollar amount
C. A decreasing rate
D. A rate determined by the error term
Check answer
Select an option first.
Correct answer: B — A constant dollar amount
Explanation: Linear trend = same absolute increase each period. A: Constant percentage growth is log‑linear. C: Linear trend does not imply decreasing growth. D: Errors add noise but do not define the trend.
Question 124
A log‑linear trend model is most appropriate when the data show:
A. Constant absolute increases
B. Constant percentage increases
C. No trend
D. A sudden structural break
Check answer
Select an option first.
Correct answer: B — Constant percentage increases
Explanation: Log‑linear models capture exponential (percentage‑based) growth. Wrong options: A: Linear trend. C: No trend → no trend model needed. D: Structural breaks require different modeling.
Question 125
If a variable grows at a constant percentage rate, its natural log will appear:
A. Curved upward
B. Curved downward
C. Approximately linear
D. Random
Check answer
Select an option first.
Correct answer: C — Approximately linear
Explanation: Log of exponential growth becomes linear. Wrong options: A/B: Curvature indicates non‑constant percentage growth. D: Not true unless the data are noise.
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Question 126
A high R² in a trend model mainly indicates:
A. The model is correctly specified
B. The model explains much of the variation in the dependent variable
C. The errors are uncorrelated
D. The model is suitable for forecasting
Check answer
Select an option first.
Correct answer: B — The model explains much of the variation in the dependent variable
Explanation: R² measures explained variation. Wrong options: A/C/D: R² alone cannot confirm assumptions or forecasting ability.
Question 127
A log‑linear model predicts future values by:
A. Adding a constant amount
B. Multiplying by a constant growth factor
C. Taking the square root of the trend
D. Using only seasonal adjustments
Check answer
Select an option first.
Correct answer: B — Multiplying by a constant growth factor
Explanation: Log‑linear → exponential growth. Wrong options: A: Linear trend. C/D: Not relevant.
Question 128
If the trend coefficient in a log‑linear model is 0.03, the approximate growth rate per period is:
A. 0.03%
B. 3%
C. 30%
D. Cannot be determined
Check answer
Select an option first.
Correct answer: B — 3%
Explanation: Small log‑growth ≈ percentage growth. Wrong options: A/C: Misinterpret scale. D: Growth is directly interpretable.
Question 129
A linear trend model is likely inappropriate if the data show:
A. Constant absolute increases
B. Constant percentage increases
C. No trend
D. A stable mean
Check answer
Select an option first.
Correct answer: B — Constant percentage increases
Explanation: Percentage growth → log‑linear. Wrong options: A: Linear OK. C/D: Not relevant.
Question 130
A log‑linear model is preferred when the variable:
A. Alternates randomly
B. Shows exponential growth
C. Has no trend
D. Is stationary
Check answer
Select an option first.
Correct answer: B — Shows exponential growth
Explanation: Exponential growth → log‑linear. Wrong options: A/C/D: Not appropriate. B. Serial Correlation & Durbin‑Watson
Question 131
A Durbin‑Watson value far below 2 suggests:
A. No serial correlation
B. Positive serial correlation
C. Negative serial correlation
D. Heteroskedasticity
Check answer
Select an option first.
Correct answer: B — Positive serial correlation
Explanation: DW < 2 → positive correlation. Wrong options: A/C/D: Incorrect interpretations.
Question 132
If errors are positively serially correlated, forecasts tend to be:
A. Too volatile
B. Too smooth
C. Unbiased
D. Random
Check answer
Select an option first.
Correct answer: B — Too smooth
Explanation: Positive correlation smooths errors over time. Wrong options: A: Opposite effect. C/D: Not implied.
Question 133
A key limitation of trend models is that they often produce:
A. Uncorrelated errors
B. Serially correlated errors
C. Negative R²
D. No trend estimates
Check answer
Select an option first.
Correct answer: B — Serially correlated errors
Explanation: Trend models frequently violate independence. Wrong options: A/C/D: Not typical.
Question 134
Durbin‑Watson cannot be used when the model includes:
A. A constant
B. A lagged dependent variable
C. A trend term
D. A dummy variable
Check answer
Select an option first.
Correct answer: B — A lagged dependent variable
Explanation: DW is invalid with lagged dependent variables. Wrong options: A/C/D: DW still applicable.
Question 135
If DW is significantly below the lower critical value, we:
A. Accept no serial correlation
B. Reject no serial correlation
C. Conclude negative correlation
D. Cannot conclude anything
Check answer
Select an option first.
Correct answer: B — Reject no serial correlation
Explanation: Low DW → reject null of no positive correlation. Wrong options: A/C/D: Incorrect.
Question 136
Serial correlation in trend models suggests:
A. The model is perfect
B. A better model may exist
C. Errors are normally distributed
D. The trend is incorrect
Check answer
Select an option first.
Correct answer: C — Errors are normally distributed
Explanation: orrect Answer: B Serial correlation → model can be improved. Wrong options: A/C/D: Not necessarily true.
Question 137
A DW value near 2 indicates:
A. Positive serial correlation
B. Negative serial correlation
C. No serial correlation
D. Model misspecification
Check answer
Select an option first.
Correct answer: C — No serial correlation
Explanation: DW ≈ 2 → independence. Wrong options: A/B/D: Incorrect. C. Stationarity
Question 138
A stationary time series must have:
A. Constant mean and variance
B. Constant growth rate
C. No randomness
D. A linear trend
Check answer
Select an option first.
Correct answer: A — Constant mean and variance
Explanation: Stationarity requires stable mean/variance. Wrong options: B/C/D: Not required.
Question 139
A time series with a strong upward trend is:
A. Stationary
B. Non‑stationary
C. Mean‑reverting
D. White noise
Check answer
Select an option first.
Correct answer: B — Non‑stationary
Explanation: Trend → non‑stationary. Wrong options: A/C/D: Incorrect.
Question 140
Using an AR model on a non‑stationary series leads to:
A. Valid inference
B. Spurious results
C. Lower variance
D. Perfect forecasts
Check answer
Select an option first.
Correct answer: B — Spurious results
Explanation: Non‑stationarity → invalid inference. Wrong options: A/C/D: Incorrect.
Question 141
A stationary series has autocovariances that:
A. Change over time
B. Depend only on the lag
C. Are always zero
D. Are always one
Check answer
Select an option first.
Correct answer: B — Depend only on the lag
Explanation: Stationarity → autocovariance depends only on lag. Wrong options: A/C/D: Incorrect.
Question 142
A series with strong seasonality is usually:
A. Stationary
B. Non‑stationary
C. White noise
D. Random walk
Check answer
Select an option first.
Correct answer: B — Non‑stationary
Explanation: Seasonality → non‑constant mean. Wrong options: A/C/D: Incorrect. D. AR Models
Question 143
An AR(1) model predicts the current value using:
A. Only the error term
B. Only the previous value
C. Two previous values
D. A moving average
Check answer
Select an option first.
Correct answer: B — Only the previous value
Explanation: AR(1) uses one lag. Wrong options: A/C/D: Incorrect.
Question 144
In an AR(1) model, the lag coefficient must be less than 1 in absolute value to ensure:
A. Serial correlation
B. Stationarity
C. Heteroskedasticity
D. Perfect fit
Check answer
Select an option first.
Correct answer: B — Stationarity
Explanation: |b₁| < 1 ensures stationarity. Wrong options: A/C/D: Incorrect.
Question 145
If the lag coefficient in an AR(1) model is 0.9, the series:
A. Reverts quickly
B. Reverts slowly
C. Does not revert
D. Is stationary only if the intercept is zero
Check answer
Select an option first.
Correct answer: B — Reverts slowly
Explanation: High persistence → slow reversion. Wrong options: A/C/D: Incorrect.
Question 146
The intercept in an AR(1) model helps determine:
A. The long‑run mean
B. The short‑run shock
C. The slope of the trend
D. The variance
Check answer
Select an option first.
Correct answer: A — The long‑run mean
Explanation: Long‑run mean = b₀/(1 – b₁). Wrong options: B/C/D: Incorrect.
Question 147
AR models are appropriate when:
A. Past values influence current values
B. Data are purely random
C. Data have no pattern
D. Data have only seasonal patterns
Check answer
Select an option first.
Correct answer: A — Past values influence current values
Explanation: AR captures dependence on past values. Wrong options: B/C/D: Incorrect. E. Residual Autocorrelation
Question 148
Residual autocorrelation is tested by comparing the autocorrelation to:
A. The R²
B. The standard error of the autocorrelation
C. The Durbin‑Watson statistic
D. The intercept
Check answer
Select an option first.
Correct answer: B — The standard error of the autocorrelation
Explanation: t‑test uses autocorrelation / SE. Wrong options: A/C/D: Not used.
Question 149
If residual autocorrelations are significantly different from zero, the model is:
A. Correctly specified
B. Misspecified
C. Stationary
D. Trend‑free
Check answer
Select an option first.
Correct answer: B — Misspecified
Explanation: Significant autocorrelation → misspecification. Wrong options: A/C/D: Incorrect.
Question 150
The standard error of an estimated autocorrelation is approximately:
A. 1/T
B. 1/√T
C. T
D. √T
Check answer
Select an option first.
Correct answer: B — 1/√T
Explanation: SE ≈ 1/√T. Wrong options: A/C/D: Incorrect.
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