Time series analysis. - Question Bank

1. When dealing with non-stationary time series that are cointegrated, the appropriate model is often a:
A) Simple OLS regression
B) Vector Autoregression (VAR) model
C) Error Correction Model (ECM)
D) ARIMA model for each series independently
2. A key indicator of a spurious regression is:
A) High R-squared and significant t-statistics, despite non-significant Durbin-Watson statistic
B) Low R-squared and insignificant t-statistics
C) A Durbin-Watson statistic close to 2
D) Stationary residuals
3. The concept of spurious regression arises when:
A) Two stationary variables are regressed on each other
B) Two non-stationary variables with no long-run relationship are regressed on each other
C) Two stationary variables are regressed on a non-stationary variable
D) Two non-stationary variables that are cointegrated are regressed
4. Which of the following is a common application of GARCH models in econometrics?
A) Forecasting GDP
B) Modeling asset price volatility
C) Estimating inflation rates
D) Analyzing unemployment trends
5. GARCH (Generalized Autoregressive Conditional Heteroskedasticity) models extend ARCH models by:
A) Including only AR terms
B) Including MA terms for the variance
C) Modeling the mean with MA terms
D) Assuming constant variance
6. ARCH (Autoregressive Conditional Heteroskedasticity) models are used to capture:
A) Time-varying mean
B) Time-varying variance
C) Non-linear relationships
D) Spurious correlations
7. A time series where the variance changes over time is called:
A) Stationary
B) Autocorrelated
C) Heteroscedastic
D) Homoscedastic
8. Granger causality tests whether:
A) One variable causes another in a true causal sense
B) Past values of one time series help predict another time series
C) Two series are cointegrated
D) A series is stationary
9. In a VAR(p) model, each variable is modeled as a linear function of:
A) Its own past values only
B) The past values of all variables in the system
C) Only the current values of other variables
D) A constant term only
10. Vector Autoregression (VAR) models are used to model:
A) A single time series
B) The interdependencies among multiple time series
C) Only stationary time series
D) Time series with only trend
11. If two non-stationary time series are cointegrated, their linear combination is:
A) Non-stationary
B) Stationary
C) Seasonal
D) Random
12. The concept of cointegration is relevant when dealing with:
A) Single time series
B) Multiple non-stationary time series that share a long-run equilibrium relationship
C) Stationary time series only
D) Time series with only seasonal components
13. What is a common issue when forecasting far into the future using ARIMA models?
A) Forecast intervals become narrower
B) Forecast accuracy tends to decrease
C) The model automatically adjusts
D) The trend component disappears
14. Forecasting with ARIMA models involves extrapolating the identified patterns into the future.
A) True
B) False
C) Only for AR models
D) Only for MA models
15. In a SARIMA model, (P,D,Q) represent the orders of the seasonal:
A) Autoregressive, Differencing, and Moving Average components
B) Autocorrelation, Deviation, and Mean Squared Error
C) Absolute, Difference, and Median
D) Average, Deterministic, and Maximum
16. A SARIMA model is often denoted as ARIMA(p,d,q)(P,D,Q)_s, where 's' represents:
A) The order of the AR component
B) The order of the MA component
C) The length of the seasonal cycle
D) The degree of differencing
17. Seasonal ARIMA (SARIMA) models are used to model time series that exhibit:
A) Only trend
B) Only cyclical patterns
C) Both regular (non-seasonal) and seasonal patterns
D) Only random fluctuations
18. The Augmented Dickey-Fuller (ADF) test is an extension of the Dickey-Fuller test that accounts for:
A) Non-linear relationships
B) Autocorrelation in the error terms
C) Presence of seasonality
D) Heteroscedasticity
19. If a time series has a unit root, it is likely to be:
A) Mean-reverting
B) Explosive or trending
C) Perfectly predictable
D) White noise
20. A unit root in a time series indicates that the series is:
A) Stationary
B) Non-stationary
C) Seasonally stationary
D) Trend-stationary
21. The Dickey-Fuller test is a statistical test used to check for:
A) Autocorrelation
B) Stationarity (specifically, the presence of a unit root)
C) Seasonality
D) Homoscedasticity
22. What is 'white noise' in the context of time series residuals?
A) A series with a constant mean, constant variance, and no autocorrelation
B) A series with a strong trend
C) A series with high seasonality
D) A series that is perfectly correlated with its past
23. After estimating an ARIMA model, what is checked to ensure the model is adequate?
A) The residuals should resemble white noise
B) The coefficients must be positive
C) The R-squared must be close to 1
D) The p-values of coefficients must be large
24. Which criterion is commonly used to select the order of AR and MA components in an ARMA/ARIMA model?
A) R-squared
B) Adjusted R-squared
C) Akaike Information Criterion (AIC) or Bayesian Information Criterion (BIC)
D) F-statistic
25. In the Box-Jenkins methodology, the identification stage typically involves examining:
A) ACF and PACF plots
B) Residual plots
C) Hypothesis tests
D) Lagrange multipliers
26. The Box-Jenkins methodology is a systematic approach for:
A) Estimating regression coefficients
B) Identifying, estimating, and checking ARIMA models
C) Decomposing time series into components
D) Testing for cointegration
27. An ARIMA(p, d, q) model implies that the d-th difference of the series is stationary and can be modeled as an ARMA(p, q) process.
A) True
B) False
C) Only if p=0
D) Only if q=0
28. The 'I' in ARIMA stands for:
A) Integrated
B) Independent
C) Intermittent
D) Iterated
29. The order of the MA component in a time series model is denoted by:
A) p
B) d
C) q
D) k
30. A Moving Average (MA) model relates the current value of a variable to:
A) Its own past values
B) Past error terms
C) Past values and past error terms
D) Future error terms
31. An AR(p) model includes lags up to order:
A) p
B) p+1
C) 1
D) 0
32. Which model is a simple model where the current value of a variable is a function of its past values and a random error term?
A) Moving Average (MA) model
B) Autoregressive (AR) model
C) ARIMA model
D) Regression model
33. The Partial Autocorrelation Function (PACF) measures the correlation between a time series and its lag after removing the effect of:
A) The trend component
B) The seasonal component
C) The correlations at shorter lags
D) The irregular component
34. The Autocorrelation Function (ACF) measures the correlation between a time series and its lags.
A) True
B) False
C) Only for stationary series
D) Only for non-stationary series
35. Autocorrelation refers to the correlation of a time series with:
A) Another unrelated time series
B) Its own past values
C) Its future values
D) A constant value
36. The difference between a time series and its lagged value (Y_t - Y_{t-1}) is known as:
A) Seasonal difference
B) First difference
C) Second difference
D) Moving average difference
37. A time series that is not stationary can often be made stationary by:
A) Adding a constant
B) Taking logarithms
C) Differencing
D) Multiplying by a variable
38. What does it mean for a time series to be stationary?
A) Its statistical properties (mean, variance, autocorrelation) do not change over time
B) Its values are always positive
C) It has no trend component
D) It is perfectly predictable
39. When calculating a centered moving average for an even order (e.g., 4-period moving average), what additional step is usually required?
A) Take the square root
B) Calculate a 2-period moving average of the moving average
C) Subtract the trend component
D) Add the seasonal component
40. A simple moving average of order 'k' for a time series at time 't' is the average of the observations from time 't-k+1' to 't'.
A) True
B) False
C) It depends on the model
D) Only if the series is stationary
41. Which method is commonly used to smooth out short-term fluctuations and highlight long-term trends in a time series?
A) Regression analysis
B) Moving averages
C) Hypothesis testing
D) Correlation analysis
42. In a multiplicative time series model, the observed value is:
A) Sum of components
B) Difference of components
C) Product of components
D) Average of components
43. The additive model for time series decomposition assumes that the components are:
A) Multiplied together
B) Added together
C) Subtracted from each other
D) Divided among themselves
44. Fluctuations in a time series that occur over periods longer than a year, often associated with economic booms and busts, are called:
A) Seasonality
B) Trend
C) Irregular component
D) Cyclical component
45. Which component of a time series represents fluctuations that are not due to trend, seasonality, or cyclical patterns?
A) Irregular component
B) Cyclical component
C) Trend
D) Seasonal component
46. Regular, predictable patterns that repeat over a fixed period (e.g., daily, weekly, yearly) in a time series are known as:
A) Trend
B) Cyclical component
C) Seasonality
D) Autocorrelation
47. A long-term increase or decrease in a time series is referred to as:
A) Seasonality
B) Cyclical component
C) Trend
D) Irregular component
48. Which of the following is NOT a typical component of a time series?
A) Trend
B) Seasonality
C) Irregular/Random component
D) Cross-sectional variation
49. What is the primary goal of time series analysis in econometrics?
A) To forecast future values of a variable
B) To identify causal relationships between variables
C) To measure the elasticity of demand
D) To calculate the GDP growth rate
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