Quiz Time series and simulation database

Which of the following is a characteristic of a stationary time series?

a) The mean and variance remain constant over time
b) The mean and variance change over time
c) The autocorrelation function changes over time
d) The series exhibits a trend or seasonal pattern

A time series is said to be weakly stationary if:

a) The mean and variance are constant over time
b) The mean is constant over time, but the variance changes
c) The variance is constant over time, but the mean changes
d) The mean and variance change over time, but the autocorrelation function is constant

A time series that exhibits a clear trend over time is said to be:

a) Stationary
b) Weakly stationary
c) Integrated
d) Non-stationary

Which of the following is a reason why stationary time series are preferred over non-stationary time series?

a) Stationary time series are easier to forecast
b) Stationary time series have a clearer relationship between variables
c) Non-stationary time series require more complex statistical models
d) All of the above

Which of the following defines covariance structure?

a. it is the covariance among the values of a time series at it lags.
b. it is the correlation between the values of noises prevalent in the data.\
c. both A and B
d. none of the above

Which of the following statements is true about white noise?

a) White noise is a predictable pattern of data.
b) White noise has a constant mean and variance.
c) White noise has a strong correlation with past observations.
d) White noise is a type of trend in time series data.

Why is white noise important in finance?

a) It helps predict future stock prices.
b) It is a useful tool for technical analysis.
c) It can be used to test the effectiveness of trading strategies.
d) It is an indicator of market volatility.

Which of the following is NOT a component of a time series?

a) Trend
b) Seasonality
c) Cyclicality
d) Randomness

What is the difference between Gaussian white noise and general white noise?

a) Gaussian white noise has a normal distribution, while general white noise can have any distribution.
b) Gaussian white noise has a constant mean and variance, while general white noise can have varying mean and variance.
c) Gaussian white noise is always stationary, while general white noise can be non-stationary.
d) There is no difference between Gaussian white noise and general white noise.

What are the properties of the lag operator?

a) It shifts a time series forward or backward in time.
b) It can be used to represent autoregressive processes.
c) It can be used to represent moving average processes.
d) All of the above.

What are the key features of the ACF and PACF of an MA(q) process?

a) The ACF cuts off after q lags, while the PACF decays exponentially.
b) The ACF decays exponentially, while the PACF cuts off after q lags.
c) Both the ACF and PACF cut off after q lags.
d) Both the ACF and PACF decay exponentially.

What is the maximum number of non-zero autocorrelations in an MA(q)?

a) q
b) q+1
c) 2q
d) 2q+1

What is the key characteristic of a non-stationary time series?

a) It has a constant mean and variance over time.
b) Its properties change over time, making it difficult to predict
c) It exhibits a strong correlation with its past values.
d) It has a well-defined seasonal pattern.

What is the unit root test used for in time series analysis?

a) To determine whether a time series is stationary or non-stationary.
b) To estimate the parameters of a regression model.
c) To forecast future values of a time series.
d) To identify the seasonal patterns in a time series.

What is the difference between trend-stationary and difference-stationary time series?

a) Trend-stationary time series have a well-defined seasonal pattern, while difference-stationary time series do not.
b) Trend-stationary time series can be made stationary by differencing, while difference-stationary time series cannot.
c) Trend-stationary time series have a non-zero mean, while difference-stationary time series have a zero mean.
d) Trend-stationary time series have a deterministic trend component, while difference-stationary time series have a stochastic trend component.

What is the main difference between a linear time trend and a log-linear time trend?

a) A linear time trend has a constant growth rate, while a log-linear time trend has a changing growth rate.
b) A linear time trend models the absolute change in the dependent variable over time, while a log-linear time trend models the percentage change in the dependent variable over time.
c) A linear time trend models the percentage change in the dependent variable over time, while a log-linear time trend models the absolute change in the dependent variable over time.
d) A linear time trend is a non-linear model, while a log-linear time trend is a linear model.

Which of the following is NOT a reason why a time series might be non-stationary?

a) Trend
b) Seasonality
c) Cyclicality
d) Randomness

What is the difference between a deterministic trend and a stochastic trend?

a) A deterministic trend is predictable, while a stochastic trend is random.
b) A deterministic trend is linear, while a stochastic trend is nonlinear.
c) A deterministic trend has a constant slope, while a stochastic trend has a varying slope.
d) There is no difference between a deterministic trend and a stochastic trend.

What is the difference between an additive seasonality model and a multiplicative seasonality model?

a) In an additive model, the seasonal component is added to the level component, while in a multiplicative model, it is multiplied by the level component.
b) In an additive model, the seasonal component varies around zero, while in a multiplicative model, it varies around one.
c) In an additive model, the seasonal component has constant variance over time, while in a multiplicative model, it has increasing variance over time.
d) There is no difference between an additive seasonality model and a multiplicative seasonality model.

What is differencing?

a) The process of removing seasonality from a time series.
b) The process of transforming non-stationary data into stationary data by taking differences between consecutive observations.
c) The process of fitting an autoregressive or moving average model to time series data.
d) The process of smoothing out noise in time series data using moving averages or other filters.

What is the order of integration of a time series?

a) The number of times it has been differenced to become stationary.
b) The number of lags in an autoregressive model.
c) The number of lags in a moving average model.
d) The number of seasonal periods in a seasonality model.

What is the difference between a random walk and a trend?

a) A random walk has a constant slope, while a trend has a varying slope.
b) A random walk is unpredictable, while a trend is predictable.
c) A random walk has no autocorrelation, while a trend has positive autocorrelation.
d) There is no difference between a random walk and a trend.

What is the difference between an autoregressive model and an autoregressive integrated moving average (ARIMA) model?

a) An ARIMA model includes differencing to make the data stationary, while an autoregressive model does not.
b) An ARIMA model includes moving average terms to capture noise in the data, while an autoregressive model does not.
c) An ARIMA model includes both differencing and moving average terms, while an autoregressive model only includes lagged values of the dependent variable.
d) There is no difference between an autoregressive model and an ARIMA model.

What is the purpose of residual diagnostics in time series modeling?

a) To check whether the residuals are normally distributed with constant variance over time.
b) To check whether there are any significant autocorrelations or partial autocorrelations in the residuals.
c) To check whether there are any outliers or influential observations in the data that may be affecting the results of the analysis.
d) All of the above.

Which of the following methods can be used to forecast future values of a time series?

a) Autoregressive models
b) Moving average models
c) Exponential smoothing models
d) All of the above

What is simulation?

The process of generating random numbers to represent uncertain variables in a model.
The process of estimating the parameters of a statistical model using maximum likelihood estimation.
The process of testing a hypothesis by comparing observed data to simulated data.
The process of fitting a model to time series data using autoregressive or moving average terms.

What is Monte Carlo simulation?

A type of simulation that uses random numbers to generate possible outcomes for a model.
A type of simulation that uses historical data to generate possible outcomes for a model.
A type of simulation that uses expert judgment to generate possible outcomes for a model.
A type of simulation that uses optimization techniques to find the best solution for a model.

What is bootstrapping?

The process of generating new samples from an existing sample by resampling with replacement.
The process of estimating the parameters of a statistical model using maximum likelihood estimation.
The process of testing a hypothesis by comparing observed data to simulated data.
The process of fitting a model to time series data using autoregressive or moving average terms.

What is the purpose of bootstrapping?

To estimate the sampling distribution and standard error of an estimator when analytical methods are not available or are too complex.
To test whether two samples come from the same population or not.
To estimate the parameters and goodness-of-fit statistics for an autoregressive or moving average model.
To forecast future values in time series data using exponential smoothing techniques.

What is the difference between parametric and nonparametric bootstrapping?

Parametric bootstrapping assumes a specific distribution for the data, while nonparametric bootstrapping makes no assumptions about the distribution.
Parametric bootstrapping uses historical data to generate possible outcomes for a model, while nonparametric bootstrapping uses expert judgment.
Parametric bootstrapping is faster and more accurate than nonparametric bootstrapping.
There is no difference between parametric and nonparametric bootstrapping.

What is the difference between a parametric and a non-parametric simulation?

A parametric simulation assumes a specific distribution for the data, while a non-parametric simulation makes no assumptions about the distribution.
A parametric simulation uses expert judgment to generate possible outcomes for a model, while a non-parametric simulation uses historical data.
A parametric simulation is faster and more accurate than a non-parametric simulation.
There is no difference between a parametric and a non-parametric simulation.

What is the purpose of resampling in bootstrapping?

To generate new samples from an existing sample by resampling with replacement.
To estimate the parameters of a statistical model using maximum likelihood estimation.
To test whether two samples come from the same population or not.
To forecast future values in time series data using exponential smoothing techniques.

What is the difference between standard error and standard deviation?

Standard error measures how much sample means vary from one another, while standard deviation measures how much individual observations vary from the mean.
Standard error measures how much individual observations vary from the mean, while standard deviation measures how much sample means vary from one another.
Standard error is always smaller than standard deviation.
There is no difference between standard error and standard deviation.

What is bias in statistics?

The difference between an estimator's expected value and its true value.
The degree to which an estimator's variance changes as sample size increases or decreases.
The degree to which an estimator's distribution deviates from normality.
The degree to which an estimator's distribution is skewed or kurtotic.

What is a pseudo-random number generator?

A computer algorithm that generates a sequence of numbers that appear to be random, but are actually deterministic.
A computer algorithm that generates a sequence of truly random numbers.
A statistical model that generates random numbers based on historical data.
A mathematical formula that generates random numbers based on expert judgment.

What is the purpose of antithetic variables in simulation?

To reduce the variance of an estimator by generating pairs of observations that are negatively correlated.
To increase the accuracy of a simulation by generating more observations than would be possible otherwise.
To test whether two samples come from the same population or not.
To forecast future values in time series data using exponential smoothing techniques.

What is control variates in simulation?

A technique for reducing the variance of an estimator by adding a known function to the model as an additional explanatory variable.
A technique for generating new samples from an existing sample by resampling with replacement.
A technique for estimating the parameters and goodness-of-fit statistics for an autoregressive or moving average model.
There is no such thing as control variates in simulation.

What is circular block bootstrapping?

A type of non-parametric bootstrapping that resamples blocks of consecutive observations instead of individual observations.
A type of parametric bootstrapping that assumes a specific distribution for the data, such as normal or lognormal.
A type of Monte Carlo simulation that uses expert judgment to generate possible outcomes for a model.
There is no such thing as circular block bootstrapping.

What are the key limitations of bootstrapping?

Bootstrapping assumes that the sample is representative of the population, which may not always be true.
Bootstrapping can be computationally intensive and time-consuming for large datasets.
Bootstrapping may not work well for small samples or rare events.
All of the above.

Quiz Time series and simulation database

Shashank 25th April 2023

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