((ARIMA and State-Space Models Final Exam, Key Concepts:: 2026- 2027.))
ARIMA and State-Space Models Final Exam, Key Concepts
Study online at https://quizlet.com/_igeto9
1. Asymptotic Infer- Asymptotic inference is the analysis of a statistic or its behavior as the sample
ence size increases. It helps to approximate situations where exact answers are not
available, often ensuring that methods perform well on large datasets.
2. Consistency via An estimator is consistent if its probability limit equals the true value being
Plim estimated. In other words, consistency means that as the sample size increases,
the estimator converges in probability to the correct parameter.
3. Confidence Inter- Confidence intervals are ranges of values, derived from sample data, that are likely
vals and Error to contain the true value of a population parameter. Error bounds indicate the
Bounds possible margin of error in the estimate.
4. Concepts of Con- Confidence intervals are ranges of values that estimate an unknown population
fidence Intervals parameter, such as a mean or proportion, with a certain level of confidence. The
concept reflects uncertainty in sample data and provides a likely range for the true
value.
5. Definition and In- A confidence interval is a range of values, estimated from sample data, that is
terpretation of likely to contain the true value of an unknown population parameter. The interval is
Confidence Inter- constructed so that, over many samples, a certain percentage (like 95%) of these
vals intervals would capture the true parameter. It reflects the uncertainty in estimating
population characteristics based on a sample.
6. Repeated Sam- The repeated sampling interpretation means that if we were to take many random
pling Interpreta- samples and construct a confidence interval from each, a certain percentage of
tion these intervals would include the true population parameter. In particular, the
percentage is given by the confidence level.
7. Error Bounds Error bounds, also known as margins of error, define how far the estimated value
and Precision in a confidence interval can be from the true population parameter. They measure
Measures the precision of the interval; smaller error bounds mean greater precision in the
estimate.
Page 1 of 18 3/31/2026
, ((ARIMA and State-Space Models Final Exam, Key Concepts:: 2026- 2027.))
ARIMA and State-Space Models Final Exam, Key Concepts
Study online at https://quizlet.com/_igeto9
8. Critical Value The margin of error is calculated by multiplying the critical value with the standard
Times Se error (SE). The critical value corresponds to the specified confidence level and
depends on the statistical distribution of the parameter.
9. Methods of Point Methods of point estimation are techniques used to provide a single best guess
Estimation of a population parameter based on sample data, common methods include the
method of moments and maximum likelihood estimation.
10. Maximum Likeli- Maximum Likelihood Estimation is a method of finding parameter values that
hood Estimation make the observed sample data most probable, by maximizing the likelihood
function with respect to those parameters.
11. Formulation of The formulation of the likelihood function involves expressing the probability of
the Likelihood observing the given data as a function of the unknown parameter. This function is
Function used to identify the parameter value that makes the observed data most probable.
12. Parameter Vec- A parameter vector is an ordered set of values representing all the unknown
tor parameters in a statistical model. In MLE, the likelihood function is expressed as
a function of this vector.
13. Sample Data The sample data likelihood refers to the value of the likelihood function for a given
Likelihood set of observed data and specific parameter values. It measures how likely it is to
observe the data given those parameters.
14. Log-Likelihood The log-likelihood function in MLE is the natural logarithm of the likelihood
Function in MLE function, used to simplify calculations and make finding the maximum easier.
15. Properties of Properties of maximum likelihood estimators refer to the characteristics of the
Maximum Likeli- estimators obtained by maximizing the likelihood function. Key properties include
hood Estimators consistency, efficiency, and asymptotic normality under certain regularity condi-
tions.
16.
Page 2 of 18 3/31/2026
, ((ARIMA and State-Space Models Final Exam, Key Concepts:: 2026- 2027.))
ARIMA and State-Space Models Final Exam, Key Concepts
Study online at https://quizlet.com/_igeto9
Asymptotic Nor- The asymptotic normality of a maximum likelihood estimator means that as the
mality of Maxi- sample size becomes very large, the distribution of the estimator approaches a
mum Likelihood normal distribution centered at the true parameter value.
Estimator
17. Adjustments for Adjustments for time-dependent data are statistical techniques used to account
Time-Dependent for the fact that observations collected over time may be correlated. These adjust-
Data ments help ensure accurate inferences when analyzing data that changes over
time.
18. Serial Correlation Serial correlation correction refers to statistical methods used to adjust for the
Correction dependence between observations that occur in sequence, such as in time series
data. This correction helps ensure that inferences about the mean vector are valid
when data points are not independent over time.
19. Lagged Covari- Lagged covariance is a statistical measure that quantifies the relationship between
ance two values of a variable at different time periods, separated by a certain lag. In
time-dependent data, it helps detect how much a variable at one time point is
related to its past values.
20. Matrix Algebra Matrix algebra provides mathematical tools to organize and manipulate data with
and Random Vec- many variables, using matrices and vectors. Random vectors are sets of variables
tors that have probabilistic properties and are key in multivariate statistics.
21. Matrix Square A matrix square root is a matrix that, when multiplied by itself, results in the
Roots original matrix. For certain matrices, especially positive definite matrices, a unique
square root can be found. This is useful in transforming random vectors and
modeling.
22. Kalman Filter Up- A Kalman filter update is a step in the recursive Kalman filter algorithm where
date estimates of system states are refined based on new measurements. The update
step uses matrix square roots to handle the covariance matrices efficiently and
maintain numerical stability.
Page 3 of 18 3/31/2026
ARIMA and State-Space Models Final Exam, Key Concepts
Study online at https://quizlet.com/_igeto9
1. Asymptotic Infer- Asymptotic inference is the analysis of a statistic or its behavior as the sample
ence size increases. It helps to approximate situations where exact answers are not
available, often ensuring that methods perform well on large datasets.
2. Consistency via An estimator is consistent if its probability limit equals the true value being
Plim estimated. In other words, consistency means that as the sample size increases,
the estimator converges in probability to the correct parameter.
3. Confidence Inter- Confidence intervals are ranges of values, derived from sample data, that are likely
vals and Error to contain the true value of a population parameter. Error bounds indicate the
Bounds possible margin of error in the estimate.
4. Concepts of Con- Confidence intervals are ranges of values that estimate an unknown population
fidence Intervals parameter, such as a mean or proportion, with a certain level of confidence. The
concept reflects uncertainty in sample data and provides a likely range for the true
value.
5. Definition and In- A confidence interval is a range of values, estimated from sample data, that is
terpretation of likely to contain the true value of an unknown population parameter. The interval is
Confidence Inter- constructed so that, over many samples, a certain percentage (like 95%) of these
vals intervals would capture the true parameter. It reflects the uncertainty in estimating
population characteristics based on a sample.
6. Repeated Sam- The repeated sampling interpretation means that if we were to take many random
pling Interpreta- samples and construct a confidence interval from each, a certain percentage of
tion these intervals would include the true population parameter. In particular, the
percentage is given by the confidence level.
7. Error Bounds Error bounds, also known as margins of error, define how far the estimated value
and Precision in a confidence interval can be from the true population parameter. They measure
Measures the precision of the interval; smaller error bounds mean greater precision in the
estimate.
Page 1 of 18 3/31/2026
, ((ARIMA and State-Space Models Final Exam, Key Concepts:: 2026- 2027.))
ARIMA and State-Space Models Final Exam, Key Concepts
Study online at https://quizlet.com/_igeto9
8. Critical Value The margin of error is calculated by multiplying the critical value with the standard
Times Se error (SE). The critical value corresponds to the specified confidence level and
depends on the statistical distribution of the parameter.
9. Methods of Point Methods of point estimation are techniques used to provide a single best guess
Estimation of a population parameter based on sample data, common methods include the
method of moments and maximum likelihood estimation.
10. Maximum Likeli- Maximum Likelihood Estimation is a method of finding parameter values that
hood Estimation make the observed sample data most probable, by maximizing the likelihood
function with respect to those parameters.
11. Formulation of The formulation of the likelihood function involves expressing the probability of
the Likelihood observing the given data as a function of the unknown parameter. This function is
Function used to identify the parameter value that makes the observed data most probable.
12. Parameter Vec- A parameter vector is an ordered set of values representing all the unknown
tor parameters in a statistical model. In MLE, the likelihood function is expressed as
a function of this vector.
13. Sample Data The sample data likelihood refers to the value of the likelihood function for a given
Likelihood set of observed data and specific parameter values. It measures how likely it is to
observe the data given those parameters.
14. Log-Likelihood The log-likelihood function in MLE is the natural logarithm of the likelihood
Function in MLE function, used to simplify calculations and make finding the maximum easier.
15. Properties of Properties of maximum likelihood estimators refer to the characteristics of the
Maximum Likeli- estimators obtained by maximizing the likelihood function. Key properties include
hood Estimators consistency, efficiency, and asymptotic normality under certain regularity condi-
tions.
16.
Page 2 of 18 3/31/2026
, ((ARIMA and State-Space Models Final Exam, Key Concepts:: 2026- 2027.))
ARIMA and State-Space Models Final Exam, Key Concepts
Study online at https://quizlet.com/_igeto9
Asymptotic Nor- The asymptotic normality of a maximum likelihood estimator means that as the
mality of Maxi- sample size becomes very large, the distribution of the estimator approaches a
mum Likelihood normal distribution centered at the true parameter value.
Estimator
17. Adjustments for Adjustments for time-dependent data are statistical techniques used to account
Time-Dependent for the fact that observations collected over time may be correlated. These adjust-
Data ments help ensure accurate inferences when analyzing data that changes over
time.
18. Serial Correlation Serial correlation correction refers to statistical methods used to adjust for the
Correction dependence between observations that occur in sequence, such as in time series
data. This correction helps ensure that inferences about the mean vector are valid
when data points are not independent over time.
19. Lagged Covari- Lagged covariance is a statistical measure that quantifies the relationship between
ance two values of a variable at different time periods, separated by a certain lag. In
time-dependent data, it helps detect how much a variable at one time point is
related to its past values.
20. Matrix Algebra Matrix algebra provides mathematical tools to organize and manipulate data with
and Random Vec- many variables, using matrices and vectors. Random vectors are sets of variables
tors that have probabilistic properties and are key in multivariate statistics.
21. Matrix Square A matrix square root is a matrix that, when multiplied by itself, results in the
Roots original matrix. For certain matrices, especially positive definite matrices, a unique
square root can be found. This is useful in transforming random vectors and
modeling.
22. Kalman Filter Up- A Kalman filter update is a step in the recursive Kalman filter algorithm where
date estimates of system states are refined based on new measurements. The update
step uses matrix square roots to handle the covariance matrices efficiently and
maintain numerical stability.
Page 3 of 18 3/31/2026
