ECS4863 Assignment 1 2026 (Answer Guide) – Due 12 May 2026
VERIFIED AND CERTIFIED ANSWERS. WRITTEN IN REQUIRED FORMAT AND WITHIN
GIVEN GUIDELINES. IT IS GOOD TO USE AS A GUIDE AND FOR REFERENCE, NEVER
PLAGARIZE. Thank you and success in your academics.
UNISA, 2026
QUESTION 1
1.1 Omitted Variable Bias (OVB)
Omitted variable bias occurs when a relevant explanatory variable that influences the
dependent variable is excluded from a regression model. This omission leads to biased
and inconsistent estimates of the coefficients of the included variables because the
omitted variable’s effect is incorrectly captured by those included.
A key condition for omitted variable bias is that the omitted variable must:
1. Affect the dependent variable, and
2. Be correlated with one or more included explanatory variables.
Positive vs Negative Bias:
Positive bias occurs when the omitted variable is positively correlated with both
the dependent variable and the included independent variable. This causes the
estimated coefficient to be overstated (larger than the true value).
Negative bias occurs when the omitted variable has an opposite relationship
(e.g., positively related to the dependent variable but negatively correlated with
the included independent variable), resulting in an understated coefficient
(smaller than the true value).
1.2 Weakly Dependent Time Series
A weakly dependent time series is a sequence of observations where the correlation
between values decreases as the time gap between them increases. In other words,
observations that are far apart in time have little or no influence on each other.
The weak dependence property implies that:
Observations are not completely independent, but their dependence is limited
and diminishes over time.
The covariance between two observations approaches zero as the lag between
them increases.
The time series does not exhibit strong persistence over long periods.
,This property is important because it ensures that:
Standard statistical methods (such as regression analysis) remain valid.
The law of large numbers and central limit theorem can be applied.
Estimators are consistent and asymptotically normal.
Examples of weakly dependent processes include many stationary autoregressive
processes.
1.3 Heteroscedasticity
Heteroscedasticity refers to a situation in which the variance of the error term in a
regression model is not constant across observations. Instead, the spread of the
residuals changes depending on the level of an independent variable or over time.
Implications for inference:
Ordinary Least Squares (OLS) estimators remain unbiased and consistent, but
They are no longer efficient (not minimum variance).
Standard errors become incorrect, leading to:
o Invalid t-tests
o Misleading confidence intervals
o Incorrect hypothesis testing
As a result, conclusions drawn from the model may be unreliable unless corrective
measures (e.g., robust standard errors) are used.
1.4 Key Concepts
(a) Covariance Stationary Process
A covariance stationary process (also called weak stationarity) is a time series whose
statistical properties remain constant over time. Specifically:
The mean is constant
The variance is constant
The covariance between two periods depends only on the lag between them,
not on time itself
This property is crucial in time series analysis because many econometric techniques
require stationarity to produce valid results.
(b) Sequential Exogeneity
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Sequential exogeneity means that the current error term is uncorrelated with all past
and present values of the explanatory variables, although it may be correlated with
future values.
Formally, this implies:
Explanatory variables can depend on past shocks (errors), but not on current
shocks.
This assumption is weaker than strict exogeneity and is often more realistic in time
series contexts where feedback effects may exist over time.
1.5 Importance of Relaxing Strict Exogeneity in Time Series Analysis
Strict exogeneity assumes that explanatory variables are uncorrelated with the error
term at all time periods (past, present, and future). However, in time series data, this
assumption is often unrealistic.
It is important to relax this assumption because:
Economic variables frequently exhibit dynamic relationships, where past
outcomes influence future explanatory variables.
Feedback mechanisms (e.g., policy responses, market adjustments) violate strict
exogeneity.
Allowing weaker assumptions such as sequential exogeneity makes models
more realistic and applicable to real-world data.
By relaxing strict exogeneity:
Models can better capture real economic behaviour
VERIFIED AND CERTIFIED ANSWERS. WRITTEN IN REQUIRED FORMAT AND WITHIN
GIVEN GUIDELINES. IT IS GOOD TO USE AS A GUIDE AND FOR REFERENCE, NEVER
PLAGARIZE. Thank you and success in your academics.
UNISA, 2026
QUESTION 1
1.1 Omitted Variable Bias (OVB)
Omitted variable bias occurs when a relevant explanatory variable that influences the
dependent variable is excluded from a regression model. This omission leads to biased
and inconsistent estimates of the coefficients of the included variables because the
omitted variable’s effect is incorrectly captured by those included.
A key condition for omitted variable bias is that the omitted variable must:
1. Affect the dependent variable, and
2. Be correlated with one or more included explanatory variables.
Positive vs Negative Bias:
Positive bias occurs when the omitted variable is positively correlated with both
the dependent variable and the included independent variable. This causes the
estimated coefficient to be overstated (larger than the true value).
Negative bias occurs when the omitted variable has an opposite relationship
(e.g., positively related to the dependent variable but negatively correlated with
the included independent variable), resulting in an understated coefficient
(smaller than the true value).
1.2 Weakly Dependent Time Series
A weakly dependent time series is a sequence of observations where the correlation
between values decreases as the time gap between them increases. In other words,
observations that are far apart in time have little or no influence on each other.
The weak dependence property implies that:
Observations are not completely independent, but their dependence is limited
and diminishes over time.
The covariance between two observations approaches zero as the lag between
them increases.
The time series does not exhibit strong persistence over long periods.
,This property is important because it ensures that:
Standard statistical methods (such as regression analysis) remain valid.
The law of large numbers and central limit theorem can be applied.
Estimators are consistent and asymptotically normal.
Examples of weakly dependent processes include many stationary autoregressive
processes.
1.3 Heteroscedasticity
Heteroscedasticity refers to a situation in which the variance of the error term in a
regression model is not constant across observations. Instead, the spread of the
residuals changes depending on the level of an independent variable or over time.
Implications for inference:
Ordinary Least Squares (OLS) estimators remain unbiased and consistent, but
They are no longer efficient (not minimum variance).
Standard errors become incorrect, leading to:
o Invalid t-tests
o Misleading confidence intervals
o Incorrect hypothesis testing
As a result, conclusions drawn from the model may be unreliable unless corrective
measures (e.g., robust standard errors) are used.
1.4 Key Concepts
(a) Covariance Stationary Process
A covariance stationary process (also called weak stationarity) is a time series whose
statistical properties remain constant over time. Specifically:
The mean is constant
The variance is constant
The covariance between two periods depends only on the lag between them,
not on time itself
This property is crucial in time series analysis because many econometric techniques
require stationarity to produce valid results.
(b) Sequential Exogeneity
Please note that these answers are downloaded by multiple students hence not
advisable to submit without proper paraphrasing.
, In case you need assistance with your assignments/ exam please email below,
your work will be handled in a professional manner with distinction and quality
work guaranteed
If you need this document in editable form please email below, ill share for free.
Thank you and all the best in your academics.
https://whatsapp.com/channel/0029Vb3iSmTIt5rqFVDPSB1X
https://t.me/unisagrouplinks2025
Sequential exogeneity means that the current error term is uncorrelated with all past
and present values of the explanatory variables, although it may be correlated with
future values.
Formally, this implies:
Explanatory variables can depend on past shocks (errors), but not on current
shocks.
This assumption is weaker than strict exogeneity and is often more realistic in time
series contexts where feedback effects may exist over time.
1.5 Importance of Relaxing Strict Exogeneity in Time Series Analysis
Strict exogeneity assumes that explanatory variables are uncorrelated with the error
term at all time periods (past, present, and future). However, in time series data, this
assumption is often unrealistic.
It is important to relax this assumption because:
Economic variables frequently exhibit dynamic relationships, where past
outcomes influence future explanatory variables.
Feedback mechanisms (e.g., policy responses, market adjustments) violate strict
exogeneity.
Allowing weaker assumptions such as sequential exogeneity makes models
more realistic and applicable to real-world data.
By relaxing strict exogeneity:
Models can better capture real economic behaviour
