Question

3. (20 points) The following data is the number of new cases per day of smallpox in the village of Abakaliki. This village had a population of 120 in 1982 when it suffered this outbreak. Data covers 29 observations over a 29 day period: (Data source: Handbook of Small Data Sets.) 13 7 2 3 0 0 1 4 5 3 2 0 2 0 5 3 1 4 0 1 1 1 2 0 1 5 0 5 5 The time series data was regressed twice, once with a constant term ($\beta_0$) and the other time with the constant term ($\beta_0$) constrained to zero. Both regressions lagged by one time period. We want to know if the data series a random walk, and is it a random walk with drift or without drift. The time series regressions were solved as: Solving as lagged by one time period, including the constant term: $X_t = \beta_0 + \beta_1X_{t-1} + \epsilon$ (Where $\epsilon$ is the error term.) Standard errors are in parenthesis underneath. $X_t = 1.644919 + .2386X_{t-1}$ (.502256) (.133) Alternatively, also solved as lagged by one time period, but in this case the constant term has been constrained to equal zero: $X_t = \beta_1X_{t-1} + \epsilon$ Standard errors are in parenthesis underneath. $X_t = .531328X_{t-1}$ (.114953) A. Use the t table to determine of the number of new cases of smallpox is a random walk. Show your work. B. In addition, determine if it is a random walk with drift, or without drift. Show your work.

          3.
(20 points) The following data is the number of new cases per day of smallpox in the
village of Abakaliki. This village had a population of 120 in 1982 when it suffered this outbreak.
Data covers 29 observations over a 29 day period: (Data source: Handbook of Small Data
Sets.)
13 7 2 3 0 0 1 4 5 3 2 0 2 0 5 3 1 4 0 1 1 1 2 0 1 5 0 5 5
The time series data was regressed twice, once with a constant term ($\beta_0$) and the other time
with the constant term ($\beta_0$) constrained to zero. Both regressions lagged by one time period.
We want to know if the data series a random walk, and is it a random walk with drift or without
drift.
The time series regressions were solved as:
Solving as lagged by one time period, including the constant term:
$X_t = \beta_0 + \beta_1X_{t-1} + \epsilon$
(Where $\epsilon$ is the error term.)
Standard errors are in parenthesis underneath.
$X_t = 1.644919 + .2386X_{t-1}$
(.502256)
(.133)
Alternatively, also solved as lagged by one time period, but in this case the constant term has
been constrained to equal zero:
$X_t = \beta_1X_{t-1} + \epsilon$
Standard errors are in parenthesis underneath.
$X_t = .531328X_{t-1}$
(.114953)
A. Use the t table to determine of the number of new cases of smallpox is a random walk.
Show your work.
B. In addition, determine if it is a random walk with drift, or without drift. Show your work.

3.
(20 points) The following data is the number of new cases per day of smallpox in the
village of Abakaliki. This village had a population of 120 in 1982 when it suffered this outbreak.
Data covers 29 observations over a 29 day period: (Data source: Handbook of Small Data
Sets.)
13 7 2 3 0 0 1 4 5 3 2 0 2 0 5 3 1 4 0 1 1 1 2 0 1 5 0 5 5
The time series data was regressed twice, once with a constant term (β0) and the other time
with the constant term (β0) constrained to zero. Both regressions lagged by one time period.
We want to know if the data series a random walk, and is it a random walk with drift or without
drift.
The time series regressions were solved as:
Solving as lagged by one time period, including the constant term:
Xt = β0 + β1Xt-1 + ϵ
(Where ϵ is the error term.)
Standard errors are in parenthesis underneath.
Xt = 1.644919 + .2386Xt-1
(.502256)
(.133)
Alternatively, also solved as lagged by one time period, but in this case the constant term has
been constrained to equal zero:
Xt = β1Xt-1 + ϵ
Standard errors are in parenthesis underneath.
Xt = .531328Xt-1
(.114953)
A. Use the t table to determine of the number of new cases of smallpox is a random walk.
Show your work.
B. In addition, determine if it is a random walk with drift, or without drift. Show your work.

Added by Melissa O.

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