Consider an infinite-horizon groundwater management problem
where xt is the stock of groundwater at time t,...
Consider an infinite-horizon groundwater management problem
where xt is the stock of groundwater at time t, yt is the quantity
of groundwater extracted at time t, g(yt) gives the amount of total
recharge to the aquifer, B(yt) is the benefit of extracting yt, and
C(xt, yt)
2
is the cost of extracting yt from a stock of size xt. Suppose
that there are property rights to groundwater, but a large number
of users. Groundwater used in agriculture is unregulated. Suppose...
g(s,t)=f(x(s,t),y(s,t)) where f(x,y)=x^2-xy^3,
x(3,4)=2, y(3,4)=-2, xs(3,4)=4 xt(3,4)=-1, ys(3,4)=10, and
yt(3,4)=-100.
Calculate gs(3,4)
g(s,t)=f(x(s,t),y(s,t)) where f(x,y)=x^2-xy^3,
x(3,4)=2, y(3,4)=-2, xs(3,4)=4 xt(3,4)=-1, ys(3,4)=10, and
yt(3,4)=-100.
Calculate gs(3,4)
1) Consider the MA(2) process, where all the {et} values are
independent white noise with variance...
1) Consider the MA(2) process, where all the {et} values are
independent white noise with variance 2 e:
Yt = et – 0.5 et – 1 – 0.3 et – 2
a) Find cov(Yt, Yt) = var(Yt).
b) Find cov(Yt, Yt – 1) and, from this, find the lag-1
autocorrelation corr(Yt, Yt – 1).
c) Find cov(Yt, Yt – 2) and, from this, find the lag-2
autocorrelation corr(Yt, Yt – 2).
d) Argue that cov(Yt, Yt – k) =...
Consider the following time series.
t
yt
1
1,234
2
1,201
3
1,103
4
987
5...
Consider the following time series.
t
yt
1
1,234
2
1,201
3
1,103
4
987
5
945
6
891
7
817
8
734
a. Construct a time series plot. What type of pattern exists in
the data? No need to include the graph just state if the line has a
horizontal pattern or a trend pattern
b. Use simple linear regression analysis to find the parameters
for the line ?
c. Find MSE for this time series.
Consider the following time series.
t
1
2
3
4
5
yt
5
10
10
15...
Consider the following time series.
t
1
2
3
4
5
yt
5
10
10
15
14
Use simple linear regression analysis to find the parameters
for the line that minimizes MSE for this time series.
If required, round your answers to two decimal places.
y-intercept, b0 =
Slope, b1 =
MSE =
(c)
What is the forecast for t = 6?
If required, round your answer to one decimal place.