Question

Calculate the autocorrelation function of the time series

Yt = w_{t} +a_{1}w_{t-1} +
a_{12} w_{t-12}

Answer #1

=

=

+

+

=

=

=

=

Autocorrelation =

=

=

=

=

= 0 , otherwise

Consider the series xt = −.8xt−2 + wt and yt = 2cos(2πt) + wt,
where wt ∼ iid N(0,1).
Determine each of the following functions:
(b) the autocovariance functions γx(s, t) and γy(s, t)
(c) the autocorrelation functions ρx(s, t) and ρy(s, t)

This is for a class in Time-Series:
Can sample autocorrelation function be used to test for iid
noise? Please explain your answer.

Consider the following time series data.
t
1
2
3
4
5
Yt
7
12
10
13
16
Develop the linear trend equation for this time series (to 1
decimal).
Tt = _____ +
_____t
What is the forecast for t = 6 (to 1
decimal)?

t = 1 Yt = 7, t= 2 Yt= 12, t= 3 Yt=9, t = 4 Yt = 14, t = 5 Yt =
15 Develop the linear trend equation for this time series to 1
decimal point. Tt = ? + t = ?
Based on above what is the forecast for t= 6 to 1 decimal point
?

1: Explain the term ‘autoregression’ in a time series regression
context.
2. Explain the term ‘autocorrelation’ and the problems it
creates when using OLS regression in time series data.

Time Series transformation
Let an annual series Yt be stationary. However, the series
transformed and differentiated Dt = ln(Yt) - ln(Yt-1) is
stationary. Moreover, we suppose that it obeys the following
theoretical model: Dt = -0.12 + 0.75 Dt-1 + et, in which the error
term and is a white noise of variance σ2 = 0.012.
How can I transform this model to get the original one before the
transformation?

1. Consider the following time series data.
t
1
2
3
4
5
Yt
6
11
9
14
15
a. Develop the linear trend equation for this
time series (to 1 decimal).
Tt = (___) + (___) t
b. What is the forecast for t=6 (to 1
decimal)?
(___)
2. Consider the following time series data.
t
1
2
3
4
5
Yt
7
11
9
14
16
a. Develop the linear trend equation for this
time series (to 1...

Why use autocorrelation instead of autocovariance when examining
stationary time series?
Please explain specifically. Thanks.

Consider the following time series.
t 1 2 3 4 5
yt 6 10 8 13 15
Use Sumple linear regression analysis to find parameters for the
line that minimizes MSE for the time series.
y-intercept, b0=
Slope, b1=
MSE=
What is the forecast for t=6?

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.

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