TS Module 10: autocorrelation functions HW


TS Module 10: autocorrelation functions HW

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NEAS
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TS Module 10: autocorrelation functions HW

 

(The attached PDF file has better formatting.)

 

Homework assignment: Sample autocorrelations

 

A time series has ten elements: {10, 8, 9, 11, 13, 12, 10, 8, 7, 12}.

 


A.     What is the sample autocorrelation of lag 1?

B.     What is the sample autocorrelation of lag 2?

C.    What is the sample autocorrelation of lag 3?


 

 

Show the derivations with a table like the one below. Remember to use the proper number of terms in the numerator, depending on the lag.

 

Entry

Entry

Deviation

Deviation Squared

Cross Product Lag1

Cross Product Lag2

Cross Product Lag3

1

10

 

 

 

 

 

2

8

 

 

 

 

 

3

9

 

 

 

 

 

4

11

 

 

 

 

 

5

13

 

 

 

 

 

6

12

 

 

 

 

 

7

10

 

 

 

 

 

8

8

 

 

 

 

 

9

7

 

 

 

 

 

10

12

 

 

 

 

 

Avg/tot

 

 

 

 

 

 

Autocorr

 

 

 

 

 

 

 

 


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BAFAphenom
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Should we be using an Excel worksheet for this like in HW 6?

[NEAS: Use an excel worksheet if you want. The computations are simple, and can be done by hand or by a calculator in a few minutes. You must solve the final exam problems without an Excel workbook, so be sure you know the procedure.]


Gautham
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NEAS - Wont the every entry in the last three columns be the same? Mean we just have to calculate r1, r2 and r3 right. Every entry in the third last column would be r1, in the second last column would be r2 and so for r3 right or am I reading the sum wrong? Please help.

[NEAS: This homework assignment works out the computation of r1, r2, and r3. Work out the deviations and the values minus the mean. For the column labeled cross product of lag 1, use deviation(t) * deviation(t-1); for the column labeled cross product of lag 2, use deviation(t) * deviation(t-2); and so forth. The sums of the products are the numerators of r1, r2, and r3. The denominator is the sum of squared deviations. Place r1, r2, and r3 in the last row of the table.

You compute r1, r2, and r3 by hand. The final exam asks similar problems.]


dditch
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Can someone tell me if r1= .2777778?


CalLadyQED
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That's what I got, dditch.
evi
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Likewise.


Cubs
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I also came up with the same positive number for r1, but I calculated a negative number for r2 of -.30556 and a negative number for r3 of -.55556.  These results seem strange to me.  Can someone confirm this is also what they came up with?  Thanks!
atkinsmt
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Hey Cubs,

I got the same r1, and r2 as you. However, I got r3= -20/32 = -0.625.
Cubs
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I calculated the denominator as 36... I'm confused how we could get the same answer for lag1 and lag2 cross product if we were using a different denominator.


Study123
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I am having trouble getting started with the assignment.  Can someone please help me?  Why are there 2 entry columns?


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