Time Series Analysis.
QUESTION 1
1.
A first order auto-regressive (AR-1) model for stock sales is Sales(t) = 80 + 1.121*Sales(t-1), where Sales(t) and Sales(t-1) are stock sales for periods t and t-1 respectively.
Find the forecast sales for 1999 when Sales(1998)=$1254. Do not include the $ sign in your answer. (round to one dec. pl.)
QUESTION 2
1.
Using exponential smoothing and the time series provided below, find the forecast for time period 6. Use 0.2 as the smoothing constant (to 3 dec. pl).
|
t |
Y(t) |
|
1 |
60 |
|
2 |
70 |
|
3 |
96 |
|
4 |
77 |
|
5 |
81 |
|
6 |
91 |
|
7 |
85 |
2.
QUESTION 3
1.
The following equation was estimated using 10 data points: Y = B0 + B1 X + error.
If the original Y values were: 2.314 3.132 2.955 4.867 4.843 1.511 1.402 3.917 2.469 7.071,
and the predicted values are: 2.753 3.869 3.322 5.687 3.717 2.702 2.511 1.899 2.545 6.323,
calculate the mean absolute deviation. (correct to 4 dec. pl.)
3 points
QUESTION 4
1.
Which of the following terms describe the overall long term tendency of a time series?
|
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Trend |
|
|
|
Cyclical component |
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|
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Irregular component |
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|
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Seasonal component. |
QUESTION 5
1.
A consulting group have tracked the average salary per week (in dollars) over time for a group of university students. The data is recorded in the file BBSALARY. Using the data from the year 1976 to the year 2000 (including 1976 and 2000) fit a trend equation to the average salary data over this period. You will need to create a new column of values (from 1 to 25) next to the YEAR column, with a value of 1 next to the year 1976, a value of 2 next to the year 1977 and a value of 25 next to the year 2000. This new column will be the data for your independent variable.
a) What is the intercept term (to 3 decimal places)?
b) Use the trend equation to forecast Average salary for the year 2008 (to 3 decimal places).
QUESTION 6
1.
Referring to the table below,
|
Period |
Y |
MA |
|
1 |
270 |
* |
|
2 |
356 |
341.333 |
|
3 |
398 |
403.333 |
|
4 |
456 |
|
|
5 |
371 |
|
|
6 |
401 |
|
|
7 |
361 |
|
|
8 |
400 |
|
2.
What is the 3-year moving average value for period 6? (to 3 dec. pl.)
3.
QUESTION 7
1.
A trend is an upward or downward movement in annual time series data which must persist for several years.
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True |
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False |
QUESTION 8
1.
An AR(1) model is derived as follows: (with the standard error of the coefficient given in the brackets)
EXP(t) = 1.68 + 0.238 * EXP(t-1)
(0.132)
where
EXP(t) = the value of exports in millions of dollars in year, t
EXP(t-1)= the value of exports in millions of dollars in year, t-1
And the number of observations for this model is 29.
An economist believes that export prices from the previous year have a significant effect on the export prices in year t and wishes to test this claim using a 5% level of significance.
1. State the direction of the alternative hypothesis used to test the economist’s claim. Type gt (greater than), ge (greater than or equal to), lt (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box.
2. Calculate the test statistic (ie. a t-stat), report your answer correct to three decimal places.
3. Use the tables in the text to determine the critical value used to conduct the test. If there are two critical values, state only the positive value (three decimal places) .
4. Is the null hypothesis rejected for this test? Type yes or no.
5. Would you achieve the same result using an F test for the overall model? Type yes or no.
