Time series analysis

Please do not simply set test questions and expect an answer. You must have an answer in the same book in which you found the question, so ask about whatever it is in the answer that you are not clear about and then I will explain.

@czxy said: Question: The following data represents a time series: X 36 Y 41 34 38 42 A series of three point moving averages produced from this data has given the first two values as 38 and 39. What are the values of (X,Y) in the original time series?

Why the question states three point moving averages, it should be four point moving averages if moving averages are calculated quarterly not 1/3 of a year. Also the question asks for the original time series but a time series is already given in the quesiton. So what is the difference between the time series given in the question and the original time series? I can not grasp the point of the question and how to approach it.

Nowhere does the question say that it is quarterly. The fact that is says that they are 3-point moving averages, means that instead of adding up 4 in the series and dividing by 4, instead we add up 3 in the series and divide by 3. In the series of figures that they have given, X and Y are the missing figures that you need to calculate. They have given the original time series, but two figures are not given (X and Y). So, the first moving average is (X + 36 + Y) / 3, and this is equal to 38. The second moving average is (36 + Y + 41) / 3, and this is equal to 39. From the second equation you can calculate what Y must be, and using this in the first equation you can calculate what X must be.