First off, I'm not 100% that I'm in the right forum so please excuse if not. Secondly if you can help me with this you are a great person and I thank you so very much
Working through a textbook solution but not following the process.
The textbook arrives at the following equation.
. . . . .\(\displaystyle \large{ y_t\, =\, \epsilon_t\, +\, 0.3\, \epsilon_{t - 1}\, +\, 0.8\, (0.3)\, \epsilon_{t -1}\, +\, 0.8^2\, (0.3)\, \epsilon_{t -3}\, +\, ... \, A\, (0.8)^t }\)
They then determine through another separate process (which we don't need to get into) that A in the equation above equals zero. So A=0
So after removing that term on the far right of the equation. They then represent the rest of the equation as follows
. . . . .\(\displaystyle \large{ \displaystyle y_t\, =\, \epsilon_t\,\, +\, 0.3\, \sum_{i\, =\, 0}^{t- 2}\, (0.8)^i\, \epsilon_{t - i - 1} }\)
The piece of this equation above that I do not understand is t-2 (on top of the sigma). Can someone explain why they've included the t-2? I do not see how the second equation I've pasted, represents the first one. I don't understand why in the second equation the upper bound of the summation range is t-2.
Thanks again
Working through a textbook solution but not following the process.
The textbook arrives at the following equation.
. . . . .\(\displaystyle \large{ y_t\, =\, \epsilon_t\, +\, 0.3\, \epsilon_{t - 1}\, +\, 0.8\, (0.3)\, \epsilon_{t -1}\, +\, 0.8^2\, (0.3)\, \epsilon_{t -3}\, +\, ... \, A\, (0.8)^t }\)
They then determine through another separate process (which we don't need to get into) that A in the equation above equals zero. So A=0
So after removing that term on the far right of the equation. They then represent the rest of the equation as follows
. . . . .\(\displaystyle \large{ \displaystyle y_t\, =\, \epsilon_t\,\, +\, 0.3\, \sum_{i\, =\, 0}^{t- 2}\, (0.8)^i\, \epsilon_{t - i - 1} }\)
The piece of this equation above that I do not understand is t-2 (on top of the sigma). Can someone explain why they've included the t-2? I do not see how the second equation I've pasted, represents the first one. I don't understand why in the second equation the upper bound of the summation range is t-2.
Thanks again
Attachments
Last edited by a moderator: