Timeline for Is the variance of the process in first differences larger than the variance of the undifferenced series?
Current License: CC BY-SA 4.0
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| Jun 22, 2022 at 12:47 | vote | accept | DLTS | ||
| Jun 14, 2022 at 19:00 | history | edited | whuber♦ | CC BY-SA 4.0 |
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| Jun 14, 2022 at 19:00 | answer | added | whuber♦ | timeline score: 4 | |
| Jun 14, 2022 at 17:37 | comment | added | DLTS | That helps a lot! Thank you! | |
| Jun 14, 2022 at 17:10 | comment | added | whuber♦ | Since you assume nothing about the process (apart from the implicit requirement of second order stationarity needed for "variance" to have any meaning), you should easily be able to construct examples where the direction of the inequality changes. As an example of a variance reduction, consider the series $X_t=X$ for all $t,$ where the differenced series is constantly zero. To create an example with a variance increase, consider the process $X_t=(-1)^t X$ where $X$ is symmetrically distributed. | |
| Jun 14, 2022 at 16:55 | history | edited | DLTS | CC BY-SA 4.0 |
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| S Jun 14, 2022 at 16:54 | review | First questions | |||
| Jun 14, 2022 at 19:57 | |||||
| S Jun 14, 2022 at 16:54 | history | asked | DLTS | CC BY-SA 4.0 |