Wikipedia:Reference desk/Archives/Mathematics/2012 August 17#Stationary problems in time series

Having issues finding the mean, covariance and variance of the following: (where Ut is i.i.d with mean 0 and variance sigma squared)

1. ) $y\_t\; =\; y\_1\; e^\{\backslash beta\; t\}\; e^\{U\_t\}$
2. ) $y\_t\; =\; \backslash beta\_0\; +\; \backslash beta\_1\; x\_t\; +\; U\_t$, where $x\_t=\; \backslash alpha\_0\; +\; V\_t$ , $V\_t$ is i.i.d with mean 0 and variance σ squared subscript v
3. ) $\backslash Delta\; y\_t\; =\; \backslash alpha\_0\; +\; \backslash alpha\_1\; \backslash Delta\; DT\_b\; +\; U\_t$, Where $DT\_b$ is equal to 0 if t is less than or equal to $T\_t$ and $t-T\_b$ if $t$ is $>\; T\_b$

— Preceding unsigned comment added by 203.28.240.65 (talk • contribs) 22:48, 16 August 2012

:We'll only help with homework questions if you show that you have attempted it yourself first. How far have you managed to get? Also, can you clarify the question: covariance between what and what? --Tango (talk) 13:36, 18 August 2012 (UTC)

I can get to working out what the formulas would be, and I think you just assume linear independence between the error terms and the independent variable, allowing the substitutions to be easier. The covariance is meant to be between the y_t or Delta y_t and the independent variable.

— Preceding unsigned comment added by 203.28.240.65 (talk • contribs) 10:11, 19 August 2012‎

How can we reach the following integration result?

:$\backslash int\_\{0\}^\{\backslash infty\}\; \backslash frac\{\backslash sinh(ax)\}\{e^\{bx\}\; -\; 1\}dx\; =\; \backslash frac\; 1\; \{2a\}\; -\; \backslash frac\; \backslash pi\; \{2b\}\; \backslash cot(\backslash frac\; a\; b\; \backslash pi)$

I am not certain if solution method can be done using Residue theorem. If so then shall we make it through a quarter circle and how?--Almuhammedi (talk) 03:36, 17 August 2012 (UTC)

:See here. Count Iblis (talk) 16:42, 17 August 2012 (UTC)