Wikipedia:Reference desk/Archives/Mathematics/2012 August 17

= 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) ) $$y_t = y_1 e^{\beta t} e^{U_t}$$
 * 2) ) $$y_t = \beta_0 + \beta_1 x_t + U_t $$, where $$ x_t= \alpha_0 + V_t $$, $$V_t$$ is i.i.d with mean 0 and variance &sigma; squared subscript v
 * 3) ) $$\Delta y_t = \alpha_0 + \alpha_1 \Delta DT_b + U_t $$, 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

Integration of sinh(ax)/(e^(bx)-1) dx from 0 to ∞
How can we reach the following integration result?
 * $$\int_{0}^{\infty} \frac{\sinh(ax)}{e^{bx} - 1}dx = \frac 1 {2a} - \frac \pi {2b} \cot(\frac a b \pi)$$

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)