Show yt−yt−1 yt ≈ logyt − logyt−1. How is this approximation useful for economics? Why do economists plot graphs with log on the vertical axis?
in another word, find E[Yt] and var[Yt] t X be a random variable with mean 0 and variance σ2. Define Yİ = (-1)'X. Is this process stationary?
Consider the model, Yt = BO + p1 Yt-1 + Ut, select the assumption(s) that are needed to prove unbiased parameter estimates. (A. E[Ut Us |X, Yt-1, Yt-2, ... ] = 0 B. |p1|< 1 C. E[ Ut? |X, Yt-1, Yt-2, ... ] = su? D. E[ Ut |X, Yt-1, Yt-2, ... ] = 0
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1. Calculate (a) BODs, (b) Le or BOD and (c) plot the O2 consumed vs time for the DO data shown below in a BOD bottle. Additionally, clearly show BODs, L. or BODult, and organic matter remaining in the plot. Time (days) DO (mg/L) 7.5 6.6 5.2 4.8 3.8 Ans.: (a) 3.4 mg/L, (b) 6.2 mg/L, (e) Plot of O, consume vs. time
Suppose that ∆Yt follows the AR(1) model ∆Yt = β0 +β1∆Yt−1 +ut . Show that Yt follows an AR(2) model.
Suppose that ∆Yt follows the AR(1) model ∆Yt = β0 +β1∆Yt−1 +ut . Show that Yt follows an AR(2) model.
1. For the ARIMA model below, give values for IE (Yt) and Var (Yt). Yt = Yt−1 − 0.08Yt−2 + et − 0.02et−1?
Convolution probems X(+)=ut)-ult-s)44) X(+)X+). Convolution then plot x C+) and yt). 2ct) = 3(u4) - ut-lo) Convo utionn and plet x() it) ancl2(t) X
1. Dressing up the graph with text, gtext, xlabel, ylabel, and tit le: Plot y = exp(r) in the interval [-3, 3] using a solid line. Now plot a linear approximation of e (i.e., y = x) using a dashed line and a 1 + r + using a dotted line. Title the plot "Gross Approximations of exp(x)." Label the y-axis as text to label the exp(a) quadratic approximations of exp(r) appropriately. Set axes limits to [-3, 3, -5, 15)....