You are given the three autoregressive time series models Xt 0.5Xt-1 + Z 4 Determine which...
2. Suppose that Ya ut where the ut are iid Normal with mean zero and variance σ2, but that you mistakenly think Yt is difference stationary. You therefore construct a new series a) Are the Xt i.i.d.? Explain b) Is X stationary? Explain c) Calculate the mean, variance, and autocorrelation function of X d) How does the answer you obtained in (c) compare with the mean, variance and autocor- relation function of Y? 2. Suppose that Ya ut where the...
Exercise 2.31 Superposition [] Given two independent weakly stationary time series Xt and Yi) with autocovariance functions x(h) and y (h), show that Zt- Xt +Yt is also weakly stationary, with autocovariance function given by yz(h)-x(h)y(h).
3. (4) Let X, be a time series. Yǐ be a transformation ofXt yt-leg (Xt +0.5) ,(E) denote the-c step" ahead focecast for Y Write down Xtt) in terus of e 3. (4) Let X, be a time series. Yǐ be a transformation ofXt yt-leg (Xt +0.5) ,(E) denote the-c step" ahead focecast for Y Write down Xtt) in terus of e
1. Consider the following autoregressive process 2+ = 4.0 + 0.8 2t-1 + Ut, where E (u+12+-1, Zt-2, ....) = 0 and Var (ut|2t-1, 2-2, ...) = 0.3. The unconditional E (Zt) and unconditional variance Var (zt) are: (a) E (2+) = 11.1111, Var (zł) = 0.8333 (b) E (2+) = 11.1111, Var (zt) = 1.5 (c) E (zt) = 20, Var (zt) = 0.8333 (d) E (2+) = 4, Var (zł) = 0.8333 (e) E (Zt) = 4,Var (z+)...
Which of the following statements is correct with regards to the concept of Time-series Models? A. Time-series models use past values of the time-series to predict future values of these time-series B. Time-series data is classified as "perfect information" C. Time-series analysis are the basis for a wide variety of forecasting methods D. All of these E. None of these
4. Consider two functions x(h),y (h), Vh> 0 and cross-covariance function 7xy(h), Vh e Z (a) (7 points) Find the Best Linear Predictor (BLP) of Y given Xt, and its Mean Square Prediction Error (MSPE), expressed in terms of x(h). (h), xy (h) jointly stationary time series (X, Y), with individual auto-covariance (b) (13 points) Find the BLP of Y given Xt, X-1,Y-1, and its MSPE, expressed in terms of 7x(h)(h), x.y (h). (Note: you don't need to solve the...
4 (10 marks). Consider a simple model of a time series ytas a function of its past (using lagged values): Yt = Bo + B1Yt-1 + €7 (1) Assume that yt is what we refer to as 'stationary - its distribution does not change over time, i.e. E[yt] = for all t. i iii Interpret the model - what does B, capture? Show that E[yt] is equal to Q = Bo/(1-B1) Now consider the model including an additional variable xt:...
help wih these question please 3. Consider the following autoregressive process Yt = Bo + B1yt-1 + B2Yt-2 + Ut, where E (UtYt-1, Yt-2, ...) = 0. You obtained the following parameter estimates: Bo= -0.2, B1 = 0.4 and B2 = -0.1. Furthermore, you have the following observations: 419 = -0.2 and Y20 = 0.3. What is the estimate for E Y 22 y 20,419)? (a) -0.3333 (b) -0.06 (C) 0.3 (d) -0.2857 (e) -0.254 4. You have estimated the...
If you model a time series Yt using a stationary ARMA process with a nonzero constant (µ unequal to 0) and use it to forecast future values of Yt, then as you forecast further and further into the future, the confidence interval widths for your forecasts will (a) continue to increase and eventually reach arbitrarily large values. (b) gradually decay to zero. (c) cutoff to zero after some lag. (d) converge to a non-zero limiting value.
3. Determine which of the following are models of Incidence Geometry. For those th are models, indicate which parallel property holds for the model. For those that a not a model, list at least one axiom that fails and illustrate why. a. Points are points in the Euclidean plane and lines are circles with positive radius. b. Points are in {(x, y) = R2 22 + y2 <9} and lines are open chords of the circle. c. Points are points...