B. Consider the GARCH (1, 1) model Xt-σ.zt, σ -00 + α1XL1 + βισ -1 where Zt are iid N (0, 1) process, ao 0, α120, ai 1 > α1 + β1. Show that 0, A > 0 and 2IV2 t-1't-2 .. B. Consider the GARCH (1, 1) model Xt-σ.zt, σ -00 + α1XL1 + βισ -1 where Zt are iid N (0, 1) process, ao 0, α120, ai 1 > α1 + β1. Show that 0, A > 0...
Please show work We fit a GARCH (1, 1) model and display the MLE of the fitted model belovw > summary(dax.garch) Call: garch(x- dax) Model: GARCHC1,1) Residuals: 1Q Median Max 12.18398 -0.47968 0.04949 0.65746 4.48048 Min 3Q Coefficient(s): Estimate Std. Error t value Pr>Itl) a0 4.639e-06 7.560e-07 6.137 8.42e-10** a1 6.833e-02 1.125e-02 b1 8.891e-01 1.652e-02 53.817 <2e-16* 1.25e-09 Signif. codes: 0 '***' 0.001 0.010.05 '.' 0.1 ''1 What is the t-value for a1? We fit a GARCH (1, 1) model...
1. An AR(1) process is given by Xų = 0.727-1 + wt, where et represents a sequence of uncorrelated random variables of zero mean and constant variance 0.4 so that Rww 0.48(n). a. If in addition wt is normally distributed then what can we say about the output Xť ? b. Compute the autocorrelation function of the output process.
c) Consider the following estimates of two different GARCH(1.1) modelas: Model 1 ft = 0.018 ht0.008+0.293ê21 0.915ht-1 (4.015) (1.619) Model 2 f 0.008 he 0.004+ 0.193e21 +0.795h (5.015) (16.969) where t is the calculated value of the t-statistic. Are the estimated coefficients of the GARCH(1,1) models of the correct sign? Does the stationary condition hold for the two models? Explain carefully [40]
11-13 The z-component of a vector can be (+), (-), or zero A True B false if A is perpendicular to B, then B middot A = 0 A True B False The x-component of a vector can be (+), (-), or zero A True B False The scalar (or dot) product of two vectors can be (+), (-) or zero A True B False If A = B times C and C = 16j, then Ay = 0 A...
Let wt for t = . . .,-2,-1, 0, 1, 2, . . . be an independent and identically distributed process with wt ~ M0, σ2). and consider the time series Determine the mean and the autocovariance function of xt and state whether it is stationary
3. We obtain autocorrelation function of residuals of the five autoregressive models: AR(1), AR(2), AR(3), AR(4) and AR(5). Choose a model that performs reasonably well, according to the plots of autocorrelation function. Explain the reason (no more than 20 words.) Autocorrelation function for AR(1) model Series ar1$residuals 1.0 RO 0.6 ACF 0.4 -0.2 0.0 0.2 0 5 10 15 Lag Autocorrelation function for AR(2) model Serles ar2$residuals 1.0 RO 0.6 ACF 0.4 -0.2 0.0 0.2 0 5 10 15 Lag...
Consider the time series of Xt = Xt−1 + Wt, whereWt are i.i.d and Wt ∼ N (0, σ2 ) and X0 = 0. Let X¯ = 1 n Pn i=1 Xi . Derive the general form for var(X¯). (Hint: Pn i=1 i 2 = n(n+1)(2n+1) 6 ) Consider the time series of X-Xi-1+Wi, whereW are i.i.d and W N(0, σ2) and Xo 0. Let X = n Σ, Derive the general form for var(X). (Hint: Σ i- n(n+1)(2n+1))
Suppose 2 ~ N(0,1). True or False: P(Z = 0) = 1/V27.
select true or false Let z € RM be a nonzero vector and let H= 1 - 2 VVT and P= I - WT VT where v= ||2||2e1 z 1. [Select ] Hz= = Z 2. [Select ] P2z=z 3. [Select] HPz= Pz Suggestion. All these questions can be determined algebraically, but it is tedious. Try to answer them using the geometric intuition behind the matrices defined.