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Res Ec 797A Lecture 13 Fall 2011

# Res Ec 797A Lecture 13 Fall 2011 - Res Ec 797A Forecasting...

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Unformatted text preview: Res Ec 797A: Forecasting Order Of Topics And Readings For Lecture 13 (October 17, 2011) Source Pagegsl Top'c Material Distributed Last Class But Not Covered BM 63 Enders 43-44 BM 64 GHJ 643-645 How do we put all of this together? Characteristic equation (and roots) vs. inverse characteristic equation (and roots) Model set-up for an AR(3) process Properties of First-Order Autoregressive Processes: AR(l) End Of Material Distributed Last Class But Not Covered BM 65 GB] 646—648 BM single, unnumbered BM single, unnumbered GHJ 648-651 GHJ 651—653 Example: AR(I) Model — Finding Theoretical Autocovariances and Autocorrelations Properties of Second-Order Autoregressive Processes More detail in deriving p1 and P2 for an AR(2) process Given coefﬁcients for a theoretical AR(2), calculate the ﬁrst two autocorrelation coefﬁcients. Using OLS to Estimate an AR(p) Process Using Partial Autocon'elations to Help Determine the Order p of the AR Process {Examﬂe 1 Take The A20) “04d Z; .03 21"; ET 1' ¢ F'mA aﬁocovavimnccg and aﬁcowfe1a115n\$ : VquZ+ 1‘- 0; VadZ‘h \ +v:o~(i*) VOW ('11.) - 0.32 “(If 1+: :3; War ‘11)[1'03] 5‘ c\\‘1 . V“ 7": 5.3515 2‘ 750 -‘7 T“ ““0““ °r‘ Z1 - Fits-k «mead-“hum : ‘5 -E(Z z ' ‘ - t +-3' \$032+.“ 5*) 2h]- E[(oaz+‘1“3+ sfzh) = 03 WW 21" '1' 0 = 0.310 ' FEVs1- adomnkﬁbn i ()ﬁ 1'- = £15 : 0.3 \$0 ‘60 ' SBuuo‘ audacbdaﬁancc ' . I - 2'14 =E (Z Z F31 + '3' ,r +43= E (o '13: 3 a )Z _1= E (0313,; 8H1 511114. -A\\ 01- 1113 au’rocowela’rions Taﬁe’rher how: a “amaze. More Detail In Deriving p1 and p2 For An AR(2) Process Pk : .9. P 4 4- 92 “(-2 La EM P\ = 9‘?° + 6’- ()4 9‘ = 9,9, 4: 61‘)‘ 9' 7. 9‘“) + 91% PI : ' 9. * 61?: “’91?- : 9| p, :- .91. . The“ m; ﬂag +k¢ovehw\ 40h: wwda‘hwg «for an AR (2) PM “93. . 6"" me, shuts {0“ 9‘ “"4 92., 5““ I am ﬂ“‘c..\lw ﬁh“ A‘F. Given The Coefﬁcients For A Theoretical AR(2), Calculate The First Two Autocorrelation Coefﬁcients 2h\$ 0;va .ml'lGVC3vcssi‘K Process 9‘ a. .e’, ' "92. Pzge1+ I'Oz. A, 9 +9 <| 4: 0.3 +0.12“ 4 ’c 0.7, “own 7‘" l9;""' a IO.“ = 034! _ 3; - o.» ‘_ P! ‘ P03 0.1 ’ 0‘65? 049" . 9., = 0.3 It a“ = 0.3+o.514:o,g|§ I413 Ah! Nohce a “Mug M" M Pa. vclq‘i’ivt' ‘i’o (’- .. ' ...
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Res Ec 797A Lecture 13 Fall 2011 - Res Ec 797A Forecasting...

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