!Analysis!the!relationship!between!consumer!confidence!index!and!other!macroeconomic!indices!using!RBF!network!!!!!!!!!Sun!Hao!!ECE539!Instructor:!Pro.Yu!Hen!Hu!Introduction:+Motiva tion:+Economists!are!always!concern!about!how!people!respond!to!the!current!economic!situations.!So!they!develop!the!consumer!confidence!index!to!measure!the!people’s!opinion!on!current!and!future!situation.!They!also!have!many!other!macroeconomic!indices,!which!measure!different!section!of!the!current!economic!situation.!But!what!is!the!relation!between!these!indices!and!other!index,!in!other!words,!which!economic!factor!has!the!greatest!effect!on!the!attitude!of!consumer!is!still!not!clear?!!Besides,!In!American,!consumption!is!account!for!70%!of!GDP,!which!is!the!main!part!of!economy.!The!power!of!consummation!is!consumers.!So!both!government!and!investors!pay!close!attention!to!the!consumer’s!attitude!on!consumption.!Some!researchers!have!shown!that!consumer!confidence!is!valuable!in!the!prediction!of!national!consummation.!If!we!can!find!the!relation!between!consumer!confidence!and!other!indices,!and!successfully!predict!the!confidence!using!these!indices,!then!it!will!be!helpful!for!us!to!predict!the!future!consummation.!!!In!my!approach,!I!try!to!use!radial!basis!function!neural!network!to!approximate!the!relation!between!the!consumer!confidence!index!and!other!indices.!Then!I!will!compare!my!result!with!multivariable!linear!regression!method.!Finally,!I!will!use!my!model!to!see!the!effect!of!each!economic!factor!on!consumer!confidence.!!!Background:+There!are!two!key!macroeconomic!indicators!describe!the!attitude!of!consumer,!one!is!(ICS)!consumer!sentiment!index!published!by!university!of!Michigan!and!consumer!confidence!index!published!by!The!Conference!Board.!These!two!indices!are!quite!similar.!In!my!approach,!I!will!use!the!consumer!sentiment!index!by!university!of!Michigan.!!The!other!indices!I!choose!is:!CPI:!Consumer!confidence!index,!which!is!a!very!important!index!measure!the!current!price!level.!This!data!is!published!every!month.!!Unemployment+Insurance+initial+claims:!it!is!published!every!week,!which!is!more!sensitive!than!the!unemployment!rate!to!the!current!labor!market.!!DJI:!Dow!Jones!Industrial!Average!Index,!which!is!a!general!index!measure!the!performance!of!stock!market.!!Disposable+household+income:!measure!how!many!money!people!can!spend.!!Dat a+an d+preprocessing:+The!data!is!from!the!website!of!Federal!Reserve!Bank!of!ST.!Louis!and!Yahoo!!Finance.!I!get!the!following!indices:!consumer!sentiment!index,!CPI,!UI!Claim,!unemployment!rate,!and!DJI!return.!These!data!is!published!at!least!monthly,!I!get!the!monthly!data!from!Jan.2005!to!Oct.2008.!!I!choose!this!data!range!since!the!economic!situation!and!consumer’s!behavior!changes!over!years.!So!the!relation!years!ago!may!be!different!from!now.!Actually,!I!also!get!the!data!from!1992!to!2008!and!do!the!training,!which!is!harder!to!fitting.!!Then!I!calculate!the!monthly!change!of!each!index.!For!some!of!the!index,!I!calculated!2nd!degree!monthly!change.!!The!next!step!is!to!choose!valuable!feature.!There!are!so!many!kinds!of!indices,!some!of!them!may!have!relation!with!ICS!and!others!may!don’t!have.!So!it!is!important!to!choose!valuable!data.!!My!method!is!to!plot!the!ICS!against!each!other!indices!to!see!weather!there!is!any!relation!I!can!see!from!the!plot.!If!it!has!relation,!I!will!remain!it!in!my!feature!vector.!Otherwise!I!will!not!choose!it.!The!result!shows!that!CPI,!UI!claims!both!have!some!extent!linear!relationship!with!ICS!and!DJI!index!has!weaker!relationship!with!ICS.!!The!ICS!in!current!month!has!stronger!linear!relationship!with!the!ICS!value!in!previous!month.!!There!is!not!obvious!relation!between!ICS!and!disposable!income!and!unemployment!rate,!the!reason!may!be!that!these!two!data!is!not!sensitive!and!accurate!enough.!The!plot!is!shown!below:!Notice!in!my!plot,!1st!change!means!the!monthly!change,!and!2nd!change!means!the!monthly!change!on!monthly!change.!For!example,!if!the!CPI!for!Jan.!is!100,!Feb.!is!120,!March!is!130,!then!the!1st!change!for!March!is!130‐120!=!10!and!2nd!change!for!March!is!(130‐120)‐(120‐100)!=!10!‐20!=!‐10.!Besides,!all!the!ICS!2nd!change!data!I!use!are!one!month!after!other!data.!For!example,!for!the!following!plot,!a!point!may!correspond!to!2nd!degree!change!of!April!and!1st!degree!change!of!CPI!in!March.!In!other!words,!I!am!doing!a!prediction!problem!on!ICS(2nd!change)!here.!!!‐400.00000!‐300.00000!‐200.00000!‐100.00000!0.00000!100.00000!200.00000!‐200$ ‐100$ 0$ 100$ 200$ 300$ 400$ 500$CPI(1st)+Vs+ICS(2nd)+!!!‐400.00000!‐300.00000!‐200.00000!‐100.00000!0.00000!100.00000!200.00000!‐400$ ‐300$ ‐200$ ‐100$ 0$ 100$ 200$ 300$CPI(2nd+change)+Vs.+ICS(2nd+change)+‐400.00000!‐300.00000!‐200.00000!‐100.00000!0.00000!100.00000!200.00000!‐150$ ‐100$ ‐50$ 0$ 50$ 100$DJI(1st)+Vs.+ICS(2nd)+‐400.00000!‐300.00000!‐200.00000!‐100.00000!0.00000!100.00000!200.00000!‐200$ ‐100$ 0$ 100$ 200$ 300$ 400$UI+claim(1st)+Vs.+ICS(2nd)+!!As!we!can!see,!ICS!(2nd!change)!has!linear!relation!ship!with!other!indices!to!some!extent.!!Then!these!selected!data!are!organized!as!my!data!set.!Which!is!shown!in!the!appendix.!‐400.00000!‐300.00000!‐200.00000!‐100.00000!0.00000!100.00000!200.00000!‐400$ ‐200$ 0$ 200$ 400$ 600$UI+claim(2nd)+Vs.+ICS(2nd)+‐400.00000!‐300.00000!‐200.00000!‐100.00000!0.00000!100.00000!200.00000!‐200.0$ ‐150.0$ ‐100.0$ ‐50.0$ 0.0$ 50.0$ 100.0$ 150.0$ICS(1st)+Vs.+ICS(2nd)+!Model+constru ctio n:+Structu
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